How much grain can this container hold?

Answer:

Part A

aₙ = 5 + (n - 1)·4

Part B

y = 4·x + 1

Step-by-step explanation:

Part A

The number of orange blocks in Figure 1 = 5

The number of orange blocks in Figure 2 = 9

The number of orange blocks in Figure 3 = 13

Therefore, we get;

5, 9, 13, ... with increments of 4

The first term, a = 5

The common difference, d = 4

The sequence is in the form of an Arithmetic Progression, therefore, we have;

aₙ = 5 + (n - 1)·4

Where;

n = The Figure number

When n = 3, we have;

a₃ = 5 + (3 - 1) × 4 = 12 orange blocks as in the diagram in the question

Part B

To express the number of blocks using the linear function, y = m·x + b, we have;

Let 'x', represent the number of each figure, let 'y' represent the total number of blocks in each figure, let 'd' represent the initial amount of blocks present when x = 0, and let 'm' represent the rate of  change of 'y' with each change in 'x'

We note that the rate of change the total number of blocks for each increase in figure number is 4, therefore, we have;

The rate of change, m = 4

∴ y = 4·x + d

When x = 1, y = 5, we get;

5 = 4 × 1 + d

∴ d = 5 - 4 = 1

d = 1

The linear equation that gives the number of blocks is therefore;

y = 4·x + 1.

Answer:

the answer is (0,-1)

Step-by-step explanation:

The Midpoint of G(1,3) and H(2,1)= (3/2, 2)

The midpoint of J(-1,-5) and K(-2,-3)= (-3/2, -4)

The midpoint of both (3/2 ,2) and (-3/2, -4)= (0,-1)

Answer:

B: 0.75

Step-by-step explanation:

Edge

Answer:

.75

Step-by-step explanation:

Unit Test

Answer:

-58

Step-by-step explanation:

We are to find tfhe dot product of u=<-8,9> and v=<5,-2>

u*v = <-8,9>*<5,-2>

u*v = -8(5)+9(-2)

u*v = -40 - 18

u*v = -58

Hence the product of the vectors is -58

Answer:

A. shifted 4 units left and 3 units up.

Step-by-step explanation:

Answer:

A. because its a short sentence but also asking people who read the story if they relate which means they are gonna want to know what the book is about if they babysat before

Step-by-step explanation:

Answer:

[tex](a)\ t = -2.146[/tex]

The null hypothesis is rejected

[tex](b)\ t = 2.014[/tex]

The null hypothesis is accepted

[tex](c)\ t = 2.128[/tex]

The null hypothesis is accepted

[tex](d)\ t = -2.146[/tex]

The null hypothesis is rejected

Step-by-step explanation:

Given

[Missing from the question]

[tex]\alpha = -1.001[/tex] --- critical value

Left tailed test

Required

State what the standardized test statistics indicates

Since it is a left-tailed test, the null hypothesis will be rejected if the standardized test statistics less than or equal to the critical value

Using the above rule, we have:

[tex](a)\ t = -2.146[/tex]

Compare t and [tex]\alpha[/tex]

[tex]-2.146 < -1.001[/tex]

The null hypothesis is rejected

[tex](b)\ t = 2.014[/tex]

Compare t and [tex]\alpha[/tex]

[tex]2.014> -1.001[/tex]

The null hypothesis is accepted

[tex](c)\ t = 2.128[/tex]

Compare t and [tex]\alpha[/tex]

[tex]2.128> -1.001[/tex]

The null hypothesis is accepted

[tex](d)\ t = -2.146[/tex]

Compare t and [tex]\alpha[/tex]

[tex]-2.146 < -1.001[/tex]

The null hypothesis is rejected

Answer:

C

Step-by-step explanation:

i am smart

Answer:

3 : 1

Step-by-step explanation:

A jewellery shop sells 240 necklaces in a month 180 of the necklaces were sold via the shop website work out the simplest form. The rest were sold in a High Street shop.

Work out the ratio of online sales to shop sales.

Give your answer in its simplest form.

Necklace sold in the shop = 240 - 180 = 60

180 : 60

to convert to simplest form, divide both numbers by 60

3 : 1

Answer:

18 days later.

Step-by-step explanation:

Rick would have gone to the supermarket twice, and Natalie would have gone three times.

oof oof oof oof oof oof

Answer:

people couldn't survive and thrive without groundwater

Answer:

F=-9

Hope This Helps!

Answer:

A = 5 units²

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂

d₁ = x + 4 = 1 + 4 = 5

d₂ = 2y - 4 = 2(3) - 4 = 6 - 4 = 2 , then

A = [tex]\frac{1}{2}[/tex] × 5 × 2 = 5 units²

Answer:

A= 5m

Step-by-step explanation:

The equation to find the area of a rhombus, when knowing the diagonals, is:

To solve this, we have to find first d1 and d2, which are marked in a parenthesis:

d1= 5m. Now, let's find d2:

Knowing the values of both diameters, we can solve the equation for the area:

The area of the rhombus is 5 meters.

Hope it helps!!

Answer:

25 miles

Step-by-step explanation:

At 1 p.m. the maximum travel distance is reached.  This is 25 miles.

Answer:

a) I donot agree with him because as we see the sequence nicely we will find an interval of 8 between any two terms and 32 and 33 don't match them

Step-by-step explanation:

b) and c) Solution:

Given,

First term (a) = 4

Common difference (d) = 12-4 = 8

Now,

Since, they are in A.P.

nth term = a + (n-1)d

              = 4 + 8(n-1)

              = 4 + 8n-8

              = 8n-4

Again,

1st method for c)

100th term = a + 99d = 4 + 99*8 = 4 + 792 = 796

200th term = a + 199d = 4 + 199*8 = 4 + 1592 = 1596

2nd method for c)

100th term = 8*100 - 4 = 800 - 4 = 796

200th term = 8*200 - 4 = 1600 - 4 = 1596

Answer:

-3.3125[tex]\frac{-10.125-(-3.5)}{4-2} =\frac{-6.625}{2} = -3.3125[/tex]

Step-by-step explanation:

Average rate of change is the slope between two points.

Slope getween points  [tex]\left(x_1,\,y_1\right)[/tex]  and  [tex]\left(x_2,\,y_2\right)[/tex]  is  [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Using the points (2, -3.5) and (4, -10.125), the slope is

Answer:

I think B .......................................

Answer:

in the first box put k-15=33

in the second box put k=48

Step-by-step explanation:

if you look at what it says, it says 33 is 15 less than k. so we know that we are going to have 33 on one side and k and 15 on the other. it also says 15 less than k, so that would be k-15

33=k-15 or k-15=33

now we have to solve this. add 15 to each side to cancel out the -15

that gives you k=48

Answer:

Solution given:Angle JKL and angle MKQ are complementary angles. The measure of angle JKL is twice the measure of angle MKQ

<JKL=2<MKQ

we have

<JKl+<MKQ=90°[complementary]

2<MKQ+<MKQ=90°

3<MKQ=90°

<MKQ=90°/3=30°

and <JkL=2×<MKQ=2×30°=60°

Answer:

Divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle to determine the scale factor for the smaller triangle to the bigger triangle.

Answer:

$405

Step-by-step explanation:

This is a proportion problem!

Build fractions that have euros on top and dollars on the bottom (or the other way around, you decide, but make it the same in both fractions).

Let's do euros over dollars.

Setup:

[tex]\frac{200}{270}=\frac{300}{d}[/tex]

"Cross multiply."

[tex]200d=300\times 270\\\\200d=81000\\\\d=\frac{81000}{200}=405[/tex]

Answer:

$45

y = 45x + 15

Step-by-step explanation:

Given :

Days Total Cost

(d) (C)

2. $105

4 $195

6 $285

10 $465

The daily rate is the slope :

Slope = Rise / Run

Slope = (y2 - y1) / (x2 - x1)

Slope = (465 - 105) / (10 - 2)

Slope = 360 / 8

Slope = 45

Daily rate = $45

Using the slope intercept relation :

y = mx + c

m = slope, c = intercept

105 = 45x + c

105 = 45(2) + c

105 = 90 + c

105 - 90 = c

15 = c

Pricing plan :

y = 45x + 15

Answer is 45 because if you divide 90/2 it equal 45

C=45d+15

Answer:

13%

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 13% as you convert 2 3/5 to an improper fraction which is 13/5. Convert this into a decimal which is 2.6 . 2.6 ÷20=0.13 ×100 (to get it as a fraction) which equals 13%.

hope this helps,have a great day!!

~Pinky~

Answer:

see explanation

Step-by-step explanation:

The length of the arc is calculated as

AB = circumference of circle × fraction of circle

(11)

AB = 2πr × [tex]\frac{90}{360}[/tex]

     = 2π × 7 × [tex]\frac{9}{36}[/tex]

     = 14π × [tex]\frac{1}{4}[/tex]

     = [tex]\frac{7}{2}[/tex] π in

(12)

AB = 2πr × [tex]\frac{135}{360}[/tex] ( r = 20 ÷ 2 = 10 )

      = 2π × 10 × [tex]\frac{3}{8}[/tex]

      = 20π × [tex]\frac{3}{8}[/tex]

      = [tex]\frac{60}{8}[/tex] π

      = [tex]\frac{15}{2}[/tex] π cm

Answer:

Step-by-step explanation:

Question 3 Reflects over x acis

Question 5 reflects over y axis

Answer:

i think 3 is reflected across the x and 5 is reflected across the y axis