The mean height of 20 boys and 14 girls is 161 cm. The mean height of 14 girls is 151 cm. Find the sum of the heights of 14 girls.

The value of x in the triangle to the nearest tenth is calculated as; 1.1

We have different trigonometric ratios such as;

sin θ = opp/hyp

cos θ = adj/hyp

tan θ = opp/adja

Thus, from the given triangle we can use the formula for cos θ to get the value of x. Thus;

cos 41° = 0.8/x

x = 0.8/cos 41

x = 1.06

To the nearest tenth, we have x = 1.1

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The number of quarters or nickels Kevin and Randy Muise have in the jar is 27 and 38 respectively.

n + q = 65

0.05n + 0.25q = 8.65

From equation (1)

n = 65 - q

substitute n = 65 - q into (2)

0.05n + 0.25q = 8.65

0.05(65 - q) + 0.25q = 8.65

3.25 - 0.05q + 0.25q = 8.65

- 0.05q + 0.25q = 8.65 - 3.25

0.20q = 5.40

q = 5.40/0.20

q = 27

Substitute into (1)

n + q = 65

n + 27 = 65

n = 65 - 27

n = 38

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[tex] \boxed{\Large {\mathcal {{{\color{orange}{Area \: of \: circle \: = \: πr²}}}}}}[/tex]

[tex]\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large πr²\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:{7.15}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\\large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{7} \: \times\:51.1225 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \frac{22}{ \cancel7} \: \times\: \cancel{51.1225} \: \: ^{ \red{7.303} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \:Area \: of \: circle }\:\large\blue\implies \tt \large {22} \: \times\:7.303 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \large \rm \pink{ \: Area \: of \: circle }\:\large\blue\implies \tt \large \: 160.666 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Hence , the area of circle is 160.66 m²

Given :-

To Find :-

Solution :-

Area of Circle = πr²

Area = 3.14×(7.15)² m²

= 160.52465 , which rounded off to 2DP would be 160.52 m²

f(p) = 3p - 2

f(2) = 3(2) - 2

f(2) = 6 - 2

f(2) = 4

Therefore, the answer is 4, so option C :)

Answer:

monomial and degree is 2

The solution of the given equation is -6 and 1.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

Here, given equation:

  (x+2)(x+3) = 12

 x(x+3)+2(x+3) = 12

 x² + 3x + 2x + 6 = 12

 x² + 5x + 6 - 12 = 0

 x² + 5x - 6 = 0

 x² + 6x - x - 6 = 0

 x(x+6) -1(x+6) = 0

 (x+6)(x-1) = 0

Now, x + 6 = 0      or      x - 1 = 0

        x = -6           or      x = 1

Thus, the solution of the given equation is -6 and 1.

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Answer:

  68 coins

Step-by-step explanation:

We can use the given information to write two equations involving the numbers of coins. One will express the total number of coins; the other will express their value.

__

Since there are equal numbers of coins of each type, we can let n represent the number of each kind of coin. The total number coins will be ...

  n +n +n +n + N . . . the sum of numbers of nickels, dimes, quarters, halves

The value of the coins is ...

  0.05n +0.10n +0.25n +0.50n = 15.30

The second equation lets us find the value of n:

  0.90n = 15.30

  n = 17 . . . . . . . . divide by 0.90

Then the number of coins in all is ...

  4n = N

 4(17) = N = 68

Carmela had 68 coins in all.

The proportional relationship given in the table is y = 1.6x, and line B shows this relationship.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

The constant of proportionality, considering the points on the table, is given as follows:

[tex]k = \frac{24}{15} = \frac{16}{10} = \frac{8}{5} = 1.6[/tex].

Hence the equation is:

y = 1.6x.

Line B gives the same points as the table, hence it shows the proportional relationship.

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Answer:

4.4

Step by step explanation: If Rafael gave the cashier 40, cashier will return 4.4 by subtracting 35.60 from 40

Answer: 1:2

Step-by-step explanation:

Well, if you're asking for the ratio, it is 1:2

For every 1 notebook bought, there would be 2 free pens.

Since she bought 8 notebooks, just multiply 2 by 8 which will result in 16.

Answer:

16 + 9 = 25

Step-by-step explanation:

For each term in the sequence, we can see that the second number being added increases by 2 each time (3, 5, 7)

And that the first number of each term increases by the value of the second term

(1 increases by 3; 4 increases by 5)

we can follow out these two observations to find T4

the first term (9) will increase by the value of the second term (7)

{the sum of the previous term is the first number}

so the first number of T4 will be 16.

Because we left off on +7, we are now on +9

so, T4 is

16 + 9 {and then do the math accordingly}

16 + 9 = 25

So, T4 is

16 + 9 = 25

hope this helps!! have a lovely day!! :)

I took the text last month

The percentage of men is more than 72 inches tall will be 0.15866.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

Suppose the mean height for men is 70 inches, with a standard deviation of 2 inches.

Then the percentage of men are more than 72 inches tall will be

z = (72 – 70) / 2

z = 1

The percentage of men is more than 72 inches tall will be

P(x > 72) = P(z > 1)

P(x > 72) = 1 – P(x < 72)

P(x > 72) = 1 – 0.84134

P(x > 72) = 0.15866

Thun, the percentage of men are more than 72 inches tall will be 0.15866.

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Answer:

-2x+3

Step-by-step explanation:

Gradient is change in y over change in x

[tex] \frac{2}{1} [/tex]

=2

and then

+3 because that's where it cuts the Y axis

Based on the graph, the interval will their systolic pressure be lowest is 4pm to 5pm.

The lowest systolic pressure can be seen from 5 and 8 hours after taken the medication.

If we look at the time details then this will fall inbetween the interval of 2pm to 5pm.

According to question, the time range is 4pm to 5pm.

Hence, the interval will their systolic pressure be lowest is 4pm to 5pm.

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Answer:

The answer is B - 12 P.M to 2 P.M

Step-by-step explanation:

Answer:

Groceries Galore

Step-by-step explanation:

1) Find the value of 1 egg for each shop.

Max's Market:

2.04 ÷ 6

= £0.34

Groceries Galore:

2.64 ÷ 8

= £0.33

Fancy Foodstuffs:

4.08 ÷ 12

= £0.34

Therefore, Groceries Galore's price per egg is cheaper.

Answer:

Groceries Galore

Step-by-step explanation:

we have to calculate the price of 2 eggs

in each shop apart ,and then we can infer

which shop offers the cheaper price.

…………………………………………………………

• At Max's market :

2 egg costs 2,04÷3 = £0,68

• At Groceries Galore :

2 egg costs 2,64÷4 = £0,66

• At Fancy Foodstuffs :

4,08÷6 = £0,68

………………………………

Conclusion :

Groceries Galore Offers the Lower price.

Note : we can just determine

the price of one egg in each store ,and then compare.

Answer:

888

Step-by-step explanation:

Sahil chooses a number, [We'll call it x]

divides it by 8 ,   [x/8]

adds 8 to the answer.  [(x/8) + 8]

Then multiples the answer with 8 .  [((x/8) + 8)*8]

He obtains the result as 952 .   [((x/8) + 8)*8 = 952]

The number he chooses in the beginning was

((x/8) + 8)*8 = 952

x + 64 = 952

x = 888

CHECK:

Does (888/8 + 8)*8 = 952?

(119)*8 = 952?   YES

The number is 888

Step-by-step explanation:

Since we have a vertical directrix, the equation of the parabola is

[tex](y - k) {}^{2} = 4p(x - h)[/tex]

Where p is the distance from the vertex to the directrix.

or the distance from the vertex to the focus.

Since we have a sideways parabola, let use the point for the directrix is (-6,0). So let find the midpoint of (-6,0) and (6,0). That would be our vertex.

[tex] \frac{ - 6 + 6)}{2} = 0[/tex]

[tex] \frac{0 + 0}{2} = 0[/tex]

So our vertex is (0,0).

So our equation become

[tex] {y}^{2} = 4px[/tex]

The distance from the focus and directrix is 6.

So p=6.

[tex] {y}^{2} = 24x[/tex]

So p is 6.

Since p is 6,

[tex] \frac{ {y}^{2} }{24} = x[/tex]

A rise of 8 and a run of 6. Then the correct option is B.

Coordinate geometry is the study of geometry using the points in space.

On a coordinate plane, a right triangle has points A (-5, -6), B (-5, -2), and C (-2, -2).

The distance between AB will be

AB² = (-5 + 5)² + (-2 + 4)²

AB² = 4²

AB = 4

The distance between BC will be

BC² = (-2 + 5)² + (-2 + 2)²

BC² = 3²

 BC = 3

Then the rise and run will be

rise / run = 4 / 3

Then this can be written as

rise / run = 8 / 6

Then the correct option is B.

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Answer:

x=(y-3)/4

Step-by-step explanation:

y=4x+3

y-3=4x

x=(y-3)/4

Answer:

Let's solve your inequality step-by-step.

−4x+7>x−13

Step 1: Subtract x from both sides.

−4x+7−x>x−13−x

−5x+7>−13

Step 2: Subtract 7 from both sides.

−5x+7−7>−13−7

−5x>−20

Step 3: Divide both sides by -5.

−5x/−5>−20/−5

x<4

Answer:

x<4

IMAGINE AN ARROW ABOVE THE NUMBERS

⇔

−7−6−5−4−3−2−1 0 1 2 3 4 5 6 7

4 is where the line is circled and the arrow is facing left

←Ф

like that

Answer:

x<4

Step-by-step explanation:

So you will put an open circle on positive 4 and a ray going to the left of the graph.

Answer:

i don't know

Step-by-step explanation:

i don' know

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

a) Yes it does, because the graph of their relationship is a Straight line

b) Independent variables are variables whose variation does not depend on another. Number of works does not depend on followers. Therefore, it is independent

C)number of followers depend on the number of locks passing. It is dependent.

D) Slope = (Y₂- Y₁)/(x₂-x₁) = (100-82)/ (3-0) =  18/3 = 6

It represents the increase in number of followers per week,

E) y-intercept is value of y when x=0

y-intercept = 82. It means his initial number of followers

F) Slope-intercept form → y = mx + c m = slope горе C = y-intercept y = no of followers x= weeks.

Y=6x+82

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Step-by-step explanation:

via the distance formula (based on Pythagoras) I can prove that ABC is a right-angled triangle, and that ADC is fully congruent to ABC.

so, together these 2 triangles (joined at their Hypotenuses, the diagonal AC) build a rectangle.

Answer:

An equilateral triangle is a triangle with all 3 sides the same in size.
If one side is 8cm, then 8x3=24 cm
The perimeter is possibly 24 cm.

Answer:

(-3,5) (-3,3) (-8,3)

Step-by-step explanation:

Answer:

(-3,5) , (-3,3) , (-8,3)

Step-by-step explanation:

bye, bye!!

Answer:

4 pi     ( = 12.566  in^2 )

Step-by-step explanation:

TOTAL area =   pi r^2    =    pi (6)^2 = 36 pi   in^2

  divide into 9 pieces    36 pi  / 9 = 4 pi   in ^2

Answer:

Simplifying -16t2 + 48t + 160 = 0

Reorder the terms: 160 + 48t + -16t2 = 0

Solving 160 + 48t + -16t2 = 0 Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'. 16(10 + 3t + -1t2) = 0

Factor a trinomial. 16((5 + -1t)(2 + t)) = 0 Ignore the factor 16.

hope it helps.