Find the product
Give your answer in simplest form.
3/5x12

Answer:

[tex]17\sqrt{3}[/tex]

Quiz Results:

The length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

The right angled triangle in which, the angles are of the measure 30, 60 and 90 degrees is called 30-60-90 Special Right Triangle.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

The wider the angle is, the larger the side opposite to is.

For this right angled triangle, the side opposite to 60 degrees angle is larger leg (let it be of x yd), and the side opposite to 30 degrees angle is shorter leg (of 17 yd).

As shown in the image below, using the sine law for non right angles,  we get:

[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b}\\\\\dfrac{\sin(30^\circ)}{17} = \dfrac{\sin(60^\circ)}{x}\\\\x =\dfrac{17 \times \sin(60^\circ)}{\sin(30^\circ)} = 17\sqrt{3} \: \rm yd[/tex]

Thus, the length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

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Answer:

Step-by-step explanation:

According to Pythagoras Theorem,

[tex]{(height)}^{2} + {(base)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] = > {12}^{2} + {5}^{2} = {x}^{2} [/tex]

[tex] = > {x}^{2} = 144 + 25[/tex]

[tex] = > {x}^{2} = 169[/tex]

[tex] = > x = \sqrt{169} [/tex]

=> x = 13 (Ans)

Answer: 73 will be your answer hope this helped

Step-by-step explanation:

Answer:

∠A = 6x + 4

Step-by-step explanation:

Hello There!

We are given the exterior angle ∠ACD and an interior angle ∠B

If you didn't know this is the rule for exterior angles of a triangle:

An exterior angle is equal to the sum of its opposite interior angles

so ∠ACD = ∠A + ∠B ( ∠A and ∠B being the opposite interior angles)

So with the information that we are given we plug them into their corresponding angle

then we would have

8x+5 = ∠A + 2x + 1

now we solve for A

Well how do we solve for A?

Well we have to isolate the variable

To do so we want to get rid of 2x + 1

We do that by subtract each side by 2x and 1

8x + 5 - (2x + 1 ) = 6x + 4

we're left with

∠A = 6x + 4

Answer:

hello

Step-by-step explanation:

yeah

Answer:

F= 42

C= 48

A= 48

B= 132

D= 132

Step-by-step explanation:

Answer: 53 degrees

Step-by-step explanation:

Complementary angles add up to 90 degrees. Subtract Za from the 90. 90-37=53.

Answer:

Solve for  x  in the first equation.

Subtract  8 y  from both sides of the equation.

2 x = 6 − 8 y

5 x + 20 y = 15

Divide each term by  2  and simplify.

Divide each term in  

2 x /2 =  6/2  − 8 y/2  

5 x + 20 y = 15

Cancel the common factor of  2 .

Cancel the common factor.

2 x /2  =  6 /2  + (− 8 y)/ 2

Step-by-step explanation:

I don't have room to put the rest. So go to math-way

Given:

The shape of all building blocks is a cube of side 4 cm.

To find:

The volume of six building blocks.

Solution:

Volume of a cube is:

[tex]V=a^3[/tex]

Where, a is the side length of the cube.

Putting [tex]a=4[/tex], we get

[tex]V=(4)^3[/tex]

[tex]V=64[/tex]

It means the volume of each building block is 64 cubic cm.

Now, the volume of six building blocks is

[tex]Volume=6\times V[/tex]

[tex]Volume=6\times 64[/tex]

[tex]Volume=384[/tex]

Therefore, the volume of six building blocks is 384 cubic cm.

Answer:

A

Step-by-step explanation:

is the circumference or perimeter of a cylinder

d=r×r

Answer:

1) g < -6

2) x < -5

3) f < 2

4) y ≤ -2

5) p ≥ 2

Answer:

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means      

Step-by-step explanation:

Step(i):-

Given that the first sample size 'n₁' = 22

Given that the mean of the first sample x₁⁻ = 120

Given that the standard deviation of the sample (s₁) = 20

Given that the mean of the second sample x₂⁻ = 100

Given that the standard deviation of the second sample (S₂) = 30

Step(ii):-

T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

     where

             [tex]S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2} S_{2} ^{2} }{n_{1} +n_{2}-2 }[/tex]

            [tex]S^{2} = \frac{22( 20)^{2}+ 15(30) ^{2} }{22 +15-2 }[/tex]

           S² =  637.1428

           S = √637.1428 = 25.24168  

The standard deviation of the sample 'S' = 25.24168   

Step(iii):-

Null Hypothesis:H₀:

There is no difference between the means

Alternative Hypothesis:H₁:

There is a difference between the means

         T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

              [tex]t = \frac{ 120 -100 }{\sqrt{637.14 (\frac{1}{22 }+\frac{1}{15 } ) } }[/tex]

             t =   2.366

Degrees of freedom

           γ = n₁+n₂ -2 = 22+15-2 = 35

     t₀.₀₅ = 2.0301

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means          

The correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex],

the critical value of t is found to be [tex]t_{\alpha/2}[/tex] , then if we get:

[tex]|t| < t_{\alpha/2}[/tex] we cannot reject the null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] , then we may reject the null hypothesis and thus, accept the alternate hypothesis.

For this case, we're specified that:

For sample of stray dogs:

For sample of stray cats:

Thus, the t-test statistic for the difference of mean of these two samples is calculated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}\\\\t = \dfrac{120-100}{\sqrt{20^2/22 + 30^2/15}} = \dfrac{20}{\sqrt{200/11 + 60}}\\\\\\t \approx 2.2619[/tex]

Thus, the correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

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Answer:

D

Step-by-step explanation:

A polynomial is an expression with variables, and this expression does not have a variable. So, answer D is not a polynomial.

Step-by-step explanation:

Let m be the price of 1 baby mice

Let p be the price of 1 baby python

Given,

[tex]3m + 2p = 103.50[/tex]

as equation 1.

and

[tex]3m + 3p = 148.50[/tex]

as equation 2

From here we can easily use elimination method

for solving simultaneous equations.

Use Equation 1 - equation 2 to eliminate m to find p.

[tex](3m - 3m) + (2p - 3p) = 103.50 - 148.50 \\ - p = - 45 \\ p = 45[/tex]

Substitute p into equation 1.

[tex]3m + 2(45) = 103.50 \\ 3m + 90 = 103.50 \\ 3m = 103.50 - 90 \\ 3m = 13.50 \\ m = 13.50 \div 3 \\ = 4.50[/tex]

therefore 1 baby mice cost $4.50 and 1 baby python costs $45.

Answer:

Baby python: $45

Baby mouse: $4.5

Step-by-step explanation:

First of all, 3 baby mice and 2 baby pythons cost $103.50. When Mr. Reyes adds a baby python (He bought 3 baby mice and 3 baby pythons for a price of $148.50.) To find the price of a baby snake, you need to subtract both prices. 148.5-103.5=45, so a baby snake costs $45. Now we need to find the price of the baby mice, so we need to remove the snakes. 45*2=90. (2 snakes). 103.5-90=13.5, and 13.5/3=4.5, so a baby mouse costs $4.5.

Thanks

Answer:

75 %

Step-by-step explanation:

To solve for the above question,

The percentage of pupils that submitted their project on time

= Number of pupils that submitted their project on time/Number of pupils × 100

Number of pupils that submitted their project on time = 30 pupils

Number of pupils = 40 pupils

= 30/40 × 100

= 75 %

The percent of the pupils that submitted their project on time is 75%

Answer:

see explanation

Step-by-step explanation:

(a)

Given

[tex]\frac{y}{3}[/tex] + [tex]\frac{y+3}{5}[/tex]

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

= [tex]\frac{5y}{15}[/tex] + [tex]\frac{3y+9}{15}[/tex] ← add numerators , leaving denominator of 15

= [tex]\frac{5y+3y+9}{15}[/tex]

= [tex]\frac{8y+9}{15}[/tex]

(b)

Given

[tex]\frac{3x}{8}[/tex] - [tex]\frac{x+5}{4}[/tex]

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

= [tex]\frac{3x}{8}[/tex] - [tex]\frac{2(x+5)}{8}[/tex] ← simplify numerators leaving denominator of 8

= [tex]\frac{3x-2x-10}{8}[/tex]

= [tex]\frac{x-10}{8}[/tex]

Answer:

a) (8y + 9)/15.

b) (5x + 10)/8.

Step-by-step explanation:

(a)  y/3 + (y + 3)/5

     The LCD of 3 and 5  is 15 so we have:

     5y/15 + 3(y + 3)/15

      = (5y + 3(y + 3)) / 15

     = (5y + 3y + 9)/15

     = (8y + 9)/15.

b)  3x/8 + (x + 5)/4

     The LCD of 4 and 8  is 8 so we have:

     3x/8 + 2(x + 5)/8

      = (3x + 2x + 10) / 8

      = (5x + 10)/8.

Answer:

the red one is the pre image because if there is two of the same letters then there is a dash behind the second letter.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST!!!!

Answer:

I got 270cm!

Hope this helped!

Answer:

Yes because you would need to divide first before subtracting

Step-by-step explanation:

Answer:

yes, because of PEMDAS

divison always comes before subtraction

Answer:

option 3, double the height and with of original bottle

The methods which will create the larger water bottle with the intended volume is 1 and IV.

Volume of a three dimensional shape is the space occupied by the shape.

Given that,

A water bottle company is designing a new larger cylindrical water bottle that is intended to hold 4 times as much water as the original cylindrical water bottle.

Volume of a cylindrical shape = π r² h

Let V be the original volume.

If radius is doubled, then the new volume is,

V' = π (2r)² h = 4(π r² h) = 4V

So 1 is an option.

When the height is Quadrupled,

V' = π r² 4h = 4(π r² h) = 4V

Hence the correct options are 1 and IV.

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Answer:

 The area of the circular plate is:  " 63.59 in² " .

______________________________________________________

Note:

______________________________________________

diameter, "d" = 9 in. (given).

radius, "r" = "d/ 2 " = "(9 inches) / 2 " = 4.5 in.

______________________________________________

Area of a circle, "A" :

A =  * r²  ;

in which:   "A = Area of circle ("plate"); in units of "square inches"; or "in² " ;

                 " = 3.14 " {approximation we shall use} ;  

                 "r = radius = 4.5 in." ;

________________________________________________________

Plug in our known values to solve for the area, "A" :

A = (3.14) * (4.5 in)² ;

A = (3.14) * (4.5)² * (in²) ;

A = (3.14) * (4.5) * (4.5) * (in²) ;

A = 63.585 in² ; round to:  " 63.59 in² " .

_____________________________________________

Step-by-step explanation:

Answer:

1) N^2 + 1

2) 5*N - 9

3) n*5 + 1    (con n entero)

4) n*2 + 1    (con n entero)

Step-by-step explanation:

1)  El cuadrado de un número aumentado en 1.

Podemos definir a N como el número.

El cuadrado de N es:

N^2

Y a esto lo tenemos que aumentar en 1, entonces tenemos:

N^2 + 1

Esto es el cuadrado de un número aumentado en 1.

2)  Cinco veces un número menos 8.

Esto es:

5*N  (5 veces un número)

Y a esto le restamos 8, para obtener:

5*N - 8

3) El número siguiente a un múltiplo de 5

Un multiplo de 5 se escribe como:

n*5

Donde n es un número entero.

El numero siguiente es:

n*5 + 1

4) Un número impar.

Bien, sabemos que un número par es un multiplo de 2.

Entonces:

n*2 es un número par.

Entonces, n*2 + 1 tiene que ser un numero impar.

En este caso la expresión algebraica es:

n*2 + 1

Answer:

El valor total de la cuenta después de 5 años es de $3,598.

Step-by-step explanation:

Para encontrar la respuesta, tienes que utilizar la fórmula para encontrar el valor futuro:

VF=VP*(1+i)^n

VF=valor futuro

VP= valor presente=$3000

i=tasa de interés=0.037

n=número de periodos de tiempo=5 años

Ahora, puedes reemplazar los valores en la fórmula:

VF=3,000*(1+0.037)^5

VF=3,000*(1.037)^5

VF=3,598

De acuerdo a esto, la respuesta es que el valor total de la cuenta después de 5 años es de $3,598.

[tex]\sqrt{11}=3.31(appx)[/tex]

3.31 lies b/w 3 and 4

Answer:

[tex]\sqrt{11}[/tex] lies between 3 and 4.

Answer:5

Step-by-step explanation:

the answer is 5 because the mode is the one that has more of

Answer:

vertex

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

36x36 + 36x60

=3456 and add squared