The area of the top of a square table
is 269 in2. What are the dimensions
of the top?

Answer:

x=-5.25

Step-by-step explanation:

Original equation:

[tex]2(3-x)-1.4(5-2x)=2x+5.3[/tex]

Distribute:

[tex]6-2x-7+2.8x=2x+5.3[/tex]

Group like terms:

[tex](6-7)+(2.8x-2x)=2x+5.3[/tex]

Add like terms:

[tex]-1+0.8x=2x+5.3[/tex]

Add 1 to both sides

[tex]0.8x=2x+6.3[/tex]

Subtract 2x from both sides

[tex]-1.2x=6.3[/tex]

Divide both sides by -1.2

[tex]x=-5.25[/tex]

The required confidence interval for μ is (-12.07, 19.27 )

Annual returns (in percent) for a mutual fund as: 13, −2, 3, 18, and −14
95% Confidence interval

The statistic is the study of mathematics which deal with relations between comprehensive data.

Mean(x) = 13-2+3+18-14/5
x = 3.6

Standard deviation = [tex]\sqrt{\frac{\sum(x_i- x)^2}{n-1} }[/tex]
S = 12.6214

Point estimate  of (μ) = 3.6

Confidence interval = mean (+,-) Tc x S/√5
                              = 3.6 (+,-) 2.7764 x 12.62/√5
                              =3.6 (+,-) 15.671
                              = (-12.07, 19.27)

Thus, the required confidence interval for μ is (-12.07, 19.27 ).

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Answer:Given

a can do a piece of work = 40 days

so, A's 1 day work =1/4

so, A's 8 day's work =8/40=1/5

remaining work = 1- 1/5= 4/5

Now, B can do  4/5  piece of work in =16 days

So, B’s 1 day's work = (4/5) /16= 4/ 5x6=1/20

Therefore, (A+B)’s 1 day's work = 1/40+1/20 =

1+2/40=3/40

∴   Both (A+B) can do a piece of work in =

1/days (3/40) = 40/3 days

= 13 1/3 days

Answer:

[tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{x^{5} y}[/tex] = [tex]x^{\frac{5}{3}} y^{\frac{1}{3} }[/tex]

Answer:

(a)  -1

(b)  4

(c)  14

(d)  61

Step-by-step explanation:

A piecewise function is a function which has different definitions for different intervals of x.

Given:

[tex]f(x)=\begin{cases}5x-1 \quad \textsf{if }-5\leq x \leq 3\\x^3-3 \quad \textsf{if }\:\:\:\:\:\:3 < x \leq 4\end{cases}[/tex]

f(x) has 2 definitions:

Definition 1

[tex]5x-1[/tex] when x is more than or equal to -5 and less than or equal to 3.  This is a linear function.

Definition 2

[tex]x^2-3[/tex] when x is more than 3 and less than or equal to 4.  This is a cubic function.

Part (a)

We have to find f(0), so when x = 0.

x = 0 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 0 in this definition:

[tex]\implies f(0)=5(0)-1=-1[/tex]

Part (b)

We have to find f(1), so when x = 1.

x = 1 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 1 in this definition:

[tex]\implies f(0)=5(1)-1=4[/tex]

Part (c)

We have to find f(3), so when x = 3.

x = 3 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

[tex]f(x)=5x-1[/tex]

Substitute x = 3 in this definition:

[tex]\implies f(0)=5(3)-1=14[/tex]

Part (d)

We have to find f(4), so when x = 4.

x = 4 satisfies the condition 3 < x ≤ 4 so the corresponding function is

[tex]f(x)=x^3-3[/tex]

Substitute x = 4 in this definition:

[tex]\implies f(4)=(4)^3-3=61[/tex]

The length of the base of the triangle is 12m

The formula for calculating the area of a triangle is expressed as:

A = 0.5 * base * height

If the height of a triangle is 4 m less than its base, then;

h = b - 4

Substitute

A = 0.5(b)(b-4)

48 = 0.5b²-2b

b²-4b - 96 = 0

Factorise

b² - 12b + 8b - 96 = 0

b(b-12)+8()b-12) = 0
b - 12 = 0

b = 12

Hence the length of the base of the triangle is 12m

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When we Simplify [(x^2)^3 × 5x] / [6x^2 × 15x^3], the result obtained is (1/18)x^2

[(x^2)^3 × 5x] / [6x^2 × 15x^3]

Recall

(M^a)^b = M^ab

Thus,

(x^2)^3 = x^6

Recall

M^a × M^b = M^(a+b)

Thus,

x^6 × 5x = 5x^(6 + 1) = 5x^7

6x^2 × 15x^3] = (6×15)x^(2 + 3) = 90x^5

Recall

M^a ÷ M^b = M^(a - b)

Thus,

5x^7 ÷ 90x^5 = (5÷90)x^(7 - 5) = (1/18)x^2

Therefore,

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Answer:

3/4

Step-by-step explanation:

A: students present
B: students on time

P(all students present and on time) = P(A and B) = 3/10
P(all students present) = P(A) = 2/5

P(A and B) = P(A).P(B|A) where P(B|A) is the probability of everyone being on time given that everyone is present

So P(B|A) = P(A and B) /P(A) = 3/10 ÷ 2/5 = 3/10 * 5/2 = 15/20 which can be reduced to 3/4 by dividing numerator and denominator by 5

Answer:

======================

Since the given is the GP, find the common ratio in terms of given values:

Equate the two values and solve for x to find the missing term:

Answer:

slope = 8

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, - 8) and (x₂, y₂ ) = (2, 32) ← 2 ordered pairs from the table

note any pair of ordered pairs will give the slope

m = [tex]\frac{32-(-8)}{2-(-3)}[/tex] = [tex]\frac{32+8}{2+3}[/tex] = [tex]\frac{40}{5}[/tex] = 8

Hello,

Step-by-step explanation:

6/7 ≈ 0,857

we have 4/4 = 1 and 3/4 = 0,75

| 0,75 - 0,857| = 0,107

| 1 - 0,857 | = 0,143

→ Answer is 3/4

Answer:

the bench mark is 1/4 and the lower range is 3/4.

Step-by-step explanation:

Estimate the fraction 6/7 using 1/4 as our benchmark: Display the fraction bar for 6/7 The lower range is 3/4 and the upper range is 1

Answer:

58080

Step-by-step explanation:

You just have to multiply it by 5280. So, 11*5280 is 58080. The answer is 58080.

Hello,

Answer:

The next number is 35 585

Step-by-step explanation:

3 × 5 - 3 = 12

5 × 12 - 5 = 55

12 × 55 -12 = 648

55 × 648 - 12 = 35 585

The next number for the given series is 35,585.

A number series is a number-based sequence. In the number series questions, we must identify the rules that lead to the formation of a number series. These series vary in nature, as do the questions that may arise from them.

Given that the series is 3,5,12,55,648. The next number will be calculated by decoding the series as below,

3 × 5 - 3 = 12

5 × 12 - 5 = 55

12 × 55 -12 = 648

55 × 648 - 12 = 35,585

Therefore, the value of the next number for the series is 35,585.

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The value of the function h(-4) is (a) -2

The function is given as

h(x) = -2x - 10

When x = -4, we have:

h(-4) = -2 * -4 - 10

Evaluate the product

h(-4) = 8 - 10

Evaluate the difference

h(-4) = -2

Hence, the value of the function h(-4) is (a) -2

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Considering the given stem-and-leaf plot, the quartiles are given as follows:

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

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Answer: a rectangle

Step-by-step explanation:

If you graph the points out you will see that it is four points high and six points wide

Answer:

It is A.Rectangle. from the given points.

Step-by-step explanation:

the graph is given in the image.

I hope it to be helpful ^=^

The equivalent equation of 4y – 1 = 15 is 20x - 13 = 15

The equations are given as:

4y – 1 = 15 and y = 5x – 3.

Substitute y = 5x – 3. in 4y – 1 = 15

4(5x – 3) – 1 = 15

Expand

20x- 12 - 1 = 15

Evaluate the like terms

20x - 13 = 15

Hence, the equivalent equation of 4y – 1 = 15 is 20x - 13 = 15

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The statement that linear pairs of angles are always adjacent is true.

What are Linear Pairs?

The pair of angles formed when two lines intersect each other at a point,  are called Linear Pairs, the angles formed are adjacent to each other and they share a common arm.

It is asked in the question that linear pairs of angles are always adjacent and the answer is yes, it is a true statement as they have a common arm and an uncommon arm, the sum of the angles is equal to 180 degrees.

Hence, the statement that linear pairs of angles are always adjacent is true.

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Final answer:

Since absolute values determine the distance between the number and the value whether the value is positive or negative. As distance is always positive.

Thus, |a| is always nonnegative, even though |a|=-a for negative values of a.

Step-by-step explanation:

Step 1

It is said that |a| is always nonnegative even though even though |a|=-a for negative values of a.

Step 2

This is because by the definition of an absolute value, any real number inside an absolute value symbol || will always be positive.

The equation of line which would intersect be

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

y = 12 x + 2

and, a line passes through (-4, 0) and (0, 2)

Equation of line

y = -1/2 (x+ 4)

y= -x/2 - 2

The equations which would intersect the line will be

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Answer:

There are 8 black marbles.

Step-by-step explanation:

First, set up your equation. You have black (b) and white (w) marbles, total of 30, so those will be your variables to set in your equation.

w + b = 30

You mentioned that there are 14 more white marbles then black. Therefore, white marbles will have b many marbles + 14, creating the equation:

w= b + 14

If w = b + 14 and w can be easily substituted in the first equation, substitute w for b + 14. This will result in having the equation of:

(b +14) + b= 30

Simplify this equation, combine like terms to break down the equation, making it easier for you to solve for b.

-Subtract 14 from both sides.

-Add b + b = 2b

Then, you will have your resulting equation in which you divided 2 from both sides to get b by itself.

2b = 16

b=8

There are 8 black marbles.

An equation is formed when two equal expressions. The cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the cost of a pound of wheat flour be x and the cost of a pound of rye flour be y.

A baker purchased 13 lb of wheat flour and 14 lb of rye flour for a total cost of $14.85.

13x + 14y = $14.85

x = (14.85-14y)/13

A second purchase, at the same prices, included 15 lb of wheat flour and 12 lb of rye flour.

15x + 12y = $14.85

Substitute the value of x from the above equation and solve for y,

[tex]\dfrac{15(14.85-14y)}{13} + 12y = 14.85\\\\222.75-210y+156y = 193.05\\\\y = 0.55[/tex]

Substitute the value of y in any one of the equations formed,

13x + 14(0.55) = 14.85

13x = 7.15

x = 0.55

Hence, the cost per pound of wheat flour is $0.55 and the cost of per pound of rye flour is $0.55.

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Answer:

51

Step-by-step explanation:

arrange in ascending order

48,49,50,52 54,62

number of terms=6

median=(3rd term+4th term)/2=(50+52)/2=102/2=51

Answer:

51

Step-by-step explanation:

Hope it helps

The units for the composite function s(w(h)) is bracelets over a week when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

To define the unit of the composite function s(w(h)), we first need to find the units of the functions s(t) and w(h).

The function s(t)  represents the number of bangles per hour, so its unit will be bangles over an hour.

The function w(h) represents the hours per week spent on making the bracelets, so its unit will be hours over a week.

Now, we can define the unit of the composite function s(w(h)).

To find the unit of the composite function we follow these steps:-

s(w(h)),

= s(hours over a week) {replacing the function w(h) by its units},

= (bangles over an hour(hours over a week)) {replacing the function s(t) with its units},

= bangles over a week {Simplifying}.

Thus, the units for the composite function s(w(h)) is bracelets over a week when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

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Answer:

$2.29

Step-by-step explanation:

$270 + 27% = $270 + (270 * 0.27)

                    = $270 + 72.9

                    = $342.9

$342.9 was the total selling price, but there are 150 articles.

$342.9 / 150 = $2.286

                     = $2.29 (Currency is rounded to two decimal places)

Answer: C.) Earthquakes

Based on the sales made by Micro Sales on bank credit cards, the journal entries would be:

Date               Account Title                                        Debit               Credit

March 4          Cash                                                 $13,095

                      Card Service expense                     $   405

                       Sales Revenue                                                         $13,500

The cash account will be debited with:

= 13,500 x (1 - 3%)

= $13,095

The Card service expense is:

= 13,500 x 3%

= $405

Sales revenue will be credited by the amount of sales which is $13,500.

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