Original price $60 markup 15%

Answer:

X=-4

Step-by-step explanation:

Answer:

x = -4

Step-by-step explanation:

-8x+4=36

          -4

-8x     =32

/-8       /-8

  x      = -4

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

about 340,000

Step-by-step explanation:

In 10 years, the population dropped to 0.88 of what it was in 2010. At the same rate, in 20 more years, it will drop to 0.88² of what it was in 2020:

2040 population = 440,000·0.88² ≈ 340,000

Answer:

Area of triangle = 6 in^2

Step-by-step explanation:

We need to find the area of triangle. The formula used is:

Area of triangle = 1/2 * b*h

where b=base and h= height

In the given question, b =2 and h= 6

Putting values in the formula:

Area of triangle = 1/2 *2*6

                          = 12/2

                          =  6 in^2

Answer:

The area is 6 in^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a negative x^2 quadratic.  I'm not sure if there's anything else you need.

A. His solution is accurate

You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x

Charles' solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]

Taking common as (1/3)x

[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]

The above expression is similar to Charles factor's of expression.

Thus, Charles solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

Learn more about the expression here:

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The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.

Volume of cone = 3.14 x 7^2 x 12/3

Volume of cone = 3.14 x 49 x 4

Volume of cone = 615.44 cubic inches.

The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)

Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)

= 1/2 x 4/3 x 3.14 x 343

= 718.01 cubic inches.

Total volume = 615.44 + 718.01 = 1333.45 cubic inches.

Rounded to the nearest tenth = 1,333.5 cubic inches.

Hello there!

Answer:

$24

Step-by-step explanation:

In order to find the answer to your problem, we're going to need to find out how much ONE liter of paint costs.

Lets gather the information of what we know:

2 1/2 liters of paint

↑ Cost $60.

With the information we know, we can solve to find the answer.

In order to get the answer, we would need to divide 60 by 2 1/2 (or 2.5). We would need to do this because when we divide it, it would allow us to get the cost for 1 liter.

Lets solve:

[tex]60 \div 2.5=24[/tex]

When you divide, you should get the answer of 24.

This means that one liter of paint cost $24.

$24 should be your FINAL answer.

Answer:

$24/liter

Step-by-step explanation:

Write the the dollar amount first and the paint volume second in this ratio:

 $60.00

--------------- = $24/liter

2.5 liters

Answer:

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

Step-by-step explanation:

* Lets explain how to solve the problem

- We need to find the product of the monomials (8x 6y)² and

   [tex]x^{3}y^{4}[/tex]

- At first lets solve the power of the first monomial

- Because the power 2 is on the bracket then each element inside the

  bracket will take power 2

∵ (8x 6y)² = (8)²(x)²(6)²(y)²

∵ (8)² = 64

∵ (x)² = x²

∵ (6)² = 36

∵ (y)² = y²

∴ (8x 6y)² = [64x² × 36y²]

∵ 64 × 36 = 2304 x²y²

∴ The first monomial is 2304 x²y²

∵ The first monomial is 2304 x²y²

∵ The second monomial is [tex]x^{3}y^{4}[/tex]

- Lets find their product

- Remember in multiplication if two terms have same bases then we

  will add their powers

∵ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] =

   2304 [ [tex]x^{2}*x^{3}[/tex] ] [ [tex]y^{2}*y^{4}[/tex] ]

∵ [tex]x^{2}*x^{3}[/tex] = [tex]x^{2+3}[/tex] = [tex]x^{5}[/tex]

∵ [tex]y^{2}*y^{4}[/tex] = [tex]y^{2+4}[/tex] = [tex]y^{6}[/tex]

∴ [2304 x²y²] × [ [tex]x^{3}y^{4}[/tex] ] = 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

The product of the monomials is 2304 [tex]x^{5}[/tex][tex]y^{6}[/tex]

Answer:

The son's age is 10 and the daughter's age is 5 now

Step-by-step explanation:

Let

x-----> the son's age now

y----> the daughter's age now

we know that

x=2y ----> equation A

(x+15)+(y+15)+(40+15)=100

x+y+85=100

x+y=15 -----> equation B

Substitute equation A in equation B and solve for y

2y+y=15

3y=15

y=5 years

Find the value of x

x=2(5)=10 years

therefore

The son's age is 10.

The daughter's age is 5

Answer:

Step-by-step explanation:

When an angle is bisected the opposite sides and the sides of the bisected angle are in a set ratio.

That translates into

(x + 8)/10 = (2x - 5)/14            Cross multiply

14* (x + 8) = 10* (2x - 5)          Remove the brackets on both sides.

14x + 112 = 20x - 50               Subtract 14x from both sides.

112 = 20x - 14x - 50                Combine

112 = 6x - 50                           Add 50 to both sides.

112+50 = 6x - 50 + 50             Combine

162 = 6x                                   Switch

6x = 162                                   Divide by 6

x = 27

11) Factors of 55 are 1,5,11,55 Factors of 75 are 1,3,5,15,25,75

The greatest common factor is 5.

12) With algebraic expressions you just simplify and multiplier in the simplification is the greatest common factor.

66yx + 30x^2y --) 6yx( 11 + 5x ) so the greatest common factor is 6yx.

13) 60y + 56x^2 --) 4( 15y + 14x^2 ) so the greatest common factor is 4.

14) 36xy^3 + 24y^2 --) 12y^2( 3xy + 2 ) so the greatest common factor is 12y^2.

15) 18y^2 + 54y^2 --) 18y^2( 1 + 3 ) so the greatest common factor is 18y^2.

16) 80x^3 + 30yx^2 --) 10x^2( 8x + 3y ) so the greatest common factor is 10x^2.

17) 105x + 30yx + 75x --) 15x( 7 + 2y + 5 ) so the greatest common factor is 15x.

18) 140n + 140m^2 + 80m --) 20( 7n + 7m^2 + 4m ) so the greatest common factor is 20.

If you want a further explanation step by step just ask :)

ANSWER

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

EXPLANATION

The recursive formula is given as:

[tex]a_n= \frac{1}{3} a_{n-1}[/tex]

where

[tex]a_1=2[/tex]

The explicit rule is given by:

[tex]a_n=a_1 {r}^{n-1}[/tex]

From the recursive rule , we have

[tex]r = \frac{1}{3} [/tex]

We substitute the known values into the formula to get;

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Therefore, the explicit rule is:

[tex]a_n=2{( \frac{1}{3}) }^{n-1}[/tex]

Rewrite [tex]f[/tex] as

[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]

and recall that for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],

[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]

Then the radius of convergence is 2.

The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula  ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.

Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.

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Answer:

a=16

Step-by-step explanation:

Given

(y-4)(y^2+4y+16)

To find the value of a in the resulting polynomial we have to solve the given expression

=y(y^2+4y+16)-4(y^2+4y+16)

= y^3+4y^2+16y-4y^2-16y-64

To find the value of a, both the polynomials will be compared

y^3+4y^2+16y-4y^2-16y-64  

y^3+4y^2+ay-4y^2-ay-64

Comparing the coefficients of both polynomials gives us that

a=16

So, the value of a is 16 ..  

Answer:

(0,3) and (3,0)

Step-by-step explanation:

The first thing to do is graph the two equations to see where they intersect. Then you know what answer to look for. The graph is below. It was done on desmos.

I take it the first equation is a typo and should be y = x^2 - 4x + 3

Equate the two equations.

-x + 3 = x^2 -4x + 3    Subtract 3 from both sides

-x = x^2 - 4x + 3-3

-x = x^2 - 4x                Add x to both sides.

0 = x^2 - 4x + x

0 = x^2 - 3x                Factor

0 = x(x - 3)

So x can equal 0

or x can equal 3

In either case the right side will reduce to 0.

Case 1. x = 0

y= - x + 3

y = 0 + 3

y = 3

So the point is (0,3)

Case 2. x = 3

y = - x + 3

y = - 3 + 3

y = 0

So the point is (3,0)

Answer:

[tex]6\frac{7}{9}[/tex]

Step-by-step explanation:

[tex]6\frac{2}{3}+\frac{1}{9} = 6\frac{6}{9}+\frac{1}{9}=6 \frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

its D

Answer:

[tex]\large\boxed{(2x+3)(4x^2-6x+9)}[/tex]

Step-by-step explanation:

[tex]8=2^3\\\\8x^3=2^3x^3=(2x)^3\\\\27=3^3\\\\8x^3+27=(2x)^3+3^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+3)\bigg((2x)^2-(2x)(3)+3^2\bigg)=(2x+3)(4x^2-6x+9)[/tex]

Answer:

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

Step-by-step explanation:

We know that the equation is

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

We can then plug -1 in for x

[tex]f(-1)=-4(-1)^3+2(-1)^2-1\\\\f(-1)=-4(-1)+2(1)-1\\\\f(-1)=4+2-1\\\\f(-1)=5[/tex]

ANSWER

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

EXPLANATION

The given function is

[tex]f(x) = - 4 {x}^{3} + 2 {x}^{2} - 1[/tex]

We substitute x=-1 to obtain:

[tex]f( - 1) = - 4 {( - 1)}^{3} + 2 {( - 1)}^{2} - 1[/tex]

We simplify to obtain;

[tex]f( - 1) = 4 + 2 - 1[/tex]

.

This evaluates to

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

Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.

In your case, we have to substitute "x" with "a+h":

[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer:

1 5/12 inches.

Step-by-step explanation:

That is 3 1/6 - 1 3/4

= 19/6 - 7/4

The lowest common denominator of 4 and 6 is 12, so we have:

38/12 - 21/12

= 17 /12

= 1 5/12 inches (answer).

The remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

The correct option is (a).

find out how much string is left when [tex]\(1 \frac{3}{4}\)[/tex] inches are cut from a piece initially measuring[tex]\(3 \frac{1}{16}\)[/tex]inches.

1. Convert the mixed numbers to improper fractions:

[tex]- \(1 \frac{3}{4}\) inches = \(\frac{7}{4}\) inches[/tex]

[tex]- \(3 \frac{1}{16}\) inches = \(\frac{49}{16}\) inches[/tex]

2. Make the denominators equal:

  - Multiply the numerator and denominator of [tex]\(\frac{7}{4}\)[/tex]by 16 to make the denominators equal:

[tex]\(\frac{7}{4} = \frac{112}{64}\)[/tex]

  - Now we have:

    - Initial length = [tex]\(\frac{49}{16}\)[/tex] inches

    - Cut length = [tex]\(\frac{112}{64}\)[/tex] inches

3. Subtract the two fractions:

  - Subtract the cut length from the initial length:

[tex]\(\frac{49}{16} - \frac{112}{64}\)[/tex]

  - To subtract, we need a common denominator. The least common multiple (LCM) of 16 and 64 is 64.

 - Convert both fractions to have a denominator of 64:

[tex]\(\frac{49}{16} = \frac{196}{64}\)[/tex]

[tex]\(\frac{112}{64}\) remains the same.[/tex]

- Subtract the numerators:

   [tex]\(\frac{196}{64} - \frac{112}{64} = \frac{84}{64}\)[/tex]

4. Simplify the result:

  - Divide both the numerator and denominator by their greatest common factor (GCF), which is 4:

[tex]\(\frac{84}{64} = \frac{21}{16}\)[/tex]

5. Convert back to a mixed number:

  - Divide the numerator by the denominator:

[tex]\(\frac{21}{16} = 1 \frac{5}{16}\)[/tex]

Therefore, the remaining string length after cutting [tex]\(1 \frac{3}{4}\)[/tex] inches is [tex](1 \frac{5}{16}\)[/tex]inches.

[tex]5 \div 100 \times 399 \times 1 = 19.95 \: and \: 4 \div 100 \times 399 \times 1 = 15.96[/tex]

Answer:178

Step-by-step explanation: I took the test :)

Answer:

The mass of the container is 178 kg.

Step-by-step explanation:

Since, the volume of a cylinder is,

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

Where r is the radius of the cylinder

And, h is its height

Here, r = 0.2 meters,

h = 1 meter,

So, the volume of the cylindrical container is,

[tex]V=\pi (0.2)^2(1)[/tex]

[tex]=3.14\times 0.04=0.1256\text{ cubic meters}[/tex]

Now,

[tex]Density = \frac{Mass}{Volume}[/tex]

[tex]\implies Mass = Density\times Volume[/tex]

Given, Density of the container = 1417 kg/m³,

By substituting the values in the above formula,

[tex]\text{Mass of the container}=1417\times 0.1256=177.9752\text{ kg}\approx 178\text{ kg}[/tex]

Answer:

  x = (4r +3)/(r +2)

Step-by-step explanation:

Collect x terms, then divide by the coefficient of x.

  x(r +2) = 4r +3

  x = (4r +3)/(r +2)

Answer:

B. 1/10 or 0.10

Step-by-step explanation:

The question asks what's the probability that a student picked randomly will be playing both basketball and soccer.

The answer is right in the diagram.

We have only one student who plays both basketball and soccer: Ella

Since we have 10 students in the selected group, the probably you'll pick Ella is:

1 / 10 = 0.10 = 10%

So, the answer is B.

The value of P(A/B) is 0.33.

Given that, the Venn diagram shows sports played by 10 students.

P(A/B) is known as conditional probability and it means the probability of event A that depends on another event B. It is also known as "the probability of A given B". The formula for P(A/B)=P(A∩B) / P(B).

Now, P(A/B)=1/3≈0.33

Therefore, the value of P(A/B) is 0.33.

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1. 10^5

2. z^5*x^3*y^2

3. 1

Answer:

x = 20

Step-by-step explanation:

Formula

x1/x2 = x3/x4

Givens

x = 11

x2 = 11 + 121 = 132

x3 = 10

x4 = 10 + 5x + 10

Solution

11/132 = 10 / (5x + 10 + 10)        Combine

11/132 = 10/(5x + 20)                Cross multiply

11*(5x + 20) = 132 * 10              Combine on the right.

11(5x + 20 ) = 1320                   Divide by 11. (You could remove the brackets, but this is easier.

11(5x + 20)/11 = 1320/11            Do the division

5x + 20 = 120                          Subtract 20 from both sides

5x + 20-20 = 120 - 20             Combine

5x = 100                                   Divide by 5

5x/5 = 100/5

x = 20

[tex]\bf \textit{Pythagorean Identities}\\\\ 1+tan^2(\theta)=sec^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sec^2(\theta )cos^2(\theta )+tan^2(\theta )\implies \cfrac{1}{\begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }\cdot \begin{matrix} cos^2(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} +tan^2(\theta ) \\\\\\ 1+tan^2(\theta )\implies sec^2(\theta )[/tex]

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

[tex]at ^ 2 + bt + c[/tex]

So

the t coordinate of the vertice is:

[tex]t =-\frac{b}{2a}[/tex]

In this case the equation is:

[tex]h(t)=72t-16t^2[/tex]

So

[tex]a=-16\\b=72\\c=0[/tex]

Therefore

[tex]t =-\frac{72}{2(-16)}[/tex]

[tex]t=2.25\ s[/tex]

Finally the maximum height that the ball will reach is

[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]

[tex]h=81\ ft[/tex]

The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.

To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.

So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.

To find out the maximum height, we just need to substitute this value of t into the equation for h(t):

h(2.25)=72*2.25-16*2.25^2

The above calculation gives a maximum height of 81 feet.

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ANSWER

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

[tex]\sec( \theta) = \frac{17}{8} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

EXPLANATION

From the Pythagoras Theorem, the hypotenuse can be found.

[tex] {h}^{2} = 1 {5}^{2} + {8}^{2} [/tex]

[tex] {h}^{2} = 289[/tex]

[tex]h = \sqrt{289} [/tex]

[tex]h = 17[/tex]

The sine ratio is negative in the fourth quadrant.

[tex] \sin( \theta) = - \frac{opposite}{hypotenuse} [/tex]

[tex]\sin( \theta) = - \frac{15}{17} [/tex]

The cosecant ratio is the reciprocal of the sine ratio.

[tex]\csc( \theta) = - \frac{17}{15} [/tex]

The cosine ratio is positive in the fourth quadrant.

[tex]\cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos( \theta) = \frac{8}{17} [/tex]

The secant ratio is the reciprocal of the cosine ratio.

[tex]\sec( \theta) = \frac{17}{8} [/tex]

The tangent ratio is negative in the fourth quadrant.

[tex]\tan( \theta) = - \frac{opposite}{adjacent} [/tex]

[tex]\tan( \theta) = - \frac{15}{8} [/tex]

The reciprocal of the tangent ratio is the cotangent ratio

[tex]\cot( \theta) = - \frac{8}{15} [/tex]

Answer:

sin=-15/17

cos=8/7

tan=-15/8

csc=-17/15

sec=17/8

cot=-8/15