When x is divided by 4, the remainder is 3. When r^2 is divided by
4, what must the remainder be?

Answer:

560cm

Step-by-step explanation:

Volume = Length × Breadth × Height

= 10 × 8 × 7

= 560 cm³

Answer:

Step-by-step explanation:

Volume =length x breadth x height

10 x 8 x 7=560cm^3

Answer:

A

Step-by-step explanation:

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given data values are;

x,      f(x)

8,     12

12,    40

6,      15

20,    20

Where;

x = The number of flowers in the bouquet

f(x) = The total cost (in dollars)

The equation for linear regression is of the form, Y = a + bX

The formula for the intercept, a, and the slope, b, are;

[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]

[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]

Where:

N = 4

∑XY = 1066

∑X = 46

∑Y = 87

∑X² = 644

(∑X)² = 2116

b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696

a = (87 - 0.5696*46)/4 = 15.1996

The standard deviation of the x- values

[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]

[tex]\sum (x_i - \mu)^2}[/tex] = 115

N = 4

Sx =√(115/4)

Sx = 5.36

[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]

[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75

N = 4

Sy =√(476.75/4)

Sy= 10.92

b = r × Sy/Sx

Where:

r = The correlation coefficient

r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28

The correct option is 0.28.

Answer:

C on edge

Step-by-step explanation:

Answer:

a = 11.71 ; b = 15.56

Step-by-step explanation:

For this problem, we need two things.  The law of sines, and the sum of the interior angles of a triangle.

The law of sines is simply:

sin(A)/a = sin(B)/b = sin(C)/c

And the sum of interior angles of a triangle is 180.

45 + 110 + <C = 180

<C = 25

We can find the sides by simply applying the law of sines.

length b

7/sin(25) = b/sin(110)

b = 7sin(110)/sin(25)

b = 15.56

length a

7/sin(25) = a/sin(45)

a = 7sin(45)/sin(25)

a = 11.71

Answer:

a) Cost

[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]

b) Sales income

[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]

c) Table of values

[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]

d) Attached

e) Breakeven point = 12.5 sheets

f) Profit at 550 sheets = $1,950

Step-by-step explanation:

a) We have a fixed cost for the image, at $50.

We also have a variable cost of $16 a sheet.

The purchased quantity is 500 sheets.

Then, the cost function is:

[tex]C(q) = 50+16q\\\\C(500)=50+16(500)=50+8,000=8,050[/tex]

b) The price for each sheet is $20, so the income from sales are:

[tex]S(q)=20q\\\\S(500)=20\cdot 500 = 10,000[/tex]

c) Table of values

[tex]\left[\begin{array}{ccc}q&C(q)&S(q)\\0&50&0\\250&4,050&5,000\\500&8,050&10,000\end{array}\right][/tex]

d) Attached

e) The minimum number of sheets the group must sell so they don't lose any money is the breakeven point (BEP) and can be calculated making the income sales equal to the cost:

[tex]S(q)=C(q)\\\\20q=50+16q\\\\(20-16)q=50\\\\4q=50\\\\q=50/4=12.5[/tex]

f) This profit can be calculated as the difference between the sales income and the cost:

[tex]P(500)=S(500)-C(500)\\\\P(500)=20\cdot 500-(50+16\cdot 500)=10,000-8,050=1,950[/tex]

The given number of 500 sheets of stamps purchased at $16/sheet with

a plan to sell each sheet for $20 gives the following values;

(a) Cost, C = 50 + 16·q

(b) Income, R = 20·q

(c) Please find the included table of values and the attached graph

(e) Approximately 403 sheets

(f) $1,950

(a) The cost per sheet of stamp = $16/sheet

The cost to create the image = $50

Amount at which they plan to sell each sheet, P = $20

Therefore

(b) The income from sale, R = Number of units sold × P

Which gives;

(c) The table of values are therefore;

C = 50 + 16·q

[tex]\begin{array}{|c|c|c|}q&C=50+16 \times q\\0&50\\1&66\\2&82\\3&98\\4&114\\5&130\\6&146\\7&162\\8&178\\9&194\\10&210\\11&226\\12&242\\13&258\\14&274\end{array}\right][/tex]

R = 20·q

[tex]\begin{array}{|c|c|c|}q&R = 20 \times q\\0&0\\1&20\\2&40\\3&60\\4&80\\5&100\\6&120\\7&140\\8&160\\9&180\\10&200\\11&220\\12&240\\13&260\\14&280\end{array}\right][/tex]

Please find attached the required graph created with MS Excel

e) The minimum number of sheets the group must sell is given as follows;

The cost of the sheets purchased = 50 + 16 × 500

Which gives;

At point of profitability; Income = Cost

50 + 16 × 500 = 20·[tex]q_{min}[/tex]

[tex]q_{min} = \dfrac{50 + 16 \times 500}{20} =402.5 \approx \mathbf{403}[/tex]

(f) The profit made by selling 500 sheets is; 20·q - (50 + 16·q)

Where;

q = 500

Which gives;

20 × 500 - (50 + 16 × 500) = 1,950

The profit made from selling 500 sheet = $1,950

Learn more about graphs of functions here:

https://brainly.com/question/22150463

Answer:

Step-by-step explanation:

Given,

x = [tex] \frac{5}{2} [/tex]

Now, let's find the value of 2x - 5

[tex]2x - 5[/tex]

plug the value of x

[tex] = 2 \times \frac{5}{2} - 5[/tex]

Reduce the number with Greatest Common Factor 2

[tex] = 5 - 5[/tex]

The sum of two opposites equals 0

[tex] = 0[/tex]

Hope this helps..

best regards!!

Answer:

0

Step-by-step explanation:

x=5/2

therefore

2(5/2)-5=10/2-5

=5-5(since 10/2=5)

=0

Answer:

The inclination of the through the points (5, 14) and (9, 18) is 45°

Step-by-step explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2,  having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

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

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

[tex]m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1[/tex]

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

[tex]tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta[/tex]

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) =  45°.

Answer:

144

Step-by-step explanation:

An angle of a regular pentagon is of 180(5-2)/5=108°

and that all the sides are equal so angle MNL=108/3=36

then MNK=180-MNL=180-36=144

I don't know if you understand this but it's hard to work without more points :)

Answer:

Multiply the first equation by -4

Step-by-step explanation:

Equation A: 3c = d − 8

Equation B: c = 4d + 8

We want to eliminate variable d

Multiply the first equation by -4

-4( 3c = d − 8)

-12c = -4d +32

Add this to the second equation

-12c = -4d +32

c = 4d + 8

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

-11c = 0d + 40

Answer:

A : Multiply equation A by −4

Step-by-step explanation:

3c = d - 8

Multiply the equation by -4.

-12c = -4d + 32

-12c = -4d + 32

c = 4d + 8

Add equations.

-11c = 0d + 40

-11c = 40

The d variable is eliminated.

Answer:

48

Step-by-step explanation:

The formula for the area of a square is A = s².  Plug in each value and see if is in between 2200 and 2400.

A = s²

A = (46)²

A = 2116

A = s²

A = (48)²

A = 2304

A = s²

A = (50)²

A = 2500

A = s²

A = (44)²

A = 1936

The only value that fits in between 220 and 2400 is 48.

Answer:

Step-by-step explanation:

put (x+2)/(x-2)=a

a-1/a=5/6

[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]

[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]

2.

put (x+3)/x=a

a+1/a=4  1/4

[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]

Answer:

200 teachers

Step-by-step explanation:

If 25% is a fourth of the teacher staff, and this value is fifty, to find out how many teachers there are you just have to multiply by 4 to find out the 100%. So this means that 50*4= 200

Answer:

Total teachers = 200

Step-by-step explanation:

Let x be the total teachers in school

Basic Maths teachers = 25 % of x

Basic Maths Teachers = 50

=> 25% of x = 50

=> [tex]\frac{25}{100} x = 50[/tex]

=> [tex]\frac{x}{4} = 50[/tex]

Multiplying both sides by 4

=> x = 200

Complete question is;

A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Answer:

The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Step-by-step explanation:

Let X = Life expectancy of the automobile tire

For the normal distribution, we are given;

μ = 34000

σ = 2700

Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.

Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:

P(X ≤ y) = 0.1

Using the z formula, we have;

P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1

Thus;

P(Z ≤ ([y - μ]/σ) = 0.1

From z-distribution table the Z-score at 0.1 is approximately -1.2816

This is P(Z ≤ -1.2816)

Thus;

[y - μ]/σ = -1.2816

(y - 34000)/2500 = -1.2816

y - 34000 = -1.2816 × 2500

y - 34000 = -3204

y = 34000 – 3204

y = 30796

So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Answer:

The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Step-by-step explanation:

Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).

To find the values in the domain where f(x) = 0, we look at the ordered pairs given.

We look for the pair in which f(x) = 0.

So f(x) = 0 in (-2.5, 0)

f(x) = 0 in (-0.75, 0)

and f(x) = 0 in (1, 0)

The corresponding values of x  in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Answer:

C. [tex]x=1[/tex]

Step-by-step explanation:

When x is 1, y is 0.

Answer:

x=7

2x+45=59

3x+55=76

Step-by-step explanation:

Answer:

7°, 59°, 76°

Step-by-step explanation:

The equation for the sum of the angles:

Solving for x:

The angles:

Answer:

4.7 feet³ of water

Step-by-step explanation:

Diameter of 4 feet

Radius = 2 feet

Height = 0.75 feet

Formula for Volume = 2·[tex]\pi[/tex]·radius·height

But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height

[tex]\pi[/tex]·2·0.75 = 4.71 feet³

Answer:

A. The time you take your dog for a walk each day

B. The temperature of the water in the local river during the day

C. How long it takes to run a lap around the track  

Step-by-step explanation:

Continuous data is quantitative data that you can measure. It can have an infinite number of possible values within a given range.

For example, you can measure times and temperatures to any number of decimal places if you have the appropriate equipment.

D is wrong. You can't measure the number of croutons in a salad. You must count them.

Answer:

50.27

Step-by-step explanation:

First, we have to find the volume of the cone using the formula V=πr^2h/3, where pi is 3.14. After plugging everything in, we get V = 75.4. Then, we have to find 2/3 of that. Rounding to the nearest hundredth, we get 2/3 x 75.4 = 50.27.

Answer:

Step-by-step explanation:

In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.

Tan(29) =26/x                Multiply both sides by x

x tan(29) = 26                 Divide by tan(29)

x = 26/tan(29)                Find tan(29)

x = 26/0.5543                Divide

x= 46.9

Answer:

[tex] Area = 538.5 m^2 [/tex]

Step-by-step Explanation:

Given:

∆XVW

m < X = 50°

m < W = 63°

XV = w = 37 m

Required:

Area of ∆XVW

Solution:

Find side length XW using Law of Sines

[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]

W = 63°

w = XV = 37 m

V = 180 - (50+63) = 67°

v = XW = ?

[tex] \frac{v}{sin(67)} = \frac{37}{sin(63)} [/tex]

Cross multiply

[tex] v*sin(63) = 37*sin(67) [/tex]

Divide both sides by sin(63) to make v the subject of formula

[tex] \frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] v = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] v = 38 [/tex] (approximated to nearest whole number)

[tex] XW = v = 38 m [/tex]

Find the area of ∆XVW

[tex] area = \frac{1}{2}*v*w*sin(X) [/tex]

[tex] = \frac{1}{2}*38*37*sin(50) [/tex]

[tex] = \frac{38*37*sin(50)}{2} [/tex]

[tex] Area = 538.5 m^2 [/tex] (to nearest tenth).

Answer:

The breadth of the room is 6 metres

Answer:

Step-by-step explanation:

Side of a tile= a  = 0.75 m

Area of one square tile = a²  = (0.75)² = 0.5625 m²

Area of 96 square tiles = 0.5625 * 96

Area of the room =  area of 96 square tiles

length * breadth = 0.5625 * 96

9 * breadth = 0.5625 * 96

     breadth = [tex]\frac{0.5625*96}{9}\\\\[/tex]

      breadth = 6 m

Answer:

x^5

Step-by-step explanation:

x^2 . x^3

x^(2+3)

x^5

Answer:

- 1

Step-by-step explanation:

Given

( [tex]\frac{1+i}{1-i}[/tex] )²

= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]

= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1

= [tex]\frac{1+2i-1}{1-2i-1}[/tex]

= [tex]\frac{2i}{-2i}[/tex]

= - 1

Answer:

Yes.

Step-by-step explanation:

You are correct except to the nearest hundredth it is 795.54 cm^2.

Answer:

The correct option is;

C. 15 in 16

Step-by-step explanation:

The given information are;

The number of press-ups required = 14 press-ups

The number of press-ups Jessica is sure to do = 10 press-ups

The chance of Jessica doing subsequent press-ups after 10 halves each time

The consequence of not completing the 14 press-ups =  Punishment

The probability that Jessica does goes on to do 11 press-ups = 1/2

The probability that Jessica does goes on to do 12 press-ups = 1/2×1/2

The probability that Jessica does goes on to do 13 press-ups = 1/2×1/2×1/2

The probability that Jessica does goes on to do (completes) 14 press-ups = 1/2×1/2×1/2×1/2 = 1/16

Therefore;

Since the probability that Jessica does not receive a punishment because she completed the 14 push-ups is 1/16, we have;

The probability that Jessica does not complete the 14 press-ups and receives a punishment = 1 - 1/16 = 15/16 which is 15 times out of 16 or 15 in 16.

Answer:

Option C is the correct option

Step-by-step explanation:

[tex] \frac{ {y}^{2} + 7y + 12}{ {y}^{2} - 2y - 15 } [/tex]

Write 7y as a sum

[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} - 2y - 15} [/tex]

Write -2y as a difference

[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} + 3y - 5y - 15} [/tex]

Factor out y from the expression

[tex] \frac{y(y + 4) + 3y + 12}{ {y}^{2} + 3y - 5y - 15 } [/tex]

Factor out 3 from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{ {y}^{2} + 3y - 5y - 15 } [/tex]

factor out y from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5y - 15} [/tex]

Factor out -5 from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5( y + 3)} [/tex]

factor out y + 4 from the expression

[tex] \frac{(y + 4)(y + 3)}{y(y + 3) - 5(y + 3)} [/tex]

Factor out y + 3 from the expression

[tex] \frac{(y + 4)(y + 3)}{(y + 3)(y - 5)} [/tex]

Reduce the fraction with y + 3

Hope this helps..

Best regards!!

Answer:

400

Step-by-step explanation:

There are 400.

Assuming the number must be at least 10,000, then:

In a 5 digit palindrome, the first and last digits must be the same, and the second and fourth digits must be the same; and:

For the first and last digit there is a choice of 4 digits {2, 4, 6, 8};

For each of these there is a choice of 10 digits {0, 1, ..., 9} for the second and fourth digits;

For each of the above choices these is a choice of 10 digits {0, 1, ..., 9} for the third digit;

Making 4 x 10 x 10 = 400 possible even 5 digit palindromes.

Answer:

Step-by-step explanation:

cosФ=0 then the angle=π/2=90 degrees

sinФ==1     sin 90=1

12) the original price of the console  that Amanda bought :

240+(240*50%)=360 dollars

the price before the tariffs:

360-(360*50^)=180 dollars