The manager of a supermarket records the waiting times of 100 customers.
He wishes to calculate an estimate for the mean waiting time.
He draws this table.
Waiting Time
Number of
Midpoint (x)
fx
(minutes)
customers (0)
0 -
0.5
5
2.5
1 -
1.5
28
2 -
2.5
32
3-
3.5
26
4-5
4.5
9
100
a)
Complete the table.

Answer:

m∠a = 50°

Step-by-step explanation:

Since this is an isosceles triangle, we know that the other unknown angle is also 65°. Since all angles in a triangle add up to 180°,

180 - 65(2) = a

a = 180 - 130

a = 50°

Answer:

a = 50

Step-by-step explanation:

In an isosceles triangle, two angles are equal. In this triangle, the base angles are equal.

65 + 65 + a = 180

Angles in a triangle add up to 180 degrees.

130 + a = 180

a = 180 - 130

a = 50

Answer:

48.56 ft

Step-by-step explanation:

==>Given:

A rectangular figure joined with a half circle with the following dimensions:

Length of rectangle (l) = 10ft

Width of rectangle (w) = 8ft

Diameter of the half circle (d) = the width of the rectangle = 8ft

π = 3.14

==>Required:

Perimeter of the figure = perimeter of a rectangle + permimeter of the half circle

==>Solution:

Perimeter of rectangle = 2(l + w)

Perimeter of half circle = ½ of circumference of a circle = ½πd

Perimeter of the figure = 2(10 + 8) + (½*3.14*8)

= 2(18) + (3.14*4)

= 36 + 12.56

Perimeter = 48.56 ft (to the nearest hundredth)

Answer:56.56

Step-by-step explanation:

For the perimeter of a rectangle

P = 2 × (a + b)

P = 2 × (8 + 10)

P = 2 × 18

P = 36

For the perimeter of a semicircle

P = (pi × r) + (2 × r)

Diameter = 8

Radius = 8/2

Radius = 4

P = (3.14 × 4) + (2 × 4)

P = 12.56 + 8

P= 20.56

Perimeter of this figure

P = r + c

P = 36 + 20.56

P = 56.56

Answer:

r = 6.69 inches

Step-by-step explanation:

We have,

Marcus is building a model of Earth using a sphere with a surface area of [tex]400\pi\ \text{inch}^2[/tex].

It is required to find the radius of the sphere Marcus is using for his model.

The surface area of a circular shaped object is given by :

[tex]A=\dfrac{4}{3}\pi r^3[/tex]

r is radius

[tex]r=(\dfrac{3A}{4\pi})^{1/3}\\\\r=(\dfrac{3\times 400\pi}{4\pi})^{1/3}\\\\r=6.69\ \text{inch}[/tex]

So, the radius of the sphere is 6.69 inches.

Answer:

C. 8

Step-by-step explanation:

This then simplifies to (10^1 times 5 ^ -1)cubed. 5^-1 is 1/5, and 10^1 is 10. 10 times 1/5 is 2, and 2^3 is equal to 8.

Answer:

It is proved that 2PQ + 2SR + 2QR + 2 PS = 4(2(OP)+2(OQ))

Step-by-step explanation:

In a rhombus, all sides are equal.

Thus, in this question;

PQ = SR = QR = PS

By inspection, QS is the same dimension as the four sides. So, QS = PQ

Thus, OQ = PQ/2

For OP, we can find it using Pythagoreas theorem since the angle that divides the diagonals is 90°

Thus;

|OP|² + |OQ|² = |PQ|²

Earlier, we saw that;OQ = PQ/2

Thus;

|OP|² + |PQ/2|² = |PQ|²

|OP|² = |PQ|² - |PQ/2|²

|OP|² = |PQ/2|²

Taking square root of both sides, we have;

OP = PQ/2

So,going back to the question, on the right hand side, we have;

4(2(OP) + 2(OQ))

Let's put,

PQ/2 for OQ and OP as gotten earlier

So,

4(2(PQ/2) + 2(PQ/2)) = 4(PQ + PQ)

Since PQ = SR = QR = PS, we can rewrite as;

4PQ + 4PQ = (PQ + SR + QR + PS) + (PQ + SR + QR + PS) = 2PQ + 2SR + 2QR + 2 PS

This is equal to the left hand side, so the equation is proved correct.

Answer:

it is 2/3

Step-by-step explanation:

well i have to do my work but im happy i could help.

Answer:

2/3

Step-by-step explanation:

To figure out this problem, we must find the LCM (Least Common Denominator) which is 15. So now we have 2/3=10/15 and 3/5=9/15.

Since 10>9, 2/3 is greater.

Hope this helps!

Answer:

Step-by-step explanation:

Pattern 6 will have 35

Answer:

[tex]y-3=5(x+1)[/tex]

Step-by-step explanation:

Point-Slope form is: [tex]y-y_1=m(x-x_1)[/tex]

'm' - Slope

(x1, y1) - Point Coordinate

We are given the point of (-1,3) and the slope of 5.

Replace 'm' with 5, 'x1' with -1, and 'y1' with 3:

[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-3=5(x+1)}[/tex]

Answer: yes this statement is true All functions are relations,but not all relations are functions.

Step-by-step explanation:

Its true because if you think of it like this

a function is a output and like the inner circle

and relations is the outer circle.

Hope this helps :)

Answer:

The answer is "64".

Step-by-step explanation:

Given:

8-sided fair die

output of Die = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

if the Dice is thrown two times. so, the possible outputs are as follows:

[tex]\to 8 \times 8=64[/tex]

[tex]\texttt{ = (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),}\\ \ \ \texttt{(1,7),( 1, 8),(2,1),(2,2),(2,3),(2,4),}[/tex]

[tex]\texttt{(2,5),(2,6),(2,7),(2,8),(3,1), (3,2),}\\ \texttt{(3,3),(3,4),(3,5),(3,6),(3,7),(3,8) ,}\\\texttt{(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),} \\[/tex]

[tex]\texttt{(4,6),(4,7),(4,8),(5,1),(5,2),(5,3),}\\\texttt{(5,4),(5,5),(5,6),(5,7),(5,8),(6,1),}\\\texttt{(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),}[/tex]

[tex]\texttt{(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),} \\\texttt{(7,6),(7,7),(7,8),(8,1),(8,2),(8,3),}\\ \texttt{(8,4),(8,5),(8,6),(8,7),(8,8)}[/tex]

That's why the product is 64.

Area = length x width

Area = 3x + 5 Cm x 8 cm

Multiply each term by each term.

Area = 24x + 40 square cm

Answer:

[tex](24x+40) \: cm^2[/tex]

Step-by-step explanation:

Area of rectangle is [tex]lw[/tex]

[tex]8 \times (3x+5)[/tex]

The length is (3x+5) cm.

The width is 8 cm.

[tex]8(3x+5)[/tex]

Expand the brackets.

[tex]8(3x)+8(5)[/tex]

[tex]24x+40[/tex]

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2(-3) *2+1

6*2+1

12+1

13

Answer:

- 17

Step-by-step explanation:

Evaluate 1 - 2 x^2 where x = -3:

1 - 2 x^2 = 1 - 2×(-3)^2

Hint: | Evaluate (-3)^2.

(-3)^2 = 9:

1 - 29

Hint: | Multiply -2 and 9 together.

-2×9 = -18:

-18 + 1

Hint: | Subtract 18 from 1.

1 - 18 = -17:

Answer:  -17

Answer:

Jayden took 5 minutes to run 1 kilometre.

Step-by-step explanation:

Jayden runs 1 lap in minutes = 2

We are given that The track is [tex]\frac{2}{5}[/tex] kilometres around.

So, she runs [tex]\frac{2}{5}[/tex] kilometres in minutes = 2

She runs 1 kilometres in minutes =[tex]\frac{2}{\frac{2}{5}}[/tex]

She runs 1 kilometres in minutes =5 minutes

Hence Jayden took 5 minutes to run 1 kilometre.

Answer:

C, rebate

Step-by-step explanation:

Hope this helps!

Answer:

a rebate

Step-by-step explanation:

he bought a product that had a rebate.

Fill out a form, send in receipt from purchase with form and sometimes the bar code from package. In about 4 to 6 weeks you receive rebate.

The exact value of a and b is 5 and 5√3 respectively. Thus option D) is correct

From triangle ABC
We have AB = 10 ; And angle A = 30°

Trigonometry is the branch of mathematics that deal with study of triangles.

Now,
cos30= AC/AB
√3/2=b/10
b=5√3

Sin30 = BC/AB
1/2 = a/10
a = 5

Thus, the required value is a = 5, b = 5√3

Learn more about trigonometry here:

brainly.com/question/22624805

#SPJ2

Answer:

its the last option

Step-by-step explanation:



Answer:

4 : 1 or 4 times

Step-by-step explanation:

V of sphere is

V = 4/3 π r³

then we can compare both of them dirextly

Vs : Vhs

4/3 π r³ : ½ (4/3 π (2r)³)

4/3 π r³ : ½ * 4/3 π 8r³

1 : ½ * 8

1 : 4

Vhs : Vs = 4 : 1

so the volume of hemisphere is 4 times bigger than the sphere.

Answer:

It is greater than the volume of the sphere.

Step-by-step explanation:

imagine math :D

Answer:

Same-side interior angles

x = -5

Step-by-step explanation:

Since the transversal already perpendicular bisects both parallel lines, x + 95 is set to 90. Therefore, you get -5 for x.

Answer:

the relationship is transversal

Step-by-step explanation:

The red box means 90 degrees

therefore since the relationship is transversal

x + 95 =90

x = 90-95

x = -5

Options

Answer:

(A)He can say the radius of the base of the tank is approximately 13 feet.

Step-by-step explanation:

If the distance around the tank is 82.1 feet, it means that:

The circumference of the circular cross-section of the tank =82.1 feet

Circumference of a Circle [tex]=2\pi r[/tex]

[tex]2\pi r=82.1\\r=\dfrac{82.1}{2\pi}\\\\r=13.07$ feet[/tex]

Therefore, Jordan can say that the radius of the base of the tank is approximately 13 feet.

Answer:

a

a

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a

its a

Step-by-step explanation:

Answer:

13.3

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

AM             AN

---------- = ------------

AM+AB          AC

6             8

---------- = ------------

6+4          AC

Using cross products

6AC = 8 * 10

6AC = 80

Divide by 6

AC = 80/6

AC =13 1/3

AC = 13.33333

Answer:

11

Step-by-step explanation:

add

Answer:

-2²

Explanation:

Doing -k² is the same thing as -(k²), so the answer will be negative. However, (-k)² will still be positive. -2² will equal -4.

Answer:

The width is 5/2 = 2.5 cm

The length is 9/2 = 4.5cm

Step-by-step explanation:

The length is 2 longer than the width

l = w+2

The perimeter is 14

P =2 ( l+w)

14 = 2 (l+w)

Replace l with w+2

14 = 2 ( w+2+w)

14 =2 (2w+2)

Divide each side by 2

14/2 = 2/2(2w+2)

7 = 2w+2

Subtract 2

7-2 = 2w+2-2

5 = 2w

Divide by 2

5/2 = w

The length is w+2

5/2+2

5/2+4/2 = 9/2

The width is 5/2 = 2.5

The length is 9/2 = 4.5

Answer:

The area of the now-enlarged shape quadruples. The units are the same; square units.

Step-by-step explanation:

The diagram of the structure isn't provided. But, we can work on a generalized principle for enlargement or reduction.

When a shape is enlarged by a scale factor of 2, it means all of its lengths are increased according to that scale facfor (doubled).

Whatever the shape of the figure was, by enlarging it by a scale factor of 2, all of its dimensions become doubled, and as area is a product of dimensions, two dimensions to be precise, the Area of the object increases by a scale of 4.

For example, if the shape was a rectangle.

A = L × B

When enlarged, new L = 2L, new B = 2B

new Area = new L × new B = 2L × 2B = 4LB = 4 × old area.

A circle

A = πr²

When enlarged, new R = 2r

new Area = π(new R)² = π(2r)² = 4πr² = 4 × old area.

Whatever the original shape was, when it is enlarged by a scale factor of 2, the Area if the new enlarged shape is quadruple of the Area of the old shape.

Hope this Helps!!!

Answer:

1

Step-by-step explanation:

=> [tex]\sqrt[3]{1}[/tex]

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

=> [tex]\sqrt[3]{1^3}[/tex]

=> 1

Answer:

The probability of a sure event is 1.

Answer:

draw a table and calculate the x axis and find the x intercept

Step-by-step explanation:

Answer:

The correct answer is ..

(-1,-2)

Step-by-step explanation:

First, you reflect over the x-axis and get (1,-2) then reflect over the y- axis and the point will be on (-1,-2)

Hope this helps!

- Quinn <3

Answer:

The probability of a customer buying carrots is 5 percent.

Step-by-step explanation:

Given that the grocery store manager reports that there is a 12% chance that the consumer will buy apples during their stay in the store, a 5% chance that they will buy apples and carrots, and a 17% chance that they will buy apples. or carrots, to determine the chances that this consumer buys only carrots we must make the following reasoning:

-Since there is a 12% probability of buying apples, and 17% of buying apples or carrots, the difference between the two should be the probability of people buying carrots only: that probability would be 5%, which in turn it is the percentage of chances that the consumer buys both vegetables.

Therefore, the chances of a consumer buying carrots at the store is 5%.

Answer:

C. 10.0 percent

Step-by-step explanation:

P(A) = 0.12

P(A\cap C)=0.05

P(A\cup C)=0.17=P(A)+P(C)-P(A\cap C)

0.17=0.12+P(C)-0.05

P(C)=0.17-0.12+0.05=0.10

Answer:

100%

Step-by-step explanation:

25/25=100%

Answer:

(0, - 5 ) and (2, - 1 )

Step-by-step explanation:

Given the 2 equations

y = 2x - 5 → (1)

y = x² - 5 → (2)

Substitute y = x² - 5 into (1)

x² - 5 = 2x - 5 ( subtract 2x - 5 from both sides )

x² - 2x = 0 ← factor out x from each term

x(x - 2) = 0

Equate each factor to zero and solve for x

x = 0

x - 2 = 0 ⇒ x = 2

Substitute these values into (1) for corresponding values of y

x = 0 : y = 2(0) - 5 = 0 - 5 = - 5 ⇒ (0, - 5 )

x = 2 : y = 2(2) - 5 = 4 - 5 = - 1 ⇒ (2, - 1 )

Answer:

y=2x-5 ......... 1

y = x² - 5 ......... 2

Substitute equation 1 into equation 2

You'll get

2x - 5 = x ² - 5

x² - 2x = -5 + 5

x² - 2x = 0

Factorize

x ( x - 2 ) = 0

x = 0 x = 2

Now put the values of x into any of the equation

When x = 0

y = 2(0) - 5

y = 5

When x = 2

y = 2(2) - 5

y = 4 - 5

y = -1

When x = 0 y = - 5

When x = 2 y = - 1

Hope this helps

Answer:

465

Step-by-step explanation:

Of means multiply

310% * 150

Change to decimal form

3.10 * 150

465

Answer:

465

Step-by-step explanation:

1 percent of 150 is 1.5.

Multiply 1.5 by 310 to 465