Lesson 4.02
A grocery store finds that the number of boxes of a new cereal sold increases each week. In the 1st week,
32 boxes of the cereal were sold. In the 2nd week, 56 boxes of the cereal were sold and in the 3rd week 80
boxes of the cereal were sold. The number of boxes of cereal sold each week represents an arithmetic
sequence.
A) State the explicit rule for the arithmetic sequence that defines the number of boxes of cereal sold in
week n.
B) Use this rule to calculate how many boxes of cereal will be sold during the 12th week.

radius r = 2 in

height h = 3 in

slant height s = 3.60555128 in

volume V = 12.5663706 in3

lateral surface area L = 22.6543468 in2

base surface area B = 12.5663706 in2

total surface area A = 35.2207174 in2

In Terms of Pi π

volume V = 4 π in3

lateral surface area L = 7.21110255 π in2

base surface area B = 4 π in2

total surface area A = 11.2111026 π in2

Answer:

For all of these triangles apply the formula;

A = BH x 1/2

Where 'B' represents the base, 'H' stands for the height, and 1/2 just means to divide the product of the two lengths (base x height) by 2.

1.

Base = 9.1

Height = 31.2

Plug into formula:

A = BH x 1/2

A = 9.1(31.2) x 1/2

A = 283.92 x 1/2

A = 283.92/2

A = 141.96 square centimetres.

2.

Base = 5

Height = 3 3/4 which can be considered 3.75

Plug into formula:

A = BH x 1/2

A = 5(3.75) x 1/2

A = 18.75 x 1/2

A = 18.75/2

A = 9.375 square kilometres.

3.

Base = 2.4

Height = 3.2

Plug into formula:

A = BH x 1/2

A = 2.4(3.2) x 1/2

A = 7.68 x 1/2

A = 7.68/2

A = 3.84 square inches.

4.

Base = 11

Height = 60

Plug into formula:

A = BH x 1/2

A = 11(60) x 1/2

A = 660 x 1/2

A = 660/2

A = 330 square millimetres.

5.

Base = 10

Height = 13 1/2 which can be considered 13.5

Plug into formula:

A = BH x 1/2

A = 10(13.5) x 1/2

A = 135 x 1/2

A = 135/2

A = 67.5 square feet.

Answer:

1. 141.96 cm²

2. 9⅜ km²

3. 3.84 in

4. 10.39mm

5. 66.67 ft

Step-by-step explanation:

Formula of Area of Triangle : ½ × base × height

1. = ½ × 9.1 × 31.2

= 9.1 × 15.6

= 141.96 cm²

2. = ½ × 3¾ × 5

= ½ × 15/4 × 5

= 15/8 × 5

= 75/8 = 9⅜ km²

3. = ½ × 3.2 × 2.4

= 3.84 in

4. = tan c = AB/BC

c = tan -¹ (AB/BC)

c = tan -¹ (60/11)

c = 79.61

A = 90 - 79.61 = 10.39mm

5. = ½ × 13⅓ × 10ft

= 66.666 ≈ 66.67 ft

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

[tex]( {x}^{2} - 5)( {x}^{2} + 9) = 0 \\ {x}^{2} - 5 = 0 \: \: \: \: \: \: \: \: {x}^{2} + 9 = 0 \\ {x}^{2} = 5 \: \: \: \: \: \: \: \: {x}^{2} = - 9 \\ x = \sqrt{5} \: \: \: \: \: \: \: \: x = \sqrt{ - 9} [/tex]

Answer:

.72x=414

Step-by-step explanation:

Answer:

9/33

Step-by-step explanation:

find the total of people that have attended college (9+12+12 =33)

now go to the number of people that are both college and conservative (9)

The probability that a randomly selected person from this group is conservative, given they have attended college; 9/33

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

Given that table shows differences in political ideology, by education, for a random sample of voters.

To find the total of people that have attended college (9+12+12 =33)

P(conservative attended college) = (Type an integer or a simplified fraction)

To the number of people that are both college and conservative (9)

P(conservative attended college) = 9/33

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ2

Answer:

x = 1

Step-by-step explanation:

[tex] {7}^{(4x - 6)} = \frac{1}{49} \\ \\ \implies {7}^{(4x - 6)} = \frac{1}{ {7}^{2} } \\ \\ \implies {7}^{(4x - 6)} = {7}^{ - 2} \\ \\ \implies \: 4x - 6 = - 2 \\ \\ \implies \: 4x = 6 - 2 \\ \\ \implies \: 4x = 4 \\ \\ \implies \: x = \frac{4}{4} \\ \\ \implies \: x = 1[/tex]

Answer:

x = 1

Step-by-step explanation:

Using Definition of Logarithm

7 ^(4x−6) = 1/49

​Use the rules of exponents and logarithms to solve the equation.

7 ^(4x−6) = 1/49

​Take the logarithm of both sides of the equation.

log(7^4x-6) = log(1/49)

The logarithm of a number raised to a power is the power times the logarithm of the number.

(4x-6)log(7) = log(1/49)

Divide both sides by log(7).

4x-6 = log(1/49)/log(7)

​By the change-of-base formula log(a)/log(b) = log(small b under) (a).

4x-6 = log(small 7 under) (1/49)

Add 6 to both sides of the equation.

4x=−2−(−6)

Divide both sides by 4.

x = 4/4 which is the same as x = 1

​

Answer:

1, -5

Step-by-step explanation:

you can this solve easily

3 - -1 = 4 units down from y = -1

x does not change in this reflection

Answer:

the answer is

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

1. 91/5 + 112/5 + 201/5

2. denominators are the same

3. 404/5

The surface area of the hexagonal pyramid is the amount of space on it

The given parameters are:

This is calculated using:

V = 1/3Bh

So, we have:

V = 1/3 * 41.5 * 6

Evaluate the product

V = 83

Hence, the volume of the pyramid is 83 cubic centimeters

This is calculated using:

S = L + B

Given that:

A hexagonal pyramid has 6 lateral sides.

So, we have:

S = 6 * 14 + 41.5

Evaluate

S = 125.5

Hence, the surface area is 125.5 square centimeters

Read more about areas and volumes at:

https://brainly.com/question/1972490

The first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.

For a quadratic function of the form [tex]y = ax^2 + bx + c[/tex], its vertex form is obtained as:

[tex]y = ax^2 + bx + c\\y =a(x^2 + bx/a) + c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2 -(b/2a)^2 )+ c\\y = a(x^2 + 2(b/2a)x + (b/2a)^2) -a \times (b/2a)^2 + c\\\\y = a(x+b/2a)^2 - a \times (b/2a)^2 + c[/tex]

For the form [tex]y = a(x-h)^2 + k[/tex], the vertex has coordinates (h, k)

Thus, for the obtained equation [tex]y = a(x+b/2a)^2 - a \times (b/2a)^2 + c[/tex], we get the coordinates of vertex as:

[tex]h = -b/2a[/tex], [tex]k = c - a\times(b/2a)^2[/tex]

Thus, the coordinates of vertex of  [tex]y = ax^2 + bx + c[/tex] is:

[tex](h,k) = (-b/2a, c - a \times (b/2a)^2 )[/tex]

The missing steps of work of Jan'ai are:

[tex]y = 5x^2-20x-25[/tex]

[tex]y = 5(-2)^2-20(-2)-25[/tex]

[tex]y = 35[/tex]

so (-2,35) is the coordinate of the vertex, which denotes the minimum.

So, as we see, in the 5th step, Jan'ai had the quadratic function [tex]f(x) = 5x^2-20x-25[/tex],

Comparing this to [tex]f(x) = ax^2 + bx + c[/tex], we get a = 5, b = -20, c = -25

The vertex's x-coordinate will be on -b/2a = -(-20)/ 2(5) = 20/10 = 2

But Jan'ai didn't putted that negative sign before b. in the 6th step.

Thus, the first error in Jan'ai's work in determining the considered function is given by: Option D: She incorrectly determined the x-coordinate of the vertex.

Learn more about the vertex form of a quadratic equation here:

https://brainly.com/question/9912128

Answer:

The answer is D on edge

Step-by-step explanation:

Answer:

a. 1710 b. 71.25

Step-by-step explanation:

the formula for simple interest is i=prt

2(9500)(0.09)= 1710

to find the monthly payment, divide by the number of months.

1710/24=71.25

Answer:

400 ft^3

Step-by-step explanation:

To find volume you simply do length x width x height

So, 10 x 8 x 5 which equals 400 ft; We make it have a power of 3 (cubed) because it is 3 dimentional object.

Hope this helps!

Answer:

B

Step-by-step explanation:

20 × 2/5 = 8

15 × 2/5 = 6

5 × 2/5 = 2

p/s : the pic is for question no 7. i thought that you want the number 7 so i solved it first. then i reread your question. then i realized u actually want number six. so...

yeah, your welcome :)

Answer:

Top is straight

Middle is reflex

Bottom is acute

Step-by-step explanation:

Straight is self explanatory

Reflex angles are greater than 180 and less than 360 degrees

Acute angles are under 90 degrees

Answer:

the very top one is straight.

8. reflex (because over 180 degrees)

9. acute (under 90 degrees)

Answer:

5x²+3x+4

Step-by-step explanation:

(2x²+x+3)+(3x²+2x+1)

add 2x² and 3x² since they're like terms

5x²+x+3+2x+1

add 2x and x = 3x

5x²+3x+3+1

add 3 and 1 = 4

5x²+3x+4

The midpoint of the coordinate pq is (-7.5, -5.5) while the distance between the two coordinate points is 5√2

The midpoint of a line is the coordinate point that divides the coordinates into two equal parts.

The formula for calculating the midpoint is expressed as:

[tex]m(x,y)=(\frac{x_1+x_1}{2} ,\frac{y_1+y_2}{2} )[/tex]

Given the coordinate points p(-10, -8) and (-5, -3).

Calculate the midpoint of pq

[tex]m(x,y)=(\frac{-10-5}{2} ,\frac{-8-3}{2} )\\m(x,y)=(\frac{-15}{2} ,\frac{-11}{2} )\\m(x,y)=(-7.5,-5.5)[/tex]

Hence the midpoint of the coordinate pq is (-7.5, -5.5)

Determine the distance pq

pq = √(-3+8)²+(-5+10)²

pq = √(5)²+(5)²

pq = √50

pq = 5√2

Hence the distance between the point pq is 5√2

Learn more on midpoint and distance here: https://brainly.com/question/17498679

Answer:

E

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

the reason is, for a direct relation between x and z we have too little information.

z could be huge, much, much bigger than y and x, or just bigger by 1 than y.

so, assume e.g. the following 2 scenarios

z = 6

y = 5

x = 4

and

z = 600

y = 26

x = 3

A

x + y > z

is true for the first scenario, but not for the second. so, it is not always true.

B

z - x < z - y

no you subtract something smaller, so the result is bigger. this is not true for any of the scenarios.

C

xz > yz

no, z is the same part in both sides, and when it gets multiplied by something smaller, the result is smaller. this is not true for any of the scenarios.

D

z/x < z/y

no, again z is the same part in both sides, and when it gets divided by something smaller, the result is bigger. this is not true for any of the scenarios.

E

yz > xy

in this case y is the same part on both sides. when it gets multiplied by something bigger, the result will be bigger. so, this is true in all cases.

Answer:

[tex](x-6)^{2} +(y-7)^{2} =81[/tex]

Step-by-step explanation:

The general equation for a circle is

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex] where (h,k) is the center of the circle and r is the radius

Plug in the (6,7) for the center and 9 for r

Answer: The answer is 13, read on to find out

Step-by-step explanation: The traingles are simliar so the values are similar as well. Find a lowest common factor of the values.

The lowest common factor is 4 because all the numbers can be divided by the number 4.

20 divided by 4 is 5 which is already shown on the graph

48 divided by 4 is 12

All we have to do now is 52 divided by 4

Hope I helped you answer the question! Have a great day/afternoon!

Answer:

3

Step-by-step explanation:

the absolute value function always returns a positive value , that is

| - a | = | a | = a

given

- 10 - | 5 - 12 | + 3 + | 5 + 12 |

= - 10 - | - 7 | + 3 + | 17 |

= - 10 - 7 + 3 + 17

= 3

Answer:

the area of triangle formula is A = B*H  / 2

so it means 16 square = (x+4) x /2

so x²+4x -32=0, D' = 2²- (-32)= 36, sqrt of D' = 6

so x = -2 -6 = -8 or x= -2 +6 = 4

x must be positive so x = 4

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

each part of circle are divided into 360

Answer:

The answer is 100 in

Step-by-step explanation:

The pythagorean theorm states that, for any right triangle where a and b are the legs and c is the hypotenuse, a^2 + b^2 = c^2. So, we can substitute and solve.

18^2 + 26^ 2 = c^2

324 + 676 = c^2

1000=c^2

Square root of 1000 = c

100.0=c

Hope this helps!

Answer:

if youre doing this on paper use a protractor

Step-by-step explanation:

place the straight line ontop of the side you're trying to read the angle from and go in a clockwise direction when using the compass until you find the angle degree.  hope that helps:-)

Answer:

4 mg

Step-by-step explanation:

Plug in everything that they have given for the equation

since x is the number of half-lives, and iodine-131 has a half-life of 8, and the question is asking for how much there will be left after 32 days, 8 * 4 = 32, so x will be 4.

y = 64(0.5)^4

and solve

y = 4

so there will be 4 mg of iodine-131 left after 32 days.

Answer:

4 mg

Step-by-step explanation:

half- life is 8 days then 32 ÷ 8 = 4 half- lives , then

y = 64 [tex](0.5)^{4}[/tex] = 64 × 0.0625 = 4 mg left

Answer:

18 plus 5 plus 17 gives 40 therefore ; p is eq 23/40

Answer:

11$

Step-by-step explanation:

20% is equivalent to 0.20, so if we multiply that by 55, it will take off 20% of the price, giving us 11$.

0.20 × 55 = 11

Brainliest please?

Answer: ✨$75✨

Step-by-step explanation: ✨Well I added them I hope this helps✨

Answer:

188

Step-by-step explanation:

25(7)-(-13)

=175 - 1(-13)

=188

Answer: 4(3)^w = 972

Answer:

(3x+50)°=(6x-10)°

3x-6x= -10°-50°

-3x/-3 = -60/-3

x=20