A small company's net income for the first months of the year was $76,500 and for the last six months it was $100,000. What is the ratio of the first six months of the year to the last six months of the year ?

Answer:

? = 5.12

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin B = opp/ hyp

sin 65= 5/ ?

? = 5/ sin 65

? =5.516889595

To the nearest hundredth

? = 5.12

Answer:

[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]

Step-by-step explanation:

You have the following polynomial:

[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}[/tex]          (1)

In order to obtain the factors of the previous polynomial, first you can multiply the polynomial for 125 to obtain only integer coefficients, but also you have to divide for 125, as follow:

[tex](8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125})\frac{125}{125}\\\\=\frac{1000p^2-300p^2+30p-1}{125}[/tex]  

[tex]=\frac{700p^2+30p-1}{125}[/tex]            (2)

Next, you use the quadratic formula to get the factors of the numerator of the previous expression:

[tex]p_{1,2}=\frac{-30\pm\sqrt{(30)^2-4(700)(-1)}}{2(700)}\\\\p_{1,2}=\frac{-30\pm 80}{1400}\\\\p_1=-\frac{11}{140}\\\\p_2=-\frac{1}{28}[/tex]

The factors are (p-p1) and (p-p2), then you have in the equation (2) the following factorization:

[tex]8p^2-\frac{12}{5}p^2+\frac{6}{25}p-\frac{1}{125}=\frac{(p+\frac{11}{140})(p+\frac{1}{125})}{125}[/tex]

Answer:

Substitute 3x - 5 for y in the second equation.

Step-by-step explanation:

Generally, to solve the system of linear equations of x and y, the first step would be trying to eliminate x (or y).

Then turn the system into the equation of only y (or x).

Next, try to solve for y (or x).

Then substitute the solved y (or x) into the original system to work out x (or y).

**********

3 options (1 addition, 2 subtractions) do not eliminate x or y (x and y still exist after manipulation).

=> Remaining option relating substitution would be a reasonable choice.

Answer:

D

Step-by-step explanation:

you can put the function in your graphing calculator & the x-intercept is where the line crosses threw the line that goes left & right vise versa for the y-intercept.

Answer:

20%

Step-by-step explanation:

25%+(35%)+(20%)=80%

100-80=20%

Answer:

h = 2s

Step-by-step explanation:

Area of square is equal to the area of triangle in this question.

the area of the square is s²

the area of the triangle is [tex]\frac{1}{2}[/tex] *h*s

s²=  [tex]\frac{1}{2}[/tex] *h*s

s = [tex]\frac{1}{2}[/tex] *h

2s = h

hope that helps

Answer:

The answer is given below

Step-by-step explanation:

The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:

[tex]f(t)=\frac{3}{2}t[/tex]

When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:

[tex]g(t)=3-\frac{3}{2}t[/tex]

a)

[tex]f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles[/tex]

[tex]g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\[/tex]

b)

[tex]h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3[/tex]

c)

According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0

[tex]h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3[/tex]

This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0

Answer:

4

Step-by-step explanation:

There are 5 points. So there are 4 segments. The segments are the line between two points.

Answer:

B

Step-by-step explanation:

The y-intercept (or initial value) is 3 which means the coefficient of the exponential term is 3. The only answer choice that follows this is choice B.

Answer:

4x-3

Step-by-step explanation:

9+4x-12

9-12 = -3

4x-3

Answer:

4x - 3

Step-by-step explanation:

You can first take out 9 and solve for 4 (x - 3) which is 4x - 12. Now, you can put 9 back into the equation so it will be 9 + 4x - 12. We can simplify a bit further which will give us 4x - 3.

Complete Question:

The number of text messages that Reza sent each day so far in this billing cycle is shown on the dot plot.

Which statement must be true according to the dot plot?

A) The data is symmetric and shows that he typically sent about 6 to 8 text messages per day.

B) The data is symmetric and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts.

C) The data is skewed and shows that he typically sent about 6 to 8 text messages per day.

D) The data is skewed and shows that he sent 11 or 12 texts with the same frequency that he sent 1 or 2 texts

*Check attachment for the dot plot referred to

Answer:

A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day

Step-by-step explanation:

Taking a look at the dot plot given in the attachment below, we can observe that most of the data set are concentrated in the middle of the dot plot than both ends of the dot plot. With this, we can infer that the distribution of the data is symmetric.

The dot plot also tells us that, 6 and 8 text messages have more frequency than any other data set on the dot plot. This also suggests that Reza usually sends 6 to 8 messages in a day.

Therefore, the statement that is true about the dot plot is:

"A. The data is symmetric and shows that he typically sent about 6 to 8 text messages per day"

Answer:

A

Step-by-step explanation:

Answer:

She found 19 pennies and 21 dimes

Step-by-step explanation:

Let the number of dimes present be d and the number of pennies present be p

From the question, the total of both is 40

Mathematically;

p + d = 40 •••••••(i)

While a penny worths 1 cent, a dime is worth 10 cents

Total penny amount would be 1 * p = p cents

While total dime amount would be 10 * d = 10d cents

Before we add both to give the total amount, let’s convert this total amount to cents and that would be 2.29 * 100 = 229 cents

So mathematically;

p + 10d = 229 •••••••(ii)

So let’s solve both equations simultaneously

From i) p = 40 - d

let’s put this into equation ii

40 - d + 10d = 229

40 + 9d = 229

9d = 229-40

9d = 189

d = 189/9

d = 21

Recall;

P = 40-d

P = 40-21

P = 19

Answer:

djal3924+3820&282039392#283830818385

Answer: Account 2

Step-by-step explanation:

Account 1)

Formula for CI

Amount = p(1 + r/n)^nt

A = 2500 (1 + .06/4)^4x10

A = 2500 (1 + 0.015)^40

A = 2500 (1.015)^40

A = 4535.05

Account 2.

Formula for CI for interest compounded continously

A = Pe^rt

A = 2500 x e^0.06 x 10

A = 2500 x e^0.6

A = 2500e^3/5

A = 4555.297

Account 2 should you choose to obtain the greater amount in 10 years.

You invest $2500 in an account to save for college. Account 1 pays 6% annual interest compounded quarterly. Account 2 pays 4% annual interest compounded continuously.

For Account 1

[tex]Amount = p(1 + r\div n)^{nt}\\\\A = 2500 (1 + .06\div 4)^4\times 10\\\\A = 2500 (1 + 0.015)^{40}\\\\A = 2500 (1.015)^{40}[/tex]

A = 4535.05

For Account 2:

A = Pe^rt

[tex]A = 2500 \times e^0.06 \times 10\\\\A = 2500 \times e^0.6\\\\A = 2500e^3/5[/tex]

A = 4555.297

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Answer:

Multiply the area of the base by the height and divide by 3.

Step-by-step explanation:

V = (1/3)Bh

where B = area of the base, and

h = height

Answer: Multiply the area of the base by the height and divide by 3.

Answer:

We khow that the volume of a pyramid is equal the product of the base and the height over 3

So he just needs to multiply them together then divide the result by 3

Answer:

                x₁ = -3√2 ,   x₂ = 3√2  

Step-by-step explanation:

x² = 18     ⇔    x = √18    or   x= -√18

√18 = √[9•2] = √9•√2 = 3•√2 = 3√2

Answer:

x₁ = -3√2

x₂ = 3√2

Step-by-step explanation:

x² = 18

x ± 3√2

x = -3√2

x = 3√2

Hope this helped! :)

Answer:

59.65

Step-by-step explanation:

2 decimal places is to the hundredths place.

Answer: 59.65

Step-by-step explanation: When rounding a number to a given place, look at the next place y o the right. If that digit is 5 or more, "round up" by adding one to the given place.

If the number to the right is 4 or less, leave the given place "as is"

In this example, the hundredths place is 4, the place to the right has an 8. So you round up the 4 to a 5. You end up with 59.65

Answer:

Hiya, Need more explanation, and since you seem to be talking of a graph, maybe provide a picture of the graph

Thanks

40% is kept for the running of the business.

Multiply the profit by 40%

1,350,000 x 0.40 = 540,000

The amount kept for the business is 540,000

Answer:

4021 cm^3

Step-by-step explanation:

The volume of a cylinder can be found using the following formula.

[tex]V=\pi r^2h[/tex]

where r is the radius and h is the height.

We know the cylinder has a height of 20 centimeters and a diameter of 8 centimeters.

h= 20 cm

d= 8 cm

Substitute these values into the formula.

[tex]V=\pi (8 cm^2) * 20 cm[/tex]

First, evaluate the exponent.

8 cm^2= 8 cm * 8 cm= 64 cm

[tex]V=\pi * 64 cm^2*20 cm[/tex]

Multiply 64 cm^2 and 20 cm

[tex]V=\pi *1280 cm^3[/tex]

Multiply 1280 cm^3 and pi

[tex]V=4021.2386 cm^3[/tex]

Round to the nearest cubic centimeter. The 2 in the tenth place tells us to leave the number as is.

[tex]V= 4,021 cm^3[/tex]

The volume is about 4,021 centimeters^3.

The approximate volume of the tube is 1005 cm³.

A cylinder is a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.

Given that a cardboard cylinder has a diameter of 8 centimeters and a height of 20 centimeters, we need to find the volume of the cylinder,

The volume of the cylinder = π × radius² × height

Radius = diameter / 2 = 8/2 = 4 cm

Therefore,

Volume = π × radius² × height

= 3.14 × 4² × 20

= 3.14 × 16 × 20

= 1004.8 ≈ 1005

Hence, the approximate volume of the tube is 1005 cm³.

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Answer: 82,020.997

Step-by-step explanation:

Answer:

N = 43.2

F = 129.6

Total books = F + N = 129.6 + 43.2 = 172.8

Please note that number of books cannot be in fraction, there is some mistake in formulating the question!

But nevertheless, the key concept here is to learn how to set up such algebraic equations.

Step-by-step explanation:

Let F denotes fiction book

Let N denotes non-fiction book

There are 3 times as many fiction books as non-fiction in a library.

Mathematically,

F = 3N          eq. 1

120 fiction books are loaned out and 24 non-fiction books

Mathematically,

F - 120 = remaining fiction books  

N - 24 =  remaining non-fiction books  

There are now twice as many fiction books as non-fiction.

Mathematically,

2(remaining fiction books) = (remaining non-fiction books)

2(F - 120) = (N - 24)         eq. 2

Substitute eq. 1 into eq. 2

2(3N - 120) = (N - 24)

Simplify the equation,

6N - 240 = N - 24

6N - N = 240 - 24

5N = 216

N = 216/5

N = 43.2

Please note that number of books cannot be in fraction, there is some mistake in formulating the question!

But nevertheless, the key concept here is to learn how to set up such algebraic equations.

So back to the problem.

F = 3N

F = 3(43.2)

F = 129.6

So the total books in the library are

Total books = fiction + non-fiction

Total books = F + N = 129.6 + 43.2 = 172.8

Answer:

F=3N

F-120 = Remaining fiction

N-24 = remaining Non fiction

F=2N

2(F-120)=N-24

2(2N-120)=N-24

4N-240 = N-24

3N=216

N=72

from Eq 1

F=3N

F=3(72)

F=216

total = F+N

total = 216 + 72

total = 288

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

6(2x-3)=-(x-9)+4x (Distributive property)

12x-18=-x+9+4x

12x-4x+x=9+18 (Collecting like terms)

9x=27 (Division)

x=3

Hope I am correct :)

Answer:

Option D is the correct option.

Step-by-step explanation:

6 ( 2x - 3 ) = - ( X - 9 ) + 4x

Distribute 6 through the parantheses

12x - 18 = - ( X - 9) + 4x

When there is a (-) in front of an expression in parantheses, change the sign of each term in the expression

12x - 18 = -x + 9 + 4x

Collect like terms

12x - 18 = 3x + 9

Move variable to Left hand side and change its sign

12x - 3x - 18 = 9

Move constant to Right hand side and change its sign

12x - 3x = 9 + 18

collect like term

9x = 9 + 18

Add the numbers

9x = 27

Divide both sides of the equation by 9

9x /9 = 27/ 9

Calculate

X = 3

Hope this helps....

Good luck on your assignment...

Answer:

Solution,

[tex] {(2x)}^{3} - 8 \\ [/tex]

[tex]( {2x)}^{3} - {(2)}^{3} [/tex]

Use the formula:

[tex] {a}^{3} - {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )[/tex]

now,

[tex](2x + 2)( {(2x)}^{2} - 2x \times 2 + {(2)}^{2} )[/tex]

[tex](2x + 2)( {4x}^{2} - 4x + 4)[/tex]

Hope this helps...

Good luck on your assignment...

Answer:

[tex]\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]

Step-by-step explanation:

Given that

[tex]x^2+y^2=2cy----(1)[/tex]

Now by differentiating the above equation with respect to x

[tex]2\times x+2\times y\times \dfrac{dy}{dx}=2\times c\times \dfrac{dy}{dx}[/tex]

[tex]x+ y\times \dfrac{dy}{dx}= c\times \dfrac{dy}{dx}-----(2)[/tex]

Form the above equation (1)

[tex]c=\dfrac{x^2+y^2}{2\times y}[/tex]

Putting the value of c in the equation (2)

[tex]x+ y\times \dfrac{dy}{dx}= \dfrac{x^2+y^2}{2\times y}\times \dfrac{dy}{dx}\\\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]

Thus the differential equation of the given curve will be

[tex]\dfrac{dy}{dx}\left ( \dfrac{x^2+y^2}{2\times y}-y \right )=x[/tex]

Curve for different value of c :

x² +y² = 2 c y

The above equation is an equation of a circle.That circle is having center on the y-axis.

Answer:

a) 896 ways

c) 910 ways

Step-by-step explanation:

The question is a combination problem since it has to do with selection. In combination, if r object is selected from a pool of n objects, this can be done in nCr ways.

nCr = n!/(n-r)!r!

If from a group of 8 women and 6 men, a committee consisting of 3 men and 3 women is to be formed, we need to first calculate the total committee formed without any condition.

8C3 × 6C3

= 8!/5!3! × 6!/3!3!

= 8×7×6×5!/5!×6 × 6×5×4×3!/3!×6

= 56×20

= 1120ways

Now if;

a) two of the men refuse to serve together.

Since two men refuse to serve together, we will select 1 man from remaining 4 men since two has already been selected then select 3 from 8 women as shown.

4C1×8C3

= 4×56

= 224ways

Number of ways this can be done will be 1120-224 = 896ways

b) 1 man and 1 woman refuse to serve together

We need to choose 2 men from remaining 5 and 2 women from the rest of the men which is 7 as shown:

= (8-1)C(3-1) × (6-1)C(3-1)

= 7C2 × 5C2

= 7!/5!2! × 5!/3!2!

= 7×6×5!/5!×2 × 5×4×3!/3!×2

= 21×10

= 210ways

The number of ways this can be done will be 1120-210 = 910ways

Answer:

7.5

Step-by-step explanation:

given:

3/4 = x/10    (multiply both sides by 10)

(3/4)(10) = x

x = 30/4

x = 7.5

The value of x is 7.5

Given:

The proportion 3/4 = x/10

3/4 = x/10

30 = 4x

30/4 = x

7.5 = x

Therefore, the final answer is 7.5.

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Answer:

yes it can form an isosceles triangle. when you join these lines AC will be the base and BC andAB will be two equal sides of an isosceles triangle.

Answer:

True i think

Step-by-step explanation:

tell me if you got it right. (btw switch to chrome its faster)

Answer:

R0,180(x,y)->(-x,-y)

Step-by-step explanation:

R0,180(x,y)->(-x,-y)

We note that

X(-2,2) has been transformed to X'(2,-2), and

Y(1,2) has been transformed to Y'(-1.-2)

[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex] are the choice that's description can be defined as follows:

Therefore, the final choice are "[tex]\bold{R_0,\ 180^{\circ}}\ \ and \ \ \bold{(x,y)\longrightarrow (-x,-y)}[/tex]".

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