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Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which may also be given in the form of a statement. Therefore the required statement in the question is option C. Add 3 to the product of one-fourth and 8, then divide by 5.

Mathematical expression involves an equation that may consist of numbers only or combined with alphabets, which can be given in the form of a statement. When a given expression consists of both numbers and alphabets, then it forms an algebraic expression. It can also be given in the form of a statement.

Given in the question:

([tex]\frac{1}{4}[/tex] x 8 + 3) ÷ 5

This can be given in a statement form as; Add 3 to the product of one-fourth and 8, then divide by 5.

The appropriate statement that describes the given expression is: Add 3 to the product of one-fourth and 8, then divide by 5 i.e Option C.

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If there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.

Given that in a secondary school class, 23 students study Economics, 6 students study both government and economics. 48 students study either government or Economics or both.

We are required to find :

Suppose E represents economics students and G students government students. In this way:

E=23

G∩E=6  (And represents intersection between sets)

G∪E=48 (Or represents union of sets)

G∪E=G+E-G∩E

48=G+23-6

G=48-17

G=31

Economics only=E-G∩E

=23-6

=17

Governments only=G-G∩E

=31-6

=25

Hence if there are 23 students study Economics,6 students study both government and economics and 48 students study either government or economics or both then there are 31 students study government, 17 students study economics only and 25 students are there who study government only.

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The required probabilities are:

A) P(D or 5) = 4/13

B) P(H and J) = 1/13

C) P(J or 8) = 2/13

D) P(H or S) = 1/2

E) P(R and F) = 3/26

F) P(R or Q) = 7/13

The ratio of favorable outcomes to the total outcomes of an event is said to be its probability.

P(E) = n(E)/n(S)

It is given that a single card is drawn at random from a standard deck of 52 cards.

So, the sample space consists of 52 cards in total

From those,

4 suits: Hearts, Clubs, Spades, Diamonds

Each of the suit has 13 cards: { Ace, 2,3,4,5,6,7,8,9,10, Jack, Queen, King}

There are 26 Red cards and 26 Black cards.

A) The probability of drawing a diamond or a 5:

P(D or 5) = P(D) + P(5) - P(D and 5)

               = 13/52 + 4/52 - 1/52

               = 16/52 = 4/13

B) The probability of drawing a heart and a jack:

P(H and J) = P(H) × P(J) (Since they are independent events)

                 = 13/52 × 4/13

                 = 1/13

C) The probability of drawing a jack or 8:

P(J or 8) = P(J) + P(8) - P(J and 8)

              = 4/52 + 4/52 - 0

              = 2/13

D) The probability of drawing a heart or a spade:

P(H or S) = P(H) + P(S) - P(H and S)

               = 13/52 + 13/52 - 0

               = 26/52 = 1/2

E) The probability of drawing a red and face card:

P(R and F) = P(R) × P(F) (Since they are independent)

                 = 26/52 × 12/52

                 = 1/2 × 3/13

                 = 3/26

(There are three face cards- jack, king, and queen: each of 4)

F) The probability of drawing a red card or a queen:

P(R or Q) = P(R) + P(Q) -P(R and Q)

               = 26/52 + 4/52 - 2/52

               = 28/52 = 7/13

Thus, the required probabilities are calculated.

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The common ratio of the given sequence is -1/4. In a geometric sequence, the common ratio is the value that is in between each number in the sequence.

The ratio of the value of a term in the sequence to the value of the previous term in the sequence is said to be the common ratio. I.e.,

C.R = (nth term)/(n - 1)th term

The given sequence is 64, -16, 4, -1, ...

Taking the ratio of the second term to the first term, we get

-16/64 = -1/4

Similarly, the ratio of the third term to the second term,

4/16 = -1/4

Since the ratios are equal, then the common ratio of the sequence is -1/4.

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Answer:

5.3333333 or 5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

30 divided by 2 equals 15.

80 divided by 15 equals 5.3333333 or 5 [tex]\frac{1}{3}[/tex].

The surface area of the new toy is given as follows:

1,439 in².

The surface area of a figure is given by the sum of the surface area of all it's compositions. This figure is given by a cylinder and a rectangular prism.

The surface area of a cylinder with radius r and height h is given by the following formula:

[tex]S = 2\pi r(r + h)[/tex]

In this problem, the dimensions are:

r = 3 in, h = 16 in.

Hence:

[tex]S = 2\pi \times 3(3 + 19) = 132\pi[/tex]

The surface area of a rectangular prism of length l, width w and height h is given as follows:

[tex]S = 2(lw + lh + wh)[/tex]

In this problem, the dimensions are:

l = 24 in, h = 10 in, w = 8 in.

Hence the surface area is:

S = 2 x (24 x 10 + 24 x 8 + 10 x 8) = 1024 in²

It is the sum of the surface areas, hence:

[tex]132\pi + 1024 = 1439 \text{in}^2[/tex]

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Answer: Here you go :)

Step-by-step explanation:

Hope it helps!

The 7th term of an Arithmetic Progression 50+45+40 is 20

The Arithmetic Progression is given as:

50+45+40

In the above Arithmetic Progression, we have

First term, a= 50

Common difference, d = 45 - 50 = -5

The nth term of the Arithmetic Progression is calculated as:

Tn = a + (n - 1)d

Substitute the known values in the above equation

Tn = 50 + (n - 1) * -5

Substitute 7 for n in the above equation

Tn = 50 + (7 - 1) * -5

Evaluate the product

Tn = 50 - 30

Evaluate the difference

T7 = 20

Hence, the 7th term of an Arithmetic Progression 50+45+40 is 20

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a. Angle BAC is a central angle.

b. Arc BEC is a major arc.

c. Arc BC is a minor arc.

d. m(BEC) = 260°

e. m(BC) = 100°

An arc that has a measure that is greater than 180 degrees or is greater than a semicircle (half a circle) is referred to as a major arc.

An arc that has a measure that is less than 180 degrees or is not up to a semicircle (half a circle) is referred to as a minor arc.

A central angle can be described as an angle with a vertex at the center of a circle and has two radii of the circle at sides.

a. Angle BAC is a central angle.

b. Arc BEC is a major arc.

c. Arc BC is a minor arc.

d. m(BEC) = 360 - 100 [central angle theorem]

m(BEC) = 260°

e. m(BC) = angle BAC = 100° [central angle theorem]

m(BC) = 100°

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well, keeping in mind that a year has 365 years, so let's see

[tex]\stackrel{Oct}{10}~~ + ~~\stackrel{Nov}{30}~~ + ~~\stackrel{Dec}{31}~~ + ~~\stackrel{Jan}{31}~~ + ~~\stackrel{Feb}{21}\implies 123~days[/tex]

so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus

[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$3694.63\\ P=\textit{original amount deposited}\dotfill & \$3600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{123}{365} \end{cases}[/tex]

[tex]3694.63=3600[1+(\frac{r}{100})(\frac{123}{365})]\implies \cfrac{3694.63}{3600}=1+\cfrac{123r}{36500} \\\\\\ \cfrac{3694.63}{3600}-1=\cfrac{123r}{36500}\implies \left( \cfrac{36500}{123} \right)\left( \cfrac{3694.63}{3600}-1 \right)=r\implies \stackrel{\%}{7.8}\approx r[/tex]

7.8% is the simple interest rate was charged if Robin repaid $3,694.63.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

A=P(1+rt)

A is final amount, P is principle amount, r is rate of interest and t is time.

We know that in a year we have 365 days.

But the time here is from oct 21 to feb 21, which has 123 days.

so the 3600 were borrowed for only 123 days of a year, that'd be 123/365 of a year, thus

Apply these values in formula

A=P(1+rt)

3694.63=3600(1+r/100(123/365))

3694.63=3600(1+123r/36500)

3694.63/3600=1+123r/36500

3694.63/3600-1=123r/36500

(3694.63-3600)/3600=123r/36500

94.63/3600=123r/36500

Apply cross multiplication

3453995=442800r

7.80=r

Hence 7.8% is the simple interest rate was charged if Robin repaid $3,694.63.

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Answer:

t = 21

Step-by-step explanation:

The ball strikes the groujd when h = 0.

[tex]-3.2t^2 + 54.4t+268.8=0 \\ \\ 32t^2 - 544t-2688=0 \\ \\ t^2 - 17t-84=0 \\ \\ (t-21)(t+4)=0 \\ \\ t=-4, 21[/tex]

Since time must be positive, t = 21.

Answer: None of these are correct

Step-by-step explanation:

I believe that the equation is showing transitive property.

Answer: [tex]x=-5[/tex]

Step-by-step explanation:

[tex]x+5=0 \implies x=-5[/tex]

Answer:

0.45 per egg

Step-by-step explanation:

since it's 3 dozen that mean it's gonna be 36 eggs divided by 16.20 so it's 0.45 per egg

Answer:

100 miles and 5.5 inches

Answer:

  D.  x = -7/3

Step-by-step explanation:

A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.

The desired form can be found by subtracting 16 from both sides of the equation:

  [tex]\left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16[/tex]

A graph is attached, showing x=-7/3 is the solution.

Using powers of 4, the equation can be rewritten ...

  [tex]\left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}[/tex]

Answer:

addition property

Step-by-step explanation:

See attached image.

Answer:

b = 133, a = 47

Step-by-step explanation:

If the two lines are parallel, then angle b is equal to 180-47 = 133 (same side interior angles), and angle is equal to angle 0 (alternate interior angles)

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:a = \theta[/tex]

( by Alternate interior angle pair )

[tex]\qquad \therefore\: \sf \:a = 47 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \:b = 180 - \theta[/tex]

( by co - interior angle pair )

[tex]\qquad❖ \: \sf \:b = 180 - 47[/tex]

[tex]\qquad \therefore \: \sf \:b = 133 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \:a = 47 \degree[/tex]

and

[tex]\qquad❖ \: \sf \:b = 133 \degree[/tex]

Assuming you had a bill of $120 when you went to the restaurant with your three friends, the 20% tip would come out to $24.

First assume an amount that the meal you ate cost. Let's assume that amount if $120.

If the tip rate if 20%, it means that you need to find out what 20% of the bill of $120 is.

If you don't want to use a calculator, there are other ways you can calculate the tip.

An easy method would be to find 10% of the bill. To find 10%, all you have to do is to move the decimal point from right to left.

The decimal point in $120 is at the far right so the 10% amount would be:
= $12.0

Now that you have the 10% amount, remember that 20% is simply twice the amount of 10% so:

= 12 x 2

= $24

The total amount then becomes:

= 120 + 24

= $144

In conclusion, your tip amount would be $24.

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The required sales in dollars needed to achieve managements target is $607,5000.

Net income is total revenue less total cost. Total cost is the sum of fixed cost and variable cost. Fixed cost is the cost that remains constant regardless of the level of output. e.g. rent. Variable cost is the cost that varies with output e.g. wages.

Net income = sales - total cost

Net income = sales - (fixed cost + variable cost)

$67,500 = sales - ($175,500 + 0.6sales)

$67,500 = sales - $175,500 - 0.6sales

$67,500 + $175,500 = sales - 0.6sales

243,000 = 0.4sales

sales = 243,000 / 0.4

sales = $607,500

Here is the complete question:

For Pharaoh Company, variable costs are 60% of sales, the fixed costs are $175,500. Managements net income goal is $67,500.Compute the required sales in dollars needed to achieve managements target net income of $67.500.

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The central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BD)/18.

Given that BD is diameter of the circle and angle BAC is 100°.

We are required to find the central angle, major arc, minor arc, m BEC, BC.

Angle is basically finding out the intensity of inclination of something on the surface.

In the circle central angles are many like BAC and CAD. We can write CAD as DAC also.

Major arc of a circle is that arc whose length is larger than all other arcs in the circle.

In our circle the major arc is arc BED.

Minor arc of a circle is that arc whose length is smaller.

In our circle the minor arc is arc ADC.

We know that arc's length is 2πr(Θ/360)

In this way BC=2π*(BD/2)*100/360

=(5π*BD)/18

We cannot find angle BEC.

Hence the central angle in the circle is ∠DAC,major arc is BED, minor arc is ADC and BC=(5π*BA)/18.

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The measures of the angles are

Angle JPK

The given parameters are:

∠KPL = 46°

∠NPH = 25°

∠MPN = ∠NPH

By vertical angle theorem, we have:

∠JPK = ∠MPH

Where

∠MPH = ∠MPN + ∠NPH

This gives

∠MPH = ∠NPH + ∠NPH

So, we have:

∠MPH = 25° + 25°

Evaluate

∠MPH = 50°

Recall that:

∠JPK = ∠MPH

So, we have:

∠JPK = 50°

Hence, the measure of angle ∠JPK is 50°

Angle LPM

The angle on a straight line is 180°.

So, we have:

∠LPM +  ∠KPL + ∠MPH = 180°

This gives

∠LPM +  46° + 50° = 180°

Evaluate

∠LPM = 84°

Hence, the measure of angle ∠LPM is 84°

Angle NPM

In (a), we have:

∠NPM = ∠NPH

This gives

∠NPM = 50°

Hence, the measure of angle ∠NPM is 50°

Angle JPI

By vertical angle theorem, we have:

∠JPI = ∠LPM

So, we have:

∠JPI = 84°

Hence, the measure of angle ∠JPI is 84°

Angle HPI

By vertical angle theorem, we have:

∠HPI = ∠KPK

So, we have:

∠HPI = 46°

Hence, the measure of angle ∠HPI is 46°

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Answer: 4.6 (rounded to the nearest tenth)

Step-by-step explanation:

I assume that 1.6 is the coefficient of x, which is what we're trying to find out in this case.

Therefore, dividing 1.6 on both sides we get

from

1.6x = 7.37

to

x = 7.37/1.6 = 4.6 (approximately, rounded to the nearest tenth).

Answer:

you better give me brainliest

Step-by-step explanation:

i think they are lying about being in jail

The volume of a cylinder is 197.82 yards³ and the surface area of ​​a cylinder is 188.4 yards².

Given a cylinder has a height of 7 yards and a radius of 3 yards.

(a) We first find the volume of the cylinder using the formula V=πr²h, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula and we get

V=π(3)²×7

V=3.14×9×7

V = 197.82 yards³

(b) We will now find the surface area of ​​the cylinder using the formula S=2πr²+2πrh, where π=3.14, r=3 yards and h=7 yards.

Substitute the values ​​in the formula, we get

S=2π(3)²+2π×3×7

S=2×3.14×9+2×3.14×21

S=56.52+131.88

S = 188.4 square yards

Therefore, the volume and area of ​​a cylinder with a height of 7 meters and a radius of 3 meters is 197.82yards³ and 188.4 yards².

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Answer:

Angle CGB is an acute angle because it's less than 90°

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

Angles having measure less than 90° are considered as Acute angles.

in the given figure,

The Acute angle is :

Answer: 22

Step-by-step explanation:

Number of floor tiles = (5.4m × 4.2m) ÷ 1m²

Number of floor tiles = 22.68

Minimum number of floor tiles = 22

Step-by-step explanation:

(2^2x²/xy²) for x=3 and y=2

we have

2^2(3)²/((3)(2²))

2^2(9)/((3)(4))

2^18/12

262144/12

21845.3

The value of  expression [tex]2^{2} x^{2}/xy^{2}[/tex]  for x=3 and y=2 is, 3

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The expression,  [tex]2^{2} x^{2}/xy^{2}[/tex]

The value of expression when, x = 3 & y = 2

⇒  2²×3²/3×2²

⇒  3

Hence, The value is 3

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The inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

The graph that completes the question is added as an attachment

The parabola

It has a vertex of (1,  -4)

So, we have:

y = a(x - 1)^2 - 4

It passes through (3, 0).

So, we have:

0 = a(3 - 1)^2 - 4

This gives

4a - 4 = 0

Solve for a

a = 1

Substitute a = 1 in y = a(x - 1)^2 - 4

y = (x - 1)^2 - 4

Expand

y = x^2 - 2x + 1 - 4

y = x^2 - 2x - 3

The inner part is shaded.

So, we have:

y > x^2 - 2x - 3

The linear equation

It passes through (0, 4).

So, we have:

y = mx + 4

It passes through (1, 7).

So, we have:

7 = m + 4

Solve for m

m = 3

Substitute m = 3 in y = mx + 4

y = 3x + 4

The upper part is shaded.

So, we have:

y > 3x + 4

Hence, the inequalities in the system of inequalities are y > x² – 2x – 3 and y > 3x + 4

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The parent function f(x) = x will undergo 3 transformations. The first transformation is vertically stretched by a factor of 2. Next, the graph will shift 4 units to the right. Finally, the graph will shift 2 units up

The function is given as:

f(x) = x

This represents the parent function.

Start by stretching the function vertically by a factor of 2

This gives

f'(x) = 2x

Next, we shift the graph 4 units to the right

This gives

f''(x) = 2(x - 4)

Finally, we shift the graph 2 units up

This gives

f'''(x) = 2(x - 4) + 2

The number of transformations above is 3

Hence, the complete statement is:

The parent function f(x) = x will undergo 3 transformations. The first transformation is vertically stretched by a factor of 2. Next, the graph will shift 4 units to the right. Finally, the graph will shift 2 units up

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