Find the largest integer which belongs to the following interval: (−∞, 8)

Answer:

Step-by-step explanation:

Let x represent the amount invested at 6%. Then 30000-x is the amount invested at 5%. Leila's total earnings for the year are ...

  0.06x +0.05(30000-x) = 1580

  0.01x +1500 = 1580 . . . . . . . . . . . . simplify

  0.01x = 80 . . . . . . . . . . . subtract 1500

  x = 8000 . . . . . . . . . . . . multiply by 100

Leila invested $8000 at 6% and $22000 at 5%.

Answer:

Complement = 15 Degrees

Supplement = 105 Degrees

Step-by-step explanation:

The complement of an angle refers to the measure that will make the angle 90 degrees.  So, the complement of 75 would be 15, since 90 - 75 = 15.

The supplement of an angle refers to the measure that will make the angle 180 degrees.  So, the supplement of 75 would be 105, since 180-75 = 105.

Cheers.

Answer:

x = -4

Step-by-step explanation:

2 - (7x + 5) = 13 - 3x

add the binomial (7x +5) to both sides

2 = (7x + 5) + 13 - 3x

combine like terms

2 = 4x + 18

subtract 18 from both sides

-16 = 4x

divide by 4

x = -4

Answer:

-4

Step-by-step explanation:

Distribute the negative signs to the values in the parentheses

2 -7x - 5 = 13 - 3x

Add like terms:

-7x - 3 = 13 - 3x

Add 3x to both sides:

-4x - 3 = 13

Add 3 to both sides:

-4x = 16

Divide both sides by -4:

x = -4

Hey There!!

The answer to this is: A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?" Line BC is parallel to line AD because their slopes is equal i.e. (0 - 0) / (7 - 2) = (5 - 5) / (8 - 3) which gives 0 / 5 = 0 / 5 giving that 0 = 0. We check whether line AB is parallel to line CD. Slope of line AB is given by (0 - 5) / (2 - 3) = -5 / -1 = 5. Slope of line CD is given by (5 - 0) / (8 - 7) = 5 / 1 = 5 We have been able to prove that the opposite sides of the quadrilateral are parallel which means that the quadrilateral is not a trapezoid. Next we check whether the length of the sides are equal. Length of line AB is given by sqrt[(0 - 5)^2 + (2 - 3)^2] = sqrt[(-5)^2 + (-1)^2] = sqrt(25 + 1) = sqrt(26) Length of line BC is given by sqrt[(0 - 0)^2 + (7 - 2)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Length of line CD is given by sqrt[(5 - 0)^2 + (8 - 7)^2] = sqrt[5^2 + 1^2] = sqrt(25 + 1) = sqrt(26) Length of line DA is given by sqrt[(5 - 5)^2 + (8 - 3)^2] = sqrt[0^2 + 5^2] = sqrt(25) = 5 Thus, the length of the sides of the quadrilateral are not equal but opposite sides are equal which means that the quadrilateral is not a rhombus. Finally, we check whether adjacent lines are perpendicular. Recall the for perpendicular lines, the product of their slopes is equal to -1. Slope of line AB = 5 while slope of line BC = 0. The product of their slopes = 5 x 0 = 0 which is not -1, thus the adjacent sides of the quadrilateral are not perpendicular which means that the quadrilateral is not a rectangle. Therefore, ABCD is a parallelogram with non-perpendicular adjacent sides. Thus, For (option A).

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

A. ABCD is a parallelogram with non-perpendicular adjacent sides.

Hope this helps!

Step-by-step explanation:

Answer:

the size of the square to be cut out for maximum volume is 1.5695 inches

Step-by-step explanation:

cardboard that measures 8 by 12 inches.

We need to determine What size square should be cut from each corner

We were given given the size of the cardboard.

let us denote the length of the square as 'x'.

Then our length, width and height will be:

Length = 8 − 2x

Width = 12− 2x

Then our Height = x

So now, the volume= length×width ×height

Volume = (8 − 2x) x (12− 2x) x (x)

After calculating volume comes out to be:

V = (96 − 40x + 4x²) (x)

V = 4x³ − 40x² + 96x

Now, we can use differentiation to equate it to zero.

So differentiate it with respect to x, we get

dV/dx = 12x² − 80x + 96

12x² − 80x + 96 = 0

So, after solving this, x comes out to be:

x = 5.097 and x = 1.5695

Looking at it the size of the square cut out cannot be 5.097 because we cannot cut out of both sides of the width, since the width is 5 inches.

Therefore, the size of the square to be cut out for maximum volume is 1.5695 inches.

Answer:

$13,450

Step-by-step explanation:

The fixed cost of production is $13,450, this is because a fixed cost of production is the amount of cost that does not change with an increase or decrease in the amount of the goods or services produced. Fixed cost of production are paid by companies. It is one of the two component of the total cost of goods or services along with the variable cost.

In regard to the information given in the  question, no matter how many spinners the company produces, the fixed cost will remain the same.

Assuming x is the variable cost which signifies the number of spinners produced, this literally implies that the cost to produce each spinner is $1.28 and the fixed cost which is independent  of the production is $13,450.

Hence, the  fixed cost of production is $13,450.

Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]

Step-by-step explanation:

The complete question is provided in the attachment.

Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds

[tex]=\dfrac{5}{4}[/tex] pounds.

Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds

[tex]=\dfrac{7}{2}[/tex] pounds

Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans

[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds

[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]

Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]

Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away

=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]

She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.

Answer:

work is shown and pictured

Answer:

Base = 11 cm

Height = 13 cm

Step-by-step explanation:

It is given that the height of a triangle is 2 centimetres more than the base.

Let x cm be the base of triangle. So height of the triangle is x+2 cm.

It is given that if the height is increased by 2 centimetres while the base remains the same, the new area becomes 82.5 centimetres square.

New height = (x+2)+2 = x+4 cm

Area of a triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

[tex]82.5=\dfrac{1}{2}\times x\times (x+4)[/tex]

[tex]165=x^2+4x[/tex]

[tex]x^2+4x-165=0[/tex]

Splitting the middle term, we get

[tex]x^2+15x-11x-165=0[/tex]

[tex]x(x+15)-11(x+15)=0[/tex]

[tex](x+15)(x-11)=0[/tex]

Using zero product property, we get

[tex]x=-15,11[/tex]

Base of a triangle can not be negative, therefore x=11.

Base = 11 cm

Height = 11+2 = 13 cm

Therefore, the base of original triangle is 11 cm and height is 13 cm.

Answer:

x=2y/3

Step-by-step explanation:

Answer:

x = 2y/3

Step-by-step explanation:

5(x + y) = 2x + 7y

5x + 5y = 2x + 7y

5x - 2x = 7y - 5y

3x = 2y

x = 2y/3

Thus, The value of x = 2y/3

Answer: [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

This is a multiplication problem. You are multiplying [tex]\frac{1}{3}[/tex] by 4. This also means 4 divided by 3. They are both the same.

Answer:

[tex]\huge\boxed{26}[/tex]

Step-by-step explanation:

[tex]\sf x^2-4x+5\\Given \ that \ x = -3\\(-3)^2-4(-3)+5\\9+12+5\\26[/tex]

Answer:

[tex] \boxed{26}[/tex]

Step-by-step explanation:

[tex] \mathsf{ {x}^{2} - 4x + 5}[/tex]

[tex] \mathrm{Plug \: the \: value \: of \: x}[/tex]

⇒[tex] {( - 3)}^{2} - 4 \times(- 3 )+ 5[/tex]

[tex] \mathrm{Evaluate \: the \: power}[/tex]

⇒[tex] \mathsf{9 - 4 \times(- 3 ) + 5}[/tex]

[tex] \mathrm{Multiply \: the \: numbers}[/tex]

⇒[tex] \mathsf{9 + 12 + 5}[/tex]

[tex] \mathrm{Add the numbers}[/tex]

⇒[tex] \mathsf{26}[/tex]

Hope I helped!

Best regards!

Answer:

common ratio = 2

Step-by-step explanation:

T6 = ar^5

T3 = ar²

T6 = 8 x T³

ar^5 = 8 x ar²

ar^5/ar² = 8

r³ = 8

r = ³√8

r = 2

Answer:  see proof below

Step-by-step explanation:

Use the Quotient rule for derivatives:

[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]

Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]

[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]        

[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]

LHS = RHS:  [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]

Answer:

9u^3 + 6u^2 - 7u + 6

Step-by-step explanation:

Answer:

( x-2)^2 + ( y +8) ^2 =121

Step-by-step explanation:

The equation of a circle can be written as

( x-h)^2 + ( y-k) ^2 = r^2

where ( h,k) is the center of the circle and r is the radius

( x-2)^2 + ( y- -8) ^2 = 11^2

( x-2)^2 + ( y +8) ^2 =121

Answer:

(x - 2)² + (y + 8)² = 11²

Step-by-step explanation:

General equation for a circle

( x - h )² + ( y - k )² = r², where (h,k) is the center and r ,radius..

with center ( 2,-8 ) and radius 11

(x - 2)² + (y + 8)² = 11²

Answer:

[tex]\huge\boxed{\sf \frac{160rs^5}{t^6}}[/tex]

Step-by-step explanation:

[tex]\sf 5r^6t^4 ( \frac{4r^3s^tt^4}{2r^4st^6} ) ^5[/tex]

Using rule of exponents [tex]\sf a^m/a^n = a^{m-n}[/tex]

[tex]\sf 5r^6t^4 ( 2 r^{3-4} s^{2-1}t^{4-6})^5\\5r^6t^4(2r^{-1}st^{-2})^5\\5r^6t^4 * 32 r^{-5}s^5t^{-10}[/tex]

Using rule of exponents [tex]\sf a^m*a^n = a^{m+n}[/tex]

[tex]\sf 160 r^{6-5}s^5t^{4-10}[/tex]

[tex]\sf 160 rs^5 t^{-6}[/tex]

To equalize the negative sign, we'll move t to the denominator

[tex]\sf \frac{160rs^5}{t^6}[/tex]

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

Explanation:

Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees

(angle POU) + (angle UOT) + (angle TOS) = 180

4x + x + 40 = 180

5x + 40 = 180

5x = 180-40

5x = 140

x = 140/5

x = 28

Side note: if x = 28, then 4x = 4*28 = 112.

We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.

Answer:

option B

everyone has different opinions about different things, since we only recorded the survey of a fourth of the total people, the survey will definitely have bias since the people who dont have to answer survey will not be able to record their opinions

Answer:

c=-9

Step-by-step explanation:

Hello,

[tex](ax+b)(x-3)=ax(x-3)+b(x-3)=ax^2-3ax+bx-3b\\\\=ax^2+(b-3a)x+(-3b) \\\\\text{And it should be equal to } 4x^2+cx-9[/tex]

We can identify the like terms so:

a = 4

b-3a = c

3b = 9 <=> b = 3

So c = 3 - 3*4 = 3-12 = -9

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

6 lockers have both students' stickers

Step-by-step explanation:

There are 130 lockers in the hallway

Janine goes down a hallway in the school and puts a sticker on every fourth locker.

Janine= 4th, 8th, 12th, 16th, 20th, 24th, 28th, 32nd, 36th, 40th, 44th, 48th, 52nd, 56th, 60th, 64th, 68th, 72nd, 76th, 80th, 84th, 88th, 92nd, 96th, 100th, 104th, 108th, 112th, 116th, 120th, 124th, 128th.

Thor goes down the same hallway, putting one of his stickers on every fifth locker

Thor= 5th, 10th, 15th, 20th, 25th, 30th, 35th, 40th, 45th, 50th, 55th, 60th, 65th, 70th, 75th, 80th, 85th, 90th, 95th, 100th, 105th, 110th, 115th, 120th, 125th, 130th.

Common multiples of Janine fourth locker and Thor fifth locker= 20, 40, 60, 80, 100, 120

Therefore,

6 lockers have both students' stickers

Answer:

53 52 72 61 68 58 47 47 (arrange it)

47 47 52 53 58 61 68 71 (done!)

Mode: 47 (appear twice)

Median: (53+58)/2 = 55.5

Mean = 47+47+52+53+58+61+68+71/ 8

=457/8

=57.12

Answer:

Step-by-step explanation:

Hello, let's factorise as much as we can.

[tex]x^4-x^3 + 2x^2-2x\\\\=x(x^3-x^2+2x-2)\\\\=x(x-1)(x^2+2)[/tex]

So, the solutions are

[tex]0, \ 1, \ \sqrt{2}\cdot i, \ -\sqrt{2}\cdot i[/tex]

There are only 2 real roots.

Thank you.

Answer:

So, the solutions are

There are only 2 real roots.

Step-by-step explanation:

Answer:

v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?

Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation:

Answer:

Below

Step-by-step explanation:

The formula of the volule of a cone is:

● V= (1/3) × Pi × r^2 × h

h is the height and r is the radius.

■■■■■■■■■■■■■■■■■■■■■■■■■■

We are given that the volume is 30 Pi m^3

● V = 30 Pi

● 1/3 × Pi × r^2 × h = 30 Pi

If we multiply h by 6 we should do the same for 30 Pi since it's an equation

● 1/3 × Pi × r^2 × h = 30 × Pi × 6

Answer:

REVIEW: B is Correct    Exit

A right circular cone has a volume of 30π m. If the height of the cone is multiplied by 6 but the radius remains fixed, which expression represents the resulting volume of the larger cone?

A. 6 + 30π m

B. 6 x 30π m

C. 6 x 30π m

D. 6 x (30π) m

Step-by-step explanation:

The answer is be all i did was dig into what the other person was saying and got b it is correct:)

Answer:

(a) Probility Distribution

Outcome   probability

$1               5/15 = 1/3

$5              4/15

$10             3/15 = 1/5

$20            5/15 = 1/3

(b) P($9 or less) =  3/5

Step-by-step explanation:

(a) Probility Distribution

Outcome   probability

$1               5/15 = 1/3

$5              4/15

$10             3/15 = 1/5

$20            5/15 = 1/3

Any other denomination

                  0

(b)

ways to draw $9 or less in a single draw

P($1) = 1/3

P($5) = 4/15

P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5

Answer:

Step-by-step explanation:

positive integer divisible by 3 includes

3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...

less than highest possible value is 42

Answer: You are correct. The answer is choice C.

The sum of the vectors is the resultant vector, which is where the net force is directed.

An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.

Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.

The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.

Therefore, acceleration will be due in the direction of the netforce.

Learn more :https://brainly.com/question/17858024?referrer=searchResults

A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.

Answer:

0.2207

Step-by-step explanation:

Here, we want to find the probability that the sample mean is greater than 25.

What we use here is the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question;

x = 65, mean = 63, SD = 13 and n = 25

Plugging these values in the z-score equation, we have

Z-score = (65-63)/13/√25 = 2/13/5 = 0.77

So the probability we want to calculate is ;

P(z > 0.77)

This can be obtained from the standard normal distribution table

Thus;

P(z > 0.77) = 0.22065 which is 0.2207 to 4 d.p