. a) In a group of 500 students, 280 like bananas, 310 like apples, and 55 do not like both the fruits.
(i) Find the number of students who like both the fruits.
(ii) Find the number of students who like only one fruit.
(iii) Show the result in a Venn-diagram.​

The number of football helmets which are likely to be scratched from the 108 helmets is; 12.

It follows from the task content that of the initial shipment of 108 football helmets; four of them were scratched.

On this note, the number of helmets likely to be scratched from the new shipment of 108 helmets can be evaluated by ratios as;

x = (108 × 4)/36 = 12 scratched helmets.

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The total area available for cars to park is 858 square meters, the number of compact parking space is 68 and the number of non-compact parking space is 52

The total area available

The dimension of the parking lot is:

78 meters by 19 meters

The dimension of the aisle is:

8 meters by 78 meters

The total area available is the difference between the area of the parking lot and the area of the aisle.

So, we have:

Available Area = 78 * 19 - 8 * 78

Available Area = 858

Hence, the total area available for cars to park is 858 square meters

The number of parking space

The total area available for cars to park is 858 square meters, and the area of each parking spot is 12.5 square meters

So, the number of parking lot is:

n = 858/12.5

n = 68.64

Remove the decimal

n = 68

Hence, the number of parking space is 68

The number of parking space for non-compact parking space

The total area available for cars to park is 858 square meters, and the dimension of each parking spot is 5.5 meter by 3 meters

So, the number of parking lot is:

n = 858/(5.5 * 3)

n = 52

Hence, the number of parking space is 52

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Answer:

The above answer is correct!

To put it a bit more simply:

First box: C. 858

Second box: C. 68

Third box: B. 52

Step-by-step explanation:

Hope this helps!

Answer:

False

Step-by-step explanation:

Angles 1 and 2 are not adjacent because they do not share any common line segments with each other.

Answer:

False

Step-by-step explanation:

The definition of adjacent angles is two angles that share a common side and a common vertex. Also, they don't overlap

So in this case ∠1 and ∠2 share the common vertex A but do not share the common side, so these angles are not adjacent.

In this diagram, an example of adjacent angles would be ∠1 and ∠3.

Here's a visual example to understand what I meant  

The Three quarters the product of two numbers x and y is 3/4 *x* y

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.

In elementary algebra, those symbols  represent quantities without fixed values, known as variables.

As, quarters represent 1/4

So, three quarters= 3/4

Let the two number be x and y.

Then , 3 quarters of x and y product be,

=3/4*x*y

= 0.75*x*y

Hence, the expression of given statement is 3/4*x*y.

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Answer:

[tex]c = 9[/tex]

Step-by-step explanation:

[tex] {(x - a)}^{2} = {x}^{2} - 2ax + {a}^{2} \\ 2ax = 6 \\ a = 3 \\ c = {a }^{2} \\ c = 9[/tex]

Answer:

x i think its the awnser

Step-by-step explanation:

Set the denominator in 1x−4 1 x - 4 equal to 0 to find where the expression is undefined. Add 4 to both sides of the equation. The domain is all values of x that make the expression defined.

Answer

Please see attached photo below for detailed analysis

Explanation

This is a statistics problem involving Group Frequency Distribution Table. See the attached and the details below.

By dividing observations into intervals and tabulating the frequencies for each interval, data can be organized.  A grouped frequency table is the end product.

The intervals in this distribution are referred to as classes.

This is obtained by dividing the sum of the product of all mid points and their frequencies by the total number of observations.

That is Estimated Mean = (f * x)/n ------See the attached sheet.

⇒ 503/50

= 10.06

The median of the 50 observations = 28

This is arrived at by dividing the sum of 25th and the 26th number by 2.

That is (28 + 28)/28=28

This median falls in to the third class -  25-29. Hence, the median group is 25-29.

The estimated median value is computed as follows:

Estimated Median = L + (((n/2)-B)/G) x w

Where :

Inserting the values we have :

L = 25

n = 50

B = 0 + 1  = 1

G = 2

w = 5

Estimated Median = 25 + (((50/2)-1)/2 ) * 5

= 25 + (24/2) * 5

= 85

By observation, the modal group is 30-34. This is because it has the highest frequency of 4.

Hence, the Estimated Mode (EM) is arrived at using the formula:

EM = L + (fₙ-fₙ₋₁)/(fₙ-fₙ₋₁)  +  (fₙ-fₙ₊₁) x w

where:

Note that

L = 30

fn-1 = 2

fn = 4

fn+1 = 3

w = 5

Hence,

EM = 30 + (4-2)/((4-2) + (4-3)) x 5

= 30 + (2/(2+1)) x 5

= 30 + (2/3) x 5

EM =  33.33

In summary,

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Answer:

B, 12, 48.

Step-by-step explanation:

Hope this helped!

Answer:

Step-by-step explanation:

Unknown value is q.

Solve for the unknown value:

Answer:

[tex]q=19\frac{1}{2}[/tex]

Step-by-step explanation:

Step 1:  Subtract 6 from both sides

[tex]6 + q = 25\frac{1}{2}[/tex]

[tex]6 -6 + q = 25\frac{1}{2}-6[/tex]

[tex]q = (25-6)\frac{1}{2}[/tex]

[tex]q=19\frac{1}{2}[/tex]

Answer:  [tex]q=19\frac{1}{2}[/tex]

Hope this helps!  Let me know if you have any questions

Answer:

its 1/8

Step-by-step explanation:

he said 1/3 it does not match the other 2 numbers hope its right ;-; also helpfull

Answer:

Your answer is B

Step-by-step explanation:

6.14 Checkpoint: Systems of Linear Inequalities

I took the test.

Answer:

a) below

b) log_35 (8) = x

c) x = 0.58487

Step-by-step explanation:

a) 35^x=8

apply the exponent rule

xln(35) = ln(8) → x = ln(8)/ln(35) → x = 3ln(2)/ln(35)

x = 0.58487

c) log_35 (8) = x

x = log_35 (8)

base form (Rewrite 8 in power)

x = log_35 (2^3)

log rule: log_a(x^b) = b*log_a(x)

log_35 (2^3) = 3log_35(2)

x = 3log_35(2)

x = 0.58487

Answer:

$1.35

Step-by-step explanation:

8n = 10.80

Divide both sides by 8 to get n alone.

n = 10.80/8 = $1.35

Answer: 1344g

Step-by-step explanation:

if 1 ounce = 28 grams and we have 48 ounces,

multiply 48 by 28 to find the amount of grams

48×28 = 1344g

Length of the rectangle is 8 units

Step-by-step explanation:

Area of the rectangle = 48 units

Length = x + 2

⇒ Area = Length × Breadth

48 = x (x + 2)

48 = x² + 2x

x² + 2x - 48 = 0

x² + 8x - 6x + 48 = 0 (Product Sum rule to factorise)

x(x + 8) - 6(x + 8) = 0

(x - 6)(x + 8) = 0

⇒ x = 6, -8 (negative value is neglected)

∴ x = 6

x + 2 = 8

Answer:

steps below

Step-by-step explanation:

(a) first green: 8/23 AND 2nd green: 7/22

AND: multiplication.. 8/23 x 7/22 = 28/253 ≈ 0.11 (11%)

(b) 15/23 x 8/22

[tex]\\ \rm\Rrightarrow (2x^2)^3.2yx^0=8x^6.2y=16x^6y[/tex]

[tex]\\ \rm\Rrightarrow (2x^4y^3)^3.2x^4y^4=8x^{12}y^6.2x^4y^4=16x^{16}y^{10}[/tex]

[tex]\\ \rm\Rrightarrow (m^3n^0(2m^3n^2)^4)^2=(m^316m^{12}n^8)^2=(16m^{15}n^8)^2=256m^{30}n^{16}[/tex]

[tex]\\ \rm\Rrightarrow (2xy^3)^2.2x^2y^0=4x^2y^6.2x^2=8x^4y^6[/tex]

Answer:

4:25

8:125

Step-by-step explanation:

Surface Ratio is the "Similarity Ratio" to the power of 2

Volume Ratio is the "Similarity Ratio" to the power of 3

It's logical and deductable by paying attention to the correlation between the "Side"s(or "Diameter"s) and the "Surface" and the "Volume"s in simple shapes like Circles and square.

By paying attention to the formula of the "Surface Area" and the "Volume" or the m /m^2 /m^3 ( the units of measurement) we can easily notice the relation.

Answer:

The graph of g(x) is shifted up 2 units.

Answer:

area: 105.3

perimeter: 66.7

Step-by-step explanation:

area: 13*16.2/2 = 105.3            formula S = B*H

perimeter: 31+16.2+19.5 = 66.7      

Answers:  

k = -3.5

Intersection point is (0.5, -2.5)

================================================

Explanation:

Apply the derivative to y=2x^2-3 and you should get dy/dx = 4x

The derivative helps determine the slope of the tangent at any point on the curve.

The slope of the tangent line y = 2x+k is 2.

We want the slope of the tangent to be 2, so we'll replace the dy/dx with 2 and solve for x.

dy/dx = 4x

2 = 4x

x = 2/4

x = 0.5

Plug this into the curve's original equation.

y = 2x^2 - 3

y = 2(0.5)^2 - 3

y = -2.5

Therefore, the tangent line y = 2x+k and the curve y = 2x^2-3 intersect at the point (0.5, -2.5). This is the point of tangency.

We'll use the coordinates of this point to determine k.

y = 2x+k

-2.5 = 2(0.5) + k

-2.5 = 1 + k

k = -2.5-1

k = -3.5

Visual verification is shown below. I used GeoGebra to make the graph, but you could use any other tool you prefer (such as Desmos).

Answer:

9 ft tall.

Step-by-step explanation:

The box that is 3 feet tall casts a 6 foot shadow, which is double the height. If we use inverse operations because we start with the shadow we will get 9 feet because 18 divided by 2 is nine.

The equation of the ellipse formed is x²/11.7² + y²/12² = 1

The formula for calculating the equation of an ellipse is expressed as;

x²/a² + y²/b² = 1

where

a and b are the minor an major axis respectively;

Given the following

b = 12

e = 0.5

Determine the value of a

e² = √b²-a²/b

0.5² = √12²-a²/12
12 * 0.25 = √144-a²

9 = 144 -  a²

a² = 136

a = 11.7

Substitute into the fomula

x²/11.7² + y²/12² = 1

Hence the equation of the ellipse formed is x²/11.7² + y²/12² = 1

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Answer:

A

Step-by-step explanation:

In this problem you'd simply distribute the 10. So 10x15 and 10*n

150+10n

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

[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]

       What is 10(15+n) equal to?

[tex]\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]

Multiply 10 times 15:-

150

Multiply 10 times n:-

10n

Add the terms:-

150+10n

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

Answer:

3/2

Step-by-step explanation:

[tex] {x}^{3} = \frac{27}{8} [/tex]

[tex] x = \sqrt[3]{ \frac{27}{8} } = \frac{3}{2} [/tex]

Answer:

The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .

area triangle:

(1.7m×2m)×2

= 1.7m²

-> 2 triangles so: 1.7m²×2= 3.4m²

area rectangles(walls):

2m×3m

= 6m²

-> 2 walls so: 6m²×2=12m²

area bottom rectangle:

3m×2m=6m²

-> total area:

6m²+12m²+3.4m²= 21.4m²