Solve the following using substitution method

Answer:

192 students

Step-by-step explanation:

60 randomly students surveyed

16 chose aquarium as their favorite field trip.

720 students in total.

[tex]\frac{16}{60}[/tex] = [tex]\frac{?}{720}[/tex] =

720 × 16 ÷ 60 =

192 students

9514 1404 393

Answer:

  p = 6

Step-by-step explanation:

The difference between the first two terms is ...

  5p -p = 4p

Since this is an arithmetic sequence, the next term will be 4p more than the last term:

  5p +4p = 9p

Then the sum of the first three terms is ...

  p + 5p + 9p = 90

  15p = 90 . . . . . . . . . . collect terms

  p = 6 . . . . . . . . . . . . divide by 15

_____

The first three terms are 6, 30, 54.

Answer:

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

Option "D"

Step-by-step explanation:

Given:

24 bran muffins required = 2.25 cups of flour

Find:

Number of cups water require for 30 muffins

Computation:

Assume;

Number of cups water require for 30 muffins = x

So,

24 / 2.25 = 30 / x

x = [30 × 2.25] / 24

x = 67.65 / 24

x = 2.8187

Number of cups water require for 30 muffins = 2.82 cups (Approx.)

Answer: a b f

Step-by-step explanation: I need brainliest for next rank I’d appreciate it

Answer:

y=-2/3x

Step-by-step explanation:

Perpendicular gradients(slopes) are negative reciprocals so first rearrange the given equation to find the gradient. y=3/2x-7/2

the gradient of the new line will be m=-2/3 then use the point (-3,-2) to find the equation of the line

y=mx+b

-2=(-2/3)(-3)+b

-2=2+b

b=0

y=-2/3x

Step-by-step explanation:

hope it helps you see the attachment for further information

Answer:

36.5

Step-by-step explanation:

First solve for x

Factor:

3x-3-5x+15 = 3

Combine Like Terms:

-2x+12=3

-2x = -9

x = 4.5

PLug it in:

7(4.5)-5

31.5-5

36.5

[tex]{\boxed{\mathcal{\red{Step-by-step\:explanation:-}}}}[/tex]

[tex]3(x - 1) - 5(x - 3) = 3 \\ ⇝3x - 3 - 5x + 15 = 3 \\ ⇝ - 2x + 12 = 3 \\ ⇝ - 2x = 3 - 12 \\ ⇝x = \frac{ - 9}{ - 2} \\ x = 4.5[/tex]

To verify:

[tex]3(4.5 - 1) - 5(4.5 - 3) = 3 \\ ✒ \: 13.5 - 3 - 22.5 + 15 = 3 \\ ✒ \: 28.5 - 25.5 = 3\\✒\: 3 = 3[/tex]

✒ L. H. S. = R. H. S.

[tex]\sf\pink{Hence\:verified.}[/tex] ✔

Now,

7 [tex]x[/tex] - 5 = 7 x 4.5 - 5

= 31.5 - 5

= 26.5

[tex]\sf\purple{Therefore,\:the\:value\:of\:''7\:x-\:5''\:is\:26.5.}[/tex]

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]

Answer:

carretilla

Step-by-step explanation:

la carretilla se encontraba a unos 18 metros de altura

The volume of the given cylinder with a diameter of 4 cm and the height of the cylinder is 16cm is 201.062 cm².

The right circular cylinder is the cylinder in which the line joining the centre of the top circle of the cylinder to the centre of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.

Suppose that the radius of the considered right circular cylinder is 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

The volume of the given cylinder is,

Volume of the cylinder = (π/4) × (4cm)² × 16cm

                                      = 201.062 cm²

Hence, the volume of the given cylinder is 201.062 cm².

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Answer:

yes i can

Step-by-step explanation:

Answer:

(2,7)

Step-by-step explanation:

Answer:

4 miles.

Step by step explanation

Answer: 3/11 would be the answer

The probability that at least three plants produce two or more seeds is 0.793915.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

The probability that out of n trials, there be x successes is given by

Use binomial distribution, with p =0.20, n=5, x=3

[tex]P(X=x)=C(n,x)p^x (1-p)^{n-x}[/tex]

P(X> = 3)

[tex]=1-(P(X=0)+P(X=1)+P(X= 5 ))\\=1-(C(20,0)0.2^0 (0.8)^{20-0}+C(20,1)0.2^1 (0.8)^{20-1}+C(20,2)0.2^2 (0.8)^{20-2})[/tex]

=1-(0.0115292+0.057646+0.136909)

=1-0.206085

=0.793915

Hence, the probability that at least three plants produce two or more seeds is 0.793915.

Learn more about binomial distribution here:

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Answer:

Coordinates:

(-3, 5)

(2, 5)

(-3, 10)

(2, 10)

Step-by-step explanation:

Perimeter formula:

length + width + length + width

Insert known value(s):

l + w + l + w = 20

Squares must have the same value for all 4 sides, so what number × 4 will equal 20? 5.

5 + 5 + 5 + 5 = 20

This means coordinates will be 5 units apart:

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

(-3, 5 + 5) = (-3, 10)

Mark these coordinates on your grid as you go to double check the shape turns becomes a square:

(2, 5 + 5) = (2, 10)

Counting between them should equal 5 units for each side: I checked using the desmos graphing calculator online.

Answer:

Functional explanations are a type of explanation offered in the natural and social sciences. In giving these explanations, researchers appeal to the functions that a structure or system has.

Answer:

arc AB = 144°/360° x 2π x 10

= 2/5 × 20π = 8π

Answer:

13.  4 sqrt(3)

14.  sqrt(7)/2

Step-by-step explanation:

13.  sqrt(2) * sqrt(3) * sqrt(8)

We know sqrt(a) * sqrt(b) = sqrt(ab)

sqrt(48)

Look for perfect squares

sqrt(16*3)

sqrt(16) sqrt(3)

4 sqrt(3)

14.  sqrt(14)/ 2 sqrt(2)

We know sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt(14/2) / 2

sqrt(7)/2

Hence, the Answer is

13.  4 sqrt(3)

14.  sqrt(7)/2

Solution:

13.  sqrt(2) * sqrt(3) * sqrt(8)

We know sqrt(a) * sqrt(b) = sqrt(ab)

sqrt(48)

Look for perfect squares

sqrt(16*3)

sqrt(16) sqrt(3)

4 sqrt(3)

14.  sqrt(14)/ 2 sqrt(2)

We know sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt(14/2) / 2

sqrt(7)/2

Answer:

A; TDC Inc., has 40 salespeople

B; Exactly half of the salespeople took fewer than 6 flights last year

F; Exactly half of the salespeople took at least 7 flights last year

Answer:

yes

Step-by-step explanation:

Answer: [tex]5.7\ cm[/tex]

Step-by-step explanation:

Given

Rectangle has an area of [tex]19.38\ cm^2[/tex]

Suppose rectangle length and width are [tex]l[/tex] and [tex]w[/tex]

If each side is increased by [tex]1.50\ cm[/tex]

Area becomes [tex]A_2=35.28\ cm^2[/tex]

We can write

[tex]\Rightarrow lw=19.38\quad \ldots(i)\\\\\Rightarrow (l+1.5)(w+1.5)=35.28\\\Rightarrow lw+1.5(l+w)+1.5^2=35.28\\\text{use (i) for}\ lw\\\Rightarrow 19.38+1.5(l+w)=35.28-2.25\\\Rightarrow l+w=9.1\quad \ldots(ii)[/tex]

Substitute the value of width from (ii) in equation (i)

[tex]\Rightarrow l(9.1-l)=19.38\\\Rightarrow l^2-9.1l+19.38=0\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{(-9.1)^2-4(1)(19.38)}}{2\times 1}\\\\\Rightarrow l=\dfrac{9.1\pm\sqrt{5.29}}{2}\\\\\Rightarrow l=\dfrac{9.1\pm2.3}{2}\\\\\Rightarrow l=3.4,\ 5.7[/tex]

Width corresponding to these lengths

[tex]w=5.7,\ 3.4[/tex]

Therfore, we can write the length of the longer side is [tex]5.7\ cm[/tex]

Answer:

83,000

Step-by-step explanation:

Thousand = 1,000s place

1,000s place of 83,243 is the 3 (3,000)

The number right before 3 is the 2 (200)

2 is closer to zero than 10 so it rounds down

83,243 then becomes 83,000 since the other numbers before the (2) round down with it.

Answer:

No.of cups for one soup : 2 cups

No.of cup for 3 soups: 2×3

=6

So , 6 cups of vegetable

HOPE IT HELPS U :)

Answer:

M(x)  =  452,56 in

Step-by-step explanation:

The volume of the open box is  500 in³

V = Area of the base times height

V(b) =  x² * h               where x is the side of the square and h the heigh

Then     500 =  x²*h

Total material to use is: material of the base + material of 4 sides

material of the base is  x²

material of one side is x*h  we have 4 sides then  4*x*h

Total material M(b)

M(b)  =  x²  +  4*x*h

And    as    h  =  500/ x²

M(x)  =  x²  +  4* x* 500/x²

M(x)  =  x²  +  2000/x

Tacking derivatives on both sides of the equation

M´(x)  =  2*x   - 200/x²

M´(x)  =  0         2*x  -  200/x²  = 0

x³ -  100  =  0

x³   =  100

x   =  4,64 in

And By substitution     h  =  500/x²

h  =  500/(4,64)²           h  =  23,22  in

How do we know that x = 4,64 make V(x) minimum

we get the second derivative

M´´(x)  =  2  +  200*2x/ x⁴    =  2  +  400/x³

M´´(x) is always positive

M´´(x) > 0     then M(x) has a minimum for  x= 4,64 in

The least amount of material is:

M(x)  =  x²    +    2000/x

M(x)  =  (4,64)²  *  2000/4,64

M(x)  = 21,53  +  431,03

M(x)  =  452,56 in

Answer: 16590

Step-by-step explanation:

Let p be the population proportion of high school students in the area who attend their home basketball games.

As per given,

prior p = 0.5

Margin of error E= 0.01

Criticfor z-value for 99% confidence = 2.576

Sample size will be computed as

[tex]n=p(1-p)(\frac{z^*}{E})^2\\\\ n= 0.5(1-0.5)(\frac{2.576}{0.01})^2\\\\=0.25(257.6)^2\\\\=0.25 (66357.76)\approx16590[/tex]

Hence, required sample size = 16590

Answer: =

Step-by-step explanation: just took the test

We will see that both angles are actually the same one (but in different units) so the symbol that we need to use is the equal symbol.

Here we have two angles, one in degrees and  the other in radians, we want to compare them. To do it, we will need to write both of the angles in the same units.

The angles are:

pi/3 rads

60°

First, remember that:

pi rads = 180°

1 rad = (180°/pi)

With this, we can change the units of the first angle to get:

pi/3 rads = pi/3*(180°/pi) = 180°/3 = 60°

So both angles are actually the same angle, then the symbol that correctly compares them is the equal symbol.

pi/3 rads = 60°

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Answer:

15

Step-by-step explanation:

a^2 + b^2 = c^2

20^2 +b^2 = 25^2

400 + b^2 = 625

-400           -400

b^2 = 225

b = √225

b = 15

Answer:

0

Step-by-step explanation:

Given that f(x) = 1/2x + 4

Let y = f(x)

y = 1/2 x + 4

Replace y with x

x = 1/2 y + 4

Make y the subject of the formula

1/2y = x - 4

y = 2(x-4)

If x = 3

y = 2(4-4)

y = 2(0)

y = 0

Hence ƒ -1(4) is 0

Answer:

Step-by-step explanation:

First make the denominators the same.

Take the LCM of (8, 12 , 8) = 24

So,

      [tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8} \ becomes \ \frac{3}{24}, \frac{22}{24}, \frac{27}{24}[/tex]

[tex]Order \ from \ least \ to \ greatest \ \\\\\frac{3}{24} < \frac{22}{24} < \frac{27}{24}[/tex]

That is,

           [tex]\frac{1}{8}, \frac{11}{12}, \frac{9}{8}[/tex]

Answer:

B would be 72 using a^2+b^2=c^2

Step-by-step explanation:

30^2 + x =78^2

in other words

900 + x =6084

6084-900= 5184

The square root of 5184 is 72