There are 30 children in a nursery at least one adult needs to be with eight children in the nursery work out the least number of adults needed in the nursery

Answer:

20x-8 ...last option

Step-by-step explanation:

Answer:

The second and fourth statements are correct.

Step-by-step explanation:

We are given the function for the graph of:

[tex]y=-(x-0.5)^2+9[/tex]

Note that this is a quadratic function in its vertex form, given by:

[tex]y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

Rewriting our given equation yields:
[tex]\displaystyle y = (-1)(x-(0.5))^2 + (9)[/tex]

Therefore, a = -1, h = 0.5, and k = 9.

Therefore, the vertex of the graph is at (0.5 ,9).

Because the leading coefficient is negative, the parabola opens downwards.

Therefore, the parabola has a maximum value.

In conclusion, the second and fourth statements are correct.

1. the vertex is (0.5, 9)

2. it has a maximum.

Answer: 140 degrees

Step-by-step explanation:

Because m2 is perpendicular to l1, the bottom angle made from m2 and l1 is a right angle = 90 degrees.  The angle vertical to 1 = 50 degrees.  Thus, the angle made from both of these is equal to 140 degrees.  Because l1 is parallel to l2, <2 is congruent to this angle, and thus equals 140 degrees.  

Wow, that would be much easier if the angles were labeled.

Hope it helps <3

Answer:

angle = 140 degrees

Step-by-step explanation:

Given:

All lines coplannar.

L1 || L2

m2 perpendicular to L1

angle 1 = 50 degrees

Solution

Refer to attached diagram

angle 4 = 90 degrees    ........... given

angle 3 = 180 - angle 4 - angle 1 = 180 - 90 - 50 = 40 degrees  .... angles on a line

angle 2 + angle 3 = 180 degrees  ............. sum interior angles between parallel lines L1 and L2

=>

angle 2 = 180 - angle 3 = 180 - 40 = 140 degrees.

Answer:

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Step-by-step explanation:

b=7x

sum of straight angle :=180

isoceles traingle = 2 sides are equal, and two angles are equal

b+a=180

7x+a=180

sum of traingle =180

2a+c=180

2a+2x=180  first equation

7x+a=180    second equation

solve by elimination ( multiply second equation by 2)

2a+2x=180

2a+14x=360 ( subtract)

2a+2x-2a-14x=180-360

-12x=-180

x=-180/12=

x=15

angle b=7*15=105

angle a=180-105=75

angle c=2x=30

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

Step-by-step explanation:

4 solids cubes A, B, C and D have been made with the same material.

Since material is same density of the material (grams per cm³) will be same.

It shows that the weight of the cubes will vary in the ratio of their volumes.

Volume of cube A = 6³ = 216 cm³

Volume of cube B = 8³ = 512 cm³

Volume of cube C = 10³ = 1000 cm³

Volume of cube D = 12³ = 1728 cm³

Therefore, weights of these cubes will be in the same proportion.

Since, Volume of D = Volume of (A + B + C)

1728 = (216 + 512 + 1000)

1728 = 1728

Therefore, weights of A, B, C, D will be arranged in the same way to balance the plates of a scale.

On one side of the scale cubes A, B, and C should be placed and on the the other side of the scale cube D should be placed to balance the scale.

Answer:

33.33%

Step-by-step explanation:

We are told that the customer paid Rs. 2034 after getting 10% discount with 13% vat on marked price (m.p.)

hence:-

2034 = m.p. × 90/100 × 113/100

m.p = (2034 × 100 × 100)/(90 × 113)

m.p. = Rs.2000

Now, due to the fact that VAT (which in this question is given to be 13%) is not the profit of the retailer, thus the selling price (s.p.) of the bag would be given by;

s.p = m.p. × 90/100

s.p = 2000 × 90/100

s.p = Rs. 1800

We are told that the retailer made a profit of 20%

Thus:-

c.p. × 120/100 = s.p.

c.p.= s.p. × 100/120

c.p.= 1800 × 100/120

c.p. = Rs.1500

Therefore, the percentage with which he marked above the c.p is;

% mark up = (m.p - c.p)/c.p) × 100

Plugging in the relevant values, we have;

(2000 - 1500)/1500) × 100

(500/1500) × 100 = 33.33%

Answer:

[tex]\frac{\sqrt{3}}{2}[/tex]

Step-by-step explanation:

The quickest way to solve this is to recognize this as a 30-60-90 triangle. The smallest angle is 30 degrees, and the answer is simply cos 30º.

You can also use the pythagorean theorem to find the length of the hypotenuse, then use SOH-CAH-TOA to get the answer.

Answer:

[tex]3x^2+2x+1[/tex]

Step-by-step explanation:

Sum means to add and second power means that the exponent is "2". So, the expression is:

=> [tex]3x^2+2x+1[/tex]

It cannot be simplified further.

Answer:

49π

Step-by-step explanation:

The formula for the area of a circle is,

[tex]\pi r^2[/tex]

If the radius is 7 inches we need to plug that in for r in the formula.

π(7)^2

7*7 = 49

Thus,

the area in terms of pi is 49π.

Hope this helps :)

Answer:

Step-by-step explanation:

[tex]r = 7\\A = ?\\A =\pi r^2\\A =\pi7^2\\A = 49\pi[/tex]

Answer:

f(x)=2(x+7)^2-103

Step-by-step explanation:

[tex]f(x)=2x^{2} +28x-5\\=2(x^2+14x)-5\\=2(x^2+2(7)x+7^2-7^2)-5\\=2(x+7)^2-2(49)-5\\=2(x+7)^2-103[/tex]

Answer: B. f(x) = 2(x + 7)² - 103

Step-by-step explanation:

[tex]y=2x^2+28x-5\\\\\\y+5=2x^2+28x\\\\\\y+5=2(x^2+14x+\underline{\quad}\ )\\.\qquad \qquad \qquad \ \ \downarrow\\.\qquad \qquad \qquad \bigg(\dfrac{14}{2}\bigg)^2=7^2 \\\\\\y + 5 + 2(7)^2=2(x^2+14x+\underline{7^2} )\\\\\\y + 5 + 98 = 2(x + 7)^2\\\\\\y+103=2(x+7)^2\\\\\\y=2(x+7)^2-103[/tex]

Answer:

Option A.

Step-by-step explanation:

See attachment.

Basically, the reason why I left it at cm(3) was because that's the standard unit for volume, any length of measurement to the third power.

Answer:

4 litres of 12% solution

2 litre of 24% solution

Step-by-step explanation:

Let the 12% solution = l

Let the 24% solution = h

Dimitri needs a total of 6 litres of both :

l + h = 6 - - - - - - - - (1)

He needs a mixture of both volumes of both to give a 16% volume

12%l + 24%h = 16% * 6

0.12l + 0.24h = 0.96 ----(2)

From (1)

l + h = 6;

l = 6 - h

Substitute l =6-h into (2)

0.12(6 - h) + 0.24h = 0.96

0.72 - 0.12h + 0.24h = 0.96

0.72 + 0.12h = 0.96

0.12h = 0.96 - 0.72

0.12h = 0.24

h = 0.24 / 0.12

h = 2

From ;

l = 6 - h

l = 6 - 2

l = 4

Answer:

Step-by-step explanation

[tex]\frac{-9}{-15}[/tex]÷ [tex]\frac{x^{-1} }{x^{5} }[/tex] ÷[tex]\frac{y^{-9} }{y^{-3} }[/tex]

[tex]\frac{3}{5}[/tex] ÷ [tex]x^{-1} -5[/tex]÷ [tex]y^{-9} -(-3)[/tex]

[tex]\frac{3}{5}[/tex] ÷ [tex]x^{-6}[/tex] ÷ [tex]y^{-9} +3[/tex]

[tex]\frac{3}{5}[/tex] ÷[tex]x^{-6}[/tex] ÷[tex]y^{-6}[/tex]

[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{1}{x^{6} }[/tex]÷[tex]\frac{1}{y^{6} }[/tex]

[tex]\frac{3}{5x^{6}y^{6} }[/tex]

Answer:

Step-by-step explanation:

From the circle it can be seen that the angle ∠EQD lies on the circumference of the circle. A circumference of a circle is known to be any point on the circle. Also we have central angle ∠ECD of 104°

In circle geometry, there is a theorem that states; Angle at the center of a circle is twice the angle at the circumference. Applying this theorem to the given question we can say, ∠ECD = 2∠EQD

Substituting the given value;

104° = 2∠EQD

Dividing both sides by 2

104/2 = 2∠EQD/2

∠EQD = 104/2

∠EQD = 72°

Answer: The answer is 52.

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

0.1  pound for one batch of cookies

3.75 pound for  x  batches of cookies

3.75/0.1=x

he can make 37.5 batches of cookies

Answer:

Square A is 4 times greater than Square B

Step-by-step explanation:

Square A is 12 feet x 12 feet = 144

Square B is 6 feet x 6 feet = 36

144 ÷ 36 = 4

Answer:

Depth of the milk = 4 cm

Step-by-step explanation:

In the figure attached,

Milk carton is in the shape of a cuboid having length = 8 cm, Width = 5 cm and Height = 15 cm

Depth of the milk in the carton = 12 cm

Milk inside the carton will have the same shape of cuboid, having same length and width but a different height.

Volume of the milk = volume of the cuboid shape of the milk

                                = Length × width × height

                                = 8 × 5 × 12

                                = 480 cm³

Now the carton is turned with its base on the shaded region.

By changing the base, dimensions of the milk inside the carton will change but the volume of the milk will remain the same.

New dimensions of the milk inside the carton will be,

Length = 15 cm

Width = 8 cm

Height = d cm (unknown side)

By using the formula of volume again,

V = l × b × h

480 = 15 × 8 × d

480 = 120d

d = [tex]\frac{480}{120}[/tex]

d = 4 cm

Therefore, depth of the milk in the carton will be 4 cm.

Answer: [tex]1\dfrac{5}{9}\text{ minutes}[/tex]

Step-by-step explanation:

Complete question is provided in the attachment below.

Given: Jacob and Issac decided to run to the basketball court

Distance between basketball court and school = [tex]5\dfrac{1}{4}[/tex] miles

[tex]=\dfrac{21}{4}[/tex] miles

Speed = [tex]3\dfrac{3}{8}[/tex] miles per hour

[tex]=\dfrac{27}{8}[/tex] miles per hour

Since, time = (distance) ÷ ( speed)

Now, the time taken by boys to arrive at the basketball court = [tex]\dfrac{21}{4}\div\dfrac{27}{8}[/tex] hours

[tex]=\dfrac{21}{4}\times\dfrac{8}{27}\\\\=\dfrac{7\times2}{9}=\dfrac{14}{9}\\\\=1\dfrac{5}{9}\text{ minutes}[/tex]

Hence, the required length of time = [tex]1\dfrac{5}{9}\text{ minutes}[/tex]

Answer:

I dont give you the answer right away so you will read what i write and fully understand :D

Step-by-step explanation:

We are picking 3 balls from 30 balls, so its C(30,3) because the order of picking the balls doesnt matter. We also need to pick 2 balls from 20 balls, which is C(20,2). So the answer is C(30,3) * C(20,2).

Answer:

10 km/hr

Step-by-step explanation:

The aircraft carrier and the container ship both took 30 hours to travel their respective distances. If you divide both numbers by 30, you find that their differences is 5. We can tell that the aircraft carrier traveled 450 ÷ 30 = 15 km/hr and the container ship traveled at a speed of 300 ÷ 30 = 10 km/hr. The aircraft carrier traveled 5 km/hr faster. So, we can tell the container ship traveled at 10 km/hr.

Hope this helps! Plz give me brainliest, it will help me achieve my next rank.

Answer:  Given.

Step-by-step explanation:  The last sentence of the directions, Begin. . .

ends with:  Construct line RS a bisector of ∠PQR

Answer:

Which of the following numbers is a composite number that is divisible by 3? A. 49 B. 103 C. 163 D. 261 Answer: B) 245

Step-by-step explanation:

Answer:

Ajay has 10 rupees and Ragu has 20 rupees.

Step-by-step explanation:

Let's say Ajay has a rupees, and Ragu has r rupees.

Ragu lends 5 rupees to Ajay.

r - 5 = a + 5

r = a + 10

Ajay lends 5 rupees to Ragu.

5(a - 5) = r + 5

5a - 25 = r + 5

r + 5 = 5a - 25

r = 5a - 30

5a - 30 = a + 10

4a = 40

a = 10 rupees

r = 5 * 10 - 30

r = 50 - 30

r = 20 rupees

Hope this helps!

Answer:

Ajay has 15 Rupees while Ragu has 45 Rupees

Step-by-step explanation:

I believe by " one five", you mean fifteen

Let the original amount that Ajay has be "a"

Let the original amount that Ragu has be "r"

If Ragu lends Ajay 15 rupees, Ragu will now have, (r - 15) while Ajay will have (a + 15)

Since both of them will have equal amount, r - 15 = a + 15

r = a + 30.............(1)

If Ajay lends Ragu 5 rupees, Ajay will have a - 5 while Ragu will have r + 5.

Since Ragu will now have 5 times the amount Ajay has, r + 5 = 5(a - 5)

r + 5 = 5a - 25

r = 5a - 30.............(2)

Equating equations (1) and (2):

a + 30 = 5a - 30

4a = 60

a = 15

Substitute a = 15 into equation (2)

r = 5(15) - 30

r = 75 - 30

r = 45

Ajay has 15 Rupees while Ragu has 45 Rupees

Question options :

a. They should be between 64 and 76 inches tall.

b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.

c. They should be at or below the 95th percentile, which is 74.92 inches.

d. None of the above.

Answer: a. They should be between 64 and 76 inches tall.

Step-by-step explanation:

Given the following :

Assume men's height follow a normal curve ; and :

Mean height = 70 inches

Standard deviation= 3 inches

According to the empirical rule ;

Assuming a normal distribution with x being random variables ;

About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.

Using the empirical rule :

95% will fall between + or - 2 standard deviation of the mean.

Lower limit = - 2(3) = - 6

Upper limit = 2(3) = 6

(-6+mean) and (+6+ mean)

(-6 + 70) and (6+70)

64 and 76

The range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

According to the given data

The mean height for adult males in the U.S. is about 70 inches

The standard deviation of heights is about 3 inches.

Considering the data to be normally distributed

According  to the empirical rule for normal distribution we can write that

95.45% of the data lies with in the range of

[tex]\rm \mu - 2\sigma \; to \; \mu +2\sigma\\\\where \\\mu = Mean\\\sigma = Standard \; deviation[/tex]

We have to to determine that  using the Empirical Rule 95% of adult males should fall into what height range

According to the given data

[tex]\rm \mu = 70\\\rm \sigma = 3 \\[/tex]

[tex]\rm Lower \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 - 2(3) = 64[/tex]

[tex]\rm Upper \; limit \; of \; the\; range \; of\; variation\; of \; height\; range = 70 +2(3) = 76[/tex]

So we can conclude that the range of height of adult males in U.S. using the 95% empirical rule is 64 to 76 inches

For more information please refer to the link given below

https://brainly.com/question/25394084

Answer:

Step-by-step explanation:

"or" means sum, that is all x≤-2 plus all x≥3

≤-2  mens all numbers less than -2 and the -2

≥3  mens all numbers greater than 3 and the 3

Answer:

[tex]2a - 3b + 4c = 1[/tex]

Step-by-step explanation:

Given

[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]

Required

Determine [tex]2a - 3b + 4c[/tex]

[tex]a^2 + b^2 + c^2 = 2(a - b - c) - 3[/tex]

Open bracket

[tex]a^2 + b^2 + c^2 = 2a - 2b - 2c - 3[/tex]

Equate the equation to 0

[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 3 = 0[/tex]

Express 3 as 1 + 1 + 1

[tex]a^2 + b^2 + c^2 - 2a + 2b + 2c + 1 + 1 + 1 = 0[/tex]

Collect like terms

[tex]a^2 - 2a + 1 + b^2 + 2b + 1 + c^2 + 2c + 1 = 0[/tex]

Group each terms

[tex](a^2 - 2a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]

Factorize (starting with the first bracket)

[tex](a^2 - a -a + 1) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]

[tex](a(a - 1) -1(a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1) (a - 1)) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + (b^2 + 2b + 1) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + (b^2 + b+b + 1) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + (b(b + 1)+1(b + 1)) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)(b + 1)) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + 2c + 1) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)^2) + (c^2 + c+c + 1) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)^2) + (c(c + 1)+1(c + 1)) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)(c + 1)) = 0[/tex]

[tex]((a - 1)^2) + ((b + 1)^2) + ((c + 1)^2) = 0[/tex]

Express 0 as 0 + 0 + 0

[tex](a - 1)^2 + (b + 1)^2 + (c + 1)^2 = 0 + 0+ 0[/tex]

By comparison

[tex](a - 1)^2 = 0[/tex]

[tex](b + 1)^2 = 0[/tex]

[tex](c + 1)^2 = 0[/tex]

Solving for [tex](a - 1)^2 = 0[/tex]

Take square root of both sides

[tex]a - 1 = 0[/tex]

Add 1 to both sides

[tex]a - 1 + 1 = 0 + 1[/tex]

[tex]a = 1[/tex]

Solving for [tex](b + 1)^2 = 0[/tex]

Take square root of both sides

[tex]b + 1 = 0[/tex]

Subtract 1 from both sides

[tex]b + 1 - 1 = 0 - 1[/tex]

[tex]b = -1[/tex]

Solving for [tex](c + 1)^2 = 0[/tex]

Take square root of both sides

[tex]c + 1 = 0[/tex]

Subtract 1 from both sides

[tex]c + 1 - 1 = 0 - 1[/tex]

[tex]c = -1[/tex]

Substitute the values of a, b and c in [tex]2a - 3b + 4c[/tex]

[tex]2a - 3b + 4c = 2(1) - 3(-1) + 4(-1)[/tex]

[tex]2a - 3b + 4c = 2 +3 -4[/tex]

[tex]2a - 3b + 4c = 1[/tex]

Answer:

1/21

Step-by-step explanation:

=> [tex]\frac{1}{7} / 3[/tex]

=> [tex]\frac{1}{7} * \frac{1}{3}[/tex]

=> [tex]\frac{1*1}{7*3}[/tex]

=> 1/21

Answer:

The correct option is;

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).

Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give

Step-by-step explanation:

We have that for reflection across the x-axis, (x, y) → (x, -y)

For reflection across the y-axis, (x, y) → (-x, y)

Therefore, given that the pre-image before the reflection across the y-axis is (x, -y), we have;

For reflection across the y-axis, (x, -y) → (-x, -y)

For reflection across the line, y = x, gives (x, y) → (y, x) which is not the same as (-x, -y)

Answer:

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-arrow (x, -y).

If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) Right-Arrow (-x, y).

Taking the result from the first reflection (x, -y) and applying the second mapping rule will result in (-x, -y), not (y, x), which reflection across the line y = x should give

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.

Thus, the value of f(0), is simply the output value we would get, given an input value of "0".

So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.

Answer: 6

Step-by-step explanation: