Find x.
60°
45°
6
—————

Answer:

x = 3

Step-by-step explanation:

This process is called cross multiplication.

Multiply 6 · 4 = 24

Divide 24 ÷ 8 = 3

x = 3

Answer:

x = 3

Step-by-step explanation:

x/4 = 6/8

Using cross products

x*8 = 4*6

8x = 24

Divide by 8

8x/8 = 24/8

x = 3

Answer:

h = 5 cm

Step-by-step explanation:

Given that,

The volume of ice-cream in the cone is half the volume of the cone.

Volume of cone is given by :

[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]

r is radius of cone, r = 3 cm

h is height of cone, h = 6 cm

So,

[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]

Let [tex]V_i[/tex] is the volume of icecream in the cone. So,

[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]

Let H be the depth of the icecream.

Two triangles formed by the cone and the icecream will be similiar. SO,

[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]

So, volume of icecream in the cone is :

[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]

or

h = 5 cm

So, the depth of the ice-cream is 5 cm.

Answer:

Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.

Answer:

Mean= 242.5 pounds

Median= 236 pounds

Mode= 208 and 278 pounds

Range=117 pounds

Mid-range= 58.5 pounds

B. The results are likely to be representative because a championship team is most likely representative of the entire league.

Step-by-step explanation:

278 303 186 292  276 205 208 236 278 198 208

Arranged in ascending order is

186 198 205 208 208 236 276 278 278 292 303

Mean = (186 +198+ 205+ 208 +208 +236 + 276+ 278 +278+ 292 +303)/11

Mean =2668/11

Mean= 242.5 pounds

Median = the middle number

Median= 236 pounds

Mode = highest occuring number(s)

Mode= 208 and 278 pounds

Range= highest number- smallest number

Range=303-186

Range=117 pounds

Mid-range= range/2

Mid-range= 117/2

Mid-range= 58.5 pounds

Answer:

$198

Step-by-step explanation:

198x.07=13.86

198+13.86=211.86

Answer:

Mark me brainlist please please please please

Answer:

Step-by-step explanation:

Answer:

[tex]\boxed{ (x - 2)(x - 7)}[/tex]

Step-by-step explanation:

Hey there!

To factor,

[tex]x^2-7x+10[/tex]

We need 2 numbers that multiply to get 10 and add to get -7 which is,

-2 and -5.

-2*-5 = 10

-2x + -5x = -7x

x*x=x^2

Factored - (x - 2)(x - 7)

Hope this helps :)

Answer:  [tex]\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Step-by-step explanation:

[tex]n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2[/tex]

Answer:

3m = -3

Step-by-step explanation:

2m−6=8m

Subtract 2m from each side

2m−6-2m=8m-2m

-6 = 6m

Divide by 6

-6/6 = 6m/6

-1 = m

3m = 3(-1) = -3

2m - 6 = 8m

2m - 8m = 6

-6m = 6

m = -6/6

m = -1

9514 1404 393

Answer:

  b. y = f(x -3)

Step-by-step explanation:

The translation right h and up k units is ...

  y -k = f(x -h)

Here, the red graph is translated right 3 and up 0, so the translated function is ...

  y = f(x -3)

_____

Additional comment

You can check this if you like by listing a couple of corresponding points:

  y = f(x)

  1 = f(-3) . . . . left-most point on black graph.

The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...

  1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)

Answer:

3(x+8)=4+x

distribute the 3 by multiplying it with the x and the 8

3x+24=4+x

subtract x from both sides

2x+24=4

subtract 24 from both sides

2x=4-24

2x=-20

divide each side by 2

leaving the variable isolated

x=-10

Step-by-step explanation:

It is important to balance each side by doing the same to both sides such as at the end divide both sides by 2.

The unknown number will be equal to 10.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that three times, the sum of a number and eight is four more than the number.

The equation will be written as,

3(x+8)=4+x

Distribute the 3 by multiplying it with the x and the 8,

3x+24=4+x

Subtract x from both sides,

2x+24=4

Subtract 24 from both sides,

2x=4-24

2x=-20

Divide each side by 2.

x=-10

Therefore, the unknown number will be equal to 10.

To know more about an expression follow

https://brainly.com/question/25968875

#SPJ2

Answer :

1

Step-by-step-explanation :

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

[tex]{x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1[/tex]

Answer:

(x+1)  •  (x-5)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  -5  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -5 = -5  

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -4 .

     -5    +    1    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  1  

                    x2 - 5x + 1x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-5)

             Add up the last 2 terms, pulling out common factors :

                    1 • (x-5)

Step-5 : Add up the four terms of step 4 :

                   (x+1)  •  (x-5)

Answers:

First bottle's unit cost = 27 cents per oz

Second bottle's unit cost = 27 cents per oz

Both have the same unit cost.

----------------------------------------

Work Shown:

unit cost = price/(number of ounces)

1st bottle unit cost = (1.35)/(5) = 0.27 dollars per oz = 27 cents per oz

2nd bottle unit cost = (2.16)/(8) = 0.27 dollars per oz = 27 cents per oz

Both lead to the same unit cost. Therefore, you can pick either option and it doesn't matter.

Step-by-step explanation:

To find this inverse of a graph you have to multiply the current equation by -1.

-1(2x-3)

f(x)=-2x+3.

This graph will start at the point (0,3). Then according to the slope the rest of the points will go down two than right one. So the next two point will be (1,1) and (2,-1).

9514 1404 393

Answer:

  $2150

Step-by-step explanation:

The tax is 7.5% of the price, so is ...

  $2000 × 0.075 = $150

The total cost is the price with tax added:

  $2000 +150 = $2150

Answer:

B

Step-by-step explanation:

X must not be equal to -6, -1, 1 or 3

Step-by-step explanation:

let , MP =x

then,

discount amount =D% of MP

= (20/100)× x

= 0.2x

now,Sp without VAT = MP-D

=x - 0.2x

= 0.8x

NoW, SP with VAT = Sp without VAT+ VAT %of SP

or ,6328 = 0.8x + 13% of 0.8x

or, 6328 = 0.8x + (13/100) × 0.8x

or, 6328= 0.8x + 0.104x

or,. 6328= 0.904x

or, X= 6328/0.904

X= 7000 Rs.

Hence ,MP is Rs.7000

Answer:

Step-by-step explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]

From the question

a = 15

A = 70°

c = 14

So we have

[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]

[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]

[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]

C = 61.288

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

To find b we can use the sine rule

That's

[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]

[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]

[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]

b = 11.9921

Hope this helps you

Answer:

Mean= $21.5067

Median = $15.8

Standard deviation= $19.02

Coefficient of skewness= $0.8991

Step-by-step explanation:

Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8

+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15

Mean =$ 322.6/15

Mean= $21.5067

Median= middle number

Median = $15.8

Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15

Variance=$ 5424.79/15

Variance=$ 361.65

Standard deviation= √ variance

Standard deviation= √361.65

Standard deviation= $19.02

Coefficient of skewness

=3( mean-median)/standard deviation

= 3(21.5-15.8)/19.02

= 3(5.7)/19.02

= 17.1/19.02

Coefficient of skewness= 0.8991

Answer:

Graph 1

Step-by-step explanation:

The only graph that could be possible would be graph 1.

As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.

Answer:

Null Hypothesis: H0:μ ≤ 16.8

Alternative Hypothesis: Ha: μ > 16.8

Step-by-step explanation:

We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.

It means that the past value was not more than 16.8.

This follows that the null hypothesis is given as;

H0:μ ≤ 16.8

And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;

Ha: μ > 16.8

Answer:

A

Step-by-step explanation:

r=10 and the angle bln 5√3 and -5 is 330 or 11π/6

Answer:

154.2

Step-by-step explanation:

143 plus

156 plus

172 plus

133 plus

167 = 771

divide by 5 equals 154.2

Answer:

Step-by-step explanation:

-6x²+26x+20

=-2(3x²-13x-10)

=-2(3x²-15x+2x-10)

=-2[3x(x-5)+2(x-5)]

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

Answer:

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

Answer:

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Step-by-step explanation:

Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as

H0 :p 0.5   against   Ha: p ≠ 0.5

The significance level is approximately 0.05

The test statistic to be used is number of heads x.

Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution

Heads (x)        Probability (X=x)                        Cumulative     Decumulative

0                        1/16384 (1)             0.000061     0.000061

1                         1/16384  (14)         0.00085             0.000911

2                       1/16384 (91)           0.00555             0.006461

3                       1/16384(364)         0.02222

4                       1/16384(1001)         0.0611

5                       1/16384(2002)       0.122188

6                        1/16384(3003)      0.1833

7                         1/16384(3432)      0.2095

8                        1/16384(3003)       0.1833

9                        1/16384(2002)       0.122188

10                       1/16384(1001)        0.0611

11                       1/16384(364)        0.02222

12                      1/16384(91)            0.00555                             0.006461

13                     1/16384(14)              0.00085                           0.000911

14                       1/16384(1)            0.000061                            0.000061

We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If  alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).

We observe that P (X≤2) =   0.006461 > 0.025

and

P ( X≥12 ) = 0.006461 > 0.025

Therefore true significance level is

∝=  P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122

Hence critical region is (X≤0) and ( X≥14)

Computation x= 12

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Answer:

1. The bottom of the ladder is 4 meters away from the wall

2. I'm not sure about this one, someone else answer please :D

Step-by-step explanation:

We can use the Pythagorean Theorem to find how far away the bottom of the ladder is.

The ladder is creating a triangle, with 5 as it's hypotenuse and 3 as one of the left.

[tex]a^2 + 3^2 = 5^2\\a^2 + 9 = 25\\a^2 = 25-9\\a^2 = 16\\a = 4[/tex]

I'm sorry I couldn't answer the second one, but I hope this helped!

Answer:

a.  4m

b. 6m/s

Step-by-step explanation:

wall height = y = 3m

ladder length = L = 5m

distance from bottom of ladder to the wall = x

a.   y² + x² = L²   -----------eq.(1)

     3³ + x² = 5²        

    x = 4 m

b. How fast is the bottom of the ladder sliding away from the wall? = dx/dt

using eq.1  ---- y² + x² = L²

2y (dy/dt) + 2x (dx/dt) = 0

y (dy/dt) + 2 (dx/dt) = 0

we know that (dy/dt) = -8 m/s

3 (-8) + 4 (dx/dt) = 0

dx/dt =  -24 / -4

dx/dt = 6 m/s

Step-by-step explanation:

8 men can do 60 man days of work by dividing 60 man days by the 8 men, which gives us 60/8 = 7 1/2 da

Answer:

Hello,

in order to simplify, i have taken the inverses functions

Step-by-step explanation:

[tex]\int\limits^\frac{1}{2} _{-1} {(-2x^2-x+1)} \, dx \\\\=[\frac{-2x^3}{3} -\frac{x^2}{2} +x]^\frac{1}{2} _{-1}\\\\\\=\dfrac{-2-3+12}{24} -\dfrac{-5}{6} \\\\\boxed{=\dfrac{9}{8} =1.25}\\[/tex]