Find all points having an x- coordinator of 5 whose distance from the point (-1,-3) is 10. (type an ordered pair. Use a comma to separate answers as needed.)

Answers

Answer 1

Answer:

(5,5) and (5,-11)

Step-by-step explanation:

You can find this out by plotting a circle with the diameter of 10 on the point "(-1,-3)". Then find all the times the circle is on the x axis of 5.

Answer 2

Answer:

so when the mughal emperor humayun had died akbar his son was put as kind of india he was 10 yearls old when his father died and then Bairam Khan was elected as a regent for Akbar.

Step-by-step explanation:


Related Questions

You are planning to use a tile design in your new room. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 11 cm, what will be the exact area of each hexagonal shape? A. 3,993 cm^2 B. 181.5 root 3 cm^2 C. 132 root 3 cm^2 D. 33 cm^2

Answers

Answer:

  B.  181.5√3 cm^2

Step-by-step explanation:

The area of a regular hexagon with side length s is given by ...

  A = (3√3/2)s²

For side length s = 11 cm, the area is ...

  A = (3√3/2)(11 cm)² = 363√3/2 cm²

  A = 181.5√3 cm²

bahhahaha I like math

Find the total surface area of this square based
pyramid.
10 in
5 in

Answers

Answer:

  125 in²

Step-by-step explanation:

Each triangular face has a base of 5 in and a height of 10 in. The area of it is given by the formula ...

  A = (1/2)bh

  A = (1/2)(5 in)(10 in) = 25 in²

The square base has an area given by the formula ...

  A = s² . . . . . where s is the side length

  A = (5 in)² = 25 in²

The total area is the sum of the areas of the 4 faces and the base:

  total area = 4 × (area of 1 face) + (area of base)

  total area = 4 × (25 in²) + 25 in²

  total area = 125 in²

Answer: The Surface Area is 125 in^

Step-by-step explanation:

Surface area = 4 × (area of 1 face) + (area of base)

total area = 4 × (25 in²) + 25 in²

Surface area = 125 in²

PLEASE HELP WILL GIVE BRAINLY!!!!!!!
Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options.
A) q= 5/5
B) q= -5/5
C) q= 3/5
D) q= -3/5
E) q= 25/5

Answers

Answer:

q = -5[tex]\sqrt{5}[/tex]

q = 5[tex]\sqrt{5}[/tex]

Step-by-step explanation:

Since there is no constant value. This must be a special case.

So,

(q+5[tex]\sqrt{5}[/tex])(q-5[tex]\sqrt{5}[/tex])

q = -5[tex]\sqrt{5}[/tex]

q = 5[tex]\sqrt{5}[/tex]

Yeah I’m gonna have to agree with that one

Complete the statement. The line x = −2 is _______.

Answers

Answer:

see explanation

Step-by-step explanation:

The line x = - 2

Is a vertical line parallel to the y- axis

It passes through all points with an x- coordinate of - 2

Is a vertical line to the y-axis

Simplify: 15 7/12 x−9 1/3 x

Answers

I think it Should be 6.25x or 25/4x
6.25x would be the correct answer

Find the value of x.
X
10
A. 52
B. 10/2
C. 512
D. 5
А
В

URGENT

Answers

[tex] \huge{ \bold{ \bigstar \: pythagoras \bigstar}}[/tex]

Pythagoras :

[tex] {10}^{2} = {x}^{2} + {x}^{2} [/tex]

[tex]100 = 2{x}^{2}[/tex]

[tex]100 \div 2 = {x}^{2} [/tex]

[tex]50 = {x}^{2} [/tex]

[tex]x = \sqrt{50} [/tex]

[tex]x = \sqrt{25 \times 2} [/tex]

[tex] \red{x = 5 \sqrt{2} }[/tex]

Answer:

Step-by-step explanation:

Compare this to a similar figure with hypotenuse √2 and leg lengths all 1.

Write and solve an equation of ratios, as follows:

  x        10

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

  1        √2

              10√2

'then x = --------  =  5√2

                  2

                                       

A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold

Answers

Answer:

31 Pikachu bags were sold.

19 peanut bags were sold.

Step-by-step explanation:

Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.

We know that the number of Peanuts sold is 50-x (as the total needs to be 50)

We know that the total revenue is:

Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts

Using our definitions above:

Total Revenue = x * $3.68 + (50-x) * $0.76

We know that the revenue needs to be $128.52.

$128.52 = x * $3.68 + (50-x) * $0.76

Let's remove the $ signs.

128.52 = x * 3.68 + (50-x) * 0.76

Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.

128.52 = x*3.68 + 50*0.76 - x*0.76

128.52 = x*3.68 + 38 - 0.76*x

Subtracting 38 from both sides

90.52 = 3.68*x - 0.76*x

We can simplify the right side.

90.52 = 2.92*x

We can divide both sides by 2.92:

31 = x

And flip it:

x = 31

So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is

50-x = 50-31 = 19

31 Pikachu bags were sold.

19 peanut bags were sold.

[tex] \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}[/tex]

Let the number of peanut bags be x

Then, Number of pikachu bags = 50 - x

Given,

Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68

Then,

⇛ Total cost he gets from peanut bag = $0.76 × x

⇛ Total cost he gets from pikachu bag = $3.68(50 - x)

According to question,

⇛ $0.76x+ $3.68(50 - x) = $128.52

Solving this equation,

⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)

⇛ 184 - 2.92x = 128.52

⇛ 184 - 128.52 = 2.92x

⇛ 55.48 = 2.92x

Flipping the equation,

⇛ 2.92x = 55.48

⇛ x = 55.48 / 2.92

⇛ x = 19

Then,

⇛ 50 - x = 50 - 19 = 31

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}[/tex]

[tex] \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━

What is the domain of the function shown in the graph below? answer type: interval, all real values except one, all real values except two, all real numbers Interval:

Answers

Answer: the domain is negative infinity to positive infinity

Step-by-step explanation:

the graph covers all x values

The domain function of the graph is that the graph covers all x values

Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle_______ more red bottles than plant A. Plant C would recycle________________ more red bottles than plant D.

Answers

Answer:

70

80

Step-by-step explanation:

Assuming these ratios stay consistent, if each plant recycled 350 total bottles in a day, plant B would recycle___70____ more red bottles than plant A. Plant C would recycle_____80___________ more red bottles than plant D.

A = We first multiply 150 x 2.333 (2 1/3)  = 350 tbottles 60 x 2.333 = 140

B = Then multiply  350/200  = 200 x 1.75 350 tbottles  RED = 120 x 1.75=210

First answer = 210-140 = B recycles 70 more than A

C = We first multiply 175 x 2 = 350 tbottles  RED = 110 x 2 = 220

D = We first find LCM of 180 and 350

Then find 18x now equals 1/10 x 35x tbottles RED = 72 / 18 = 4  then 4 x 35 = 140

Second answer = 220-140 = C recycles 80 more than D.

Answer:

Plant B would recycle 60 more red bottles than plant A. Plant C would recycle 38 more red bottles than plant D.

Hope this helps!

Sorry for answering so late!

Help pls will give brainliest

Answers

Answer:

The surface area of the rectangular prism is 292 cm²

The surface area is 292 cm2

Order matters in a combination.

True

False

Answers

Answer:

False

Step-by-step explanation:

So, in Mathematics we use more precise language: When the order doesn't matter, it is a Combination. When the order does matter it is a Permutation.

The safest answer I’d go with is :False

CAN SOMEWON HELP ME PLZ I NEED HELP

Answers

Answer:

1.791875241e13

Step-by-step explanation:

5.67811 x 10⁵ = 567811

3.15576 x 10⁷ = 31557600

31557600 x 567811 = 1.791875241e13

Answer:

1.791875241e13

apples are on sale for $3 and 12 per kilogram is the total cost of the apples proportional to the total yes or no​

Answers

Answer:

yes the apples are porportinal

Step-by-step explanation:

Answer:

apple is proportional

Step-by-step explanation:

Perform the following calculation and express the answer in scientific
notation: 1.2 x 10^-2 m x 3.0 x 10^-6 m =

Answers

Answer:

Hey there!

1.2 x 10^-2 times 3.0 x 10^-6 = 3.6 x 10^-8 m^2.

Hope this helps :)

Help plz, thx urgent

Answers

5.trapezoid 7. Rectangle the other ones I forgot but I hope this helps

Answers:

5. Quadrilateral

6. Rhombus

7. Rectangle

8. Parallelogram

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

Explanations:

5. We don't know much about this other than it has 4 sides, so we simply say it is a quadrilateral. Quad = 4, lateral = side

-----------

6. The four sides are the same length as shown by the similar tickmarks. Therefore we have a rhombus. A rhombus is any quadrilateral with four equal sides. A square is a special type of rhombus, though in this case it appears to be a non-square type of rhombus, as the angles are not 90 degrees.

-----------

7. A rectangle has 4 angles that are all 90 degrees. Visually the tiny little square angle marker tells the reader we have a 90 degree angle.

-----------

8. We have a parallelogram here because the opposite sides are the same length. In addition, the opposite angles are the same measure. Through using the SSS congruence rule, we can do a bit of work to show that the alternate interior angles are congruent, leading to the opposite sides being parallel. So in short, the given info here is enough to prove we have opposite sides being parallel which is what makes a parallelogram possible.

A diver dives 17 2/3 yards and then comes back to the surface. Then, she dives 9 3/8 yards deeper than her first dive. What is her depth, in yards, in relation to the surface of the water?

(giving the points this website is allowed to give me)

Answers

-27 1/24

To calculate her relation to the surface of the water you would have to add the first dive to the second one. It would be negative because she is below sea level.

The total depth covered  by the diver is 27(1/24) yards.

What is yard?

Yard is a unit to measure length. 1 yard is equal to 36 inches.

1 yard= 3 feet or (0.9144 meter)

What is

Given that,

First time depth reached by diver = 17(2/3) yards

In the second time, the depth reached by the diver is 9(3/8) yards more than the first time,

To find total depth,

Add depth covered by first time and second time,

Total depth = 17(2/3)+9(3/8)

                   =53/3+75/8

                   = 27(1/24)

The total depth covered by the diver is 27(1/24) yards.

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Please solve the one w the underline please ❤️❤️

Answers

Answer:

6 ÷ 6 + 6 x 6

Step-by-step explanation:

Hope this helps :D

6 ÷ 6 + 6 x 6 there you go

How many ways can 4 people sit in a row of 7 ​chairs?

Answers

[tex]7\cdot6\cdot5\cdot4=840[/tex]

four people can sit in a row of seven in three ways

write an equation of the line that passes through the given points
(-2,9) and(1,-3)

Answers

Answer:

Y = -4x + 1

Step-by-step explanation:

1. We know the equation of a line is y=mx+b.

2. using the slope formula, [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], to find the slope. -12 / 3 = -4, so the slope is -4.

3. we need to find the Y intercept, or the Y coordinate at X=0. if at x=1 the Y is -3, and the slope is -4, then if we go down to x=0 then the Y would be 4 higher. therefore the Y intercept is 1.

4. now we can make the equation; Y = -4x + 1

Y=-4x+1 is the answer

(k) 2 cos 16A + 1 = (2 cos 2A - 1).(2 cos 2A + 1).(2 cos 4A-1).(2cos 8A-1).
I need help to prove this......
Qno. k.​

Answers

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

                              ↓                 ↓                  ↓                 ↓

                                factor last              factor 2nd    factor 1st

Proof LHS → RHS:

Given:        2 cos16A + 1

                  let α = 8A, then 2·cos2α + 1

Identity:     2(2cos²α - 1) + 1

Distribute:  4cos²α - 2 + 1

Simplify:    4cos²α - 1

Factor:     (2cosα - 1)(2cosα + 1)

Substitute: (2cos8A - 1)(2cos8A + 1)

                                       let β = 4A, then 2·cos2β + 1

Identity:                           2(2cos²β - 1) + 1

Distribute:                      4cos²β - 2 + 1

Simplify:                         4cos²β - 1

Factor:                           (2cosβ - 1)(2cosβ + 1)

Substitute:                     (2cos4A - 1)(2cos4A + 1)

                                                           let Ф = 4A, then 2·cos2Ф + 1  

Identity:                                               2(2cos²Ф - 1) + 1

Distribute:                                          4cos²Ф - 2 + 1

Simplify:                                             4cos²Ф - 1

Factor:                                               (2cosФ - 1)(2cosФ + 1)

Substitute:                                        (2cos2A - 1)(2cos2A + 1)      

(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)   [tex]\checkmark[/tex]

                 

Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

Step-by-step explanation:

How do I solve this

Answers

Answer:

-36

Step-by-step explanation:

[tex]-\frac{t}{2} -8 = 10\\-\frac{t}{2} = 18\\\frac{t}{2} = -18\\t = -36[/tex]

The answer is -36 hope that helped

If the Federal Resene sets the reserve rate to 20%, what is the resulting money multiplier?​

Answers

Answer:

5

Step-by-step explanation:

Money multiplier helps to explain how an economic activity boosts the economic output for the country. It shows how saving in terms of deposit increases the net supply of money in any economy.

Money multiplier = 1/reserve ratio

given reserve ratio = 20% = 20/100 = 0.2

thus,

Money multiplier = 1/0.2 = 5

The answer is 5
——————-

Plzz help I’ll mark brainliest

Answers

Answer:

6cot 50

Step-by-step explanation:

Tan 50=6/x

x= 6/(tan 50)

x= 6cot 50°

Answer:

? = 6 cot 50

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp /adj

tan 50 = 6 /?

? tan 50 = 6

? = 6 / tan 50

We know that 1 / tan 50 = cot 50

? = 6 cot 50

a contractor is in charge of hiring people for construction project the number of days it would take to complete a project with ex full time workers can be found using the function f (x) equals 1 26/x.assume once workers are assigned to the project no workers may be added or taken out the project until it is finished find and interpret the given function values and determine an appropriate domain for the function

Answers

The contractor is in charge of having people so it’s a contractor or 1 26/

This is about understanding domain of a function.

The domain of the function is x is a set of positive integers.  

We are given the function;

f(x) = 126/x

Where;

f(x) is the number of days it would take to complete a project with x number of workers

x is number of workers it will take to complete the project.

We want to find the domain for the given function.

Domain is defined as the set of all possible input values for which the function is defined.

Let's try x = 0 workers.

f(x) = 126/0 ; this is undefined and so x cannot be zero.

Let's try x = 1 worker

f(x) = 126/1 = 126 days

Let's try x = 10 workers

f(x) = 126/10 = 12.6 days

Let's try x = 100 workers

f(x) = 126/100 = 1.26 days

We see that every positive integer is a possible value of x that can make the function defined. Since 0 and negative numbers will make the function invalid.

Thus, the domain of the function is x is a set of all positive integers.

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A formula to find the period, T, of cyclic phenomena based on the frequency, F is T= 1/F
Solve the formula for F in terms of T

Answers

Answer:

F = 1/T

Step-by-step explanation:

In order to solve for F, you would need to isolate F.

(F)T = 1/F (F) --> multiply F on both sides to cancel out the F on the right side

FT/(T) = 1/(T) --> divide T on both sides to cancel out the T on the left, so the F is isolated

F = 1/T

Hope this helps!

Answer:

F = 1/T

Step-by-step explanation:

T= 1/F

USING CROSS MULTIPLICATION TECHNIQE

T(F) = 1

DIVIDE BOTH SIDES BY T

F = 1/(T)

Factor the following expression completely:

32
z
4
+
8
z
3

4
z
2

Answers

Answer:

40z + 5

Step-by-step explanation:

I'm assuming you need to factor 32z + 4 + 8z + 3 - 4 + 2

32z + 8z ( since they both have the same variable ) = 40z4 + 3 - 4 + 2 ( since they have to variables ) = 5

Hope this helped

Answer:

The factored expression for the given equation is 4(8z⁴ + 2z³ - z²)

Step-by-step explanation:

In the problem, we a re given an equation.

32z⁴ + 8z³ - 4z²

We can factor out this equation by finding the common factor between all of the coefficients which are 32, 8, and 4.

A common factor between them is 4 because each number can be easily divided by 4. Each number is also a multiple of 4. So, when we are factoring, we will divide each number by 4 because 4 will be on the outside of the parentheses in the final answer.

4(8z⁴ + 2z³ - z²)

So, this is your factored expression from the given equation.

Which equation represents an ellipse with foci at (3, 2) and (-9, 2)
that passes through the point (-3, 10)?

Answers

Answer:

D, since it horizontal ellipse, a is greater than b

An ellipse has two foci. The correct option is D.

What is the equation of ellipse if its major and minor axis and centre are given?

Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:

[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]

Coordinates of its foci would be:    (h±c, k) where    c² = a² - b²

If its major axis is parallel to the y-axis, then,

coordinates of its foci would be:  (h, k±c) where   c² = a² - b² and its equation would be:

[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]

Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,

[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]

Hence, the correct option is D.

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write the slope- intercept form of the equation for the line.

Y=2x-1

Y=1/2x-1

y=-2x-1

y=1/2x+1​

Answers

Answer:

The answer will be y=2x-1

Step-by-step explanation:

With the graph we are able to use the formula rise/run, which means we count down from the top point, and then over, and then divide.

Going down is 4 points, and over is 2.

4/2 is 2.

This leaves us with two answers. With this information, we look at the direction the graph is going, it is going upwards, making it positive. Which means that your answer is the first one. Plus the line goes through -1.

Thank you, if you need any more help let me know.

Y=2x-1
That was on my test

URGENT!!!! PLEASE HELP NOW!!! WHO EVER GIVES THE CORRRECT ANSWER WILL GET BRAINLIEST!!!

Items Sold at a Clothing Store
The bar graph shows the number of each item sold at a clothing store. Which
statement about the graph is true?​

Answers

Answer:

The correct ans is..... ( which i believe )

3rd option

Hope this helps...

Pls mark my ans as brainliest

If u mark my ans as brainliest u will get 3 extra points

Answer:

3rd option

Step-by-step explanation:

because 2/5 of 40 is equal to 16, and thats the equivelent of the pants sold.

abbi invested $1,000 in a certificate of deposit with a simple interest rate of 6% find the interest earned in 4 years. then find the total of principal plus interest.

Answers

Answer:

Step-by-step explanation:

1,320

God bless u and sorry if I’m wrong I tried my best
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PLEASE HELP ANSWER FAST As the vibration of molecules decreases, the _____ of the substance decreases. 1.temperature 2.internal energy 3.kinetic energy 4.all of the above When methane is burned with oxygen, the products are carbon dioxide and water. If you produce 9 grams of water and 11 grams of carbon dioxide from 16 grams of oxygen, how many Which excerpt is an example of metonymy? A. Since Number Five is out of the bathroom now, B. We think of lukewarm water and hope to get in it. C. I shall be telling this with a sigh somewhere ages and ages hence D. I watch you wrapped up like garbage The following data relate to the direct materials cost for the production of 50,000 automobile tires: Actual: 725,000 lbs. at $3.00 per lb. Standard: 730,000 lbs. at $2.95 per lb. a. Determine the direct materials price variance, direct materials quantity variance, and total direct materials cost variance. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number. I need help with this question. PLZZ HELP!!! Tim owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.He sells the shorts for $12 and the T-shirts for $8 each. Tim can work 18hours a day, at most. It takes him 30 minutes to design a T-shirt and 45minutes to design a pair of shorts. He must design at least 12 items eachday, but he cannot design more than 30 items in one day. Which set ofinequalities below represents this scenario?A. s 2 12 + $ ss 30 + tiss 24-0.66t, s2; 0; t2 0B. s> 12-tss 30 - t Ss 24 -0.66t, s 2 0; t> 0O c. s? 12-ts? 30-tss 24 -0.66t, s 2 0;t20D. S 2 12-tss 30-ts 24 -0.66t, s 20; t 0 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Group of answer choices Slave codes were laws that____. A.) defined the status of enslaved persons and the rights of their owners. B.) defined the status of indentured servants and the rights of their employers. C.) stated how many enslaved workers a plantation owner could have. D.) outlined a public education system for enslaved people.plz hurry its a test!!! Which of the following choices correctly shows an example of the way energy flows in an ecosystem? A. Rattlesnake to Hawk to Kangaroo Rat to Fungus to Cactus B. Fungus to Hawk toRattlesnake to Kangaroo Rat to Cactus C. Cactus to Kangaroo Rat to Rattlesnake to Hawk to Fungus D. Cactus to Fungus to Kangaroo Rat to Hawk to Rattlesnake Bi-Lo Traders is considering a project that will produce sales of $33,300 and have costs of $19,700. Taxes will be $3,500 and the depreciation expense will be $1,900. An initial cash outlay of $1,600 is required for net working capital. What is the project's operating cash flow? who was the president of India Karmen returned a bicycle to Earl's Bike Shop. The sales receipt showed a total paid price of $211.86, including the 7% sales tax. What was the cost of the bicycle without the sales tax? Any help would be very appreciated! Thank you very much! rationalise the following 1/7 A plane is on its approach to land on the runway. The jets height above the ground is given in feet as a function of the time in seconds. The following table tracks the plane as it lands. t (in seconds) h (in feet) 0 4000 5 3500 10 3000 15 2500 20 2000 25 1500. Determine where the graph crosses the h-axis. Then write the equation in slope-intercept form. a. (4000, 0); h = negative 100 t + 4000 b. (0, 4000); h = negative 100 t + 4000 c. (0, 4000); h = negative 4000 t + 100 d. (100, 0); h = 4000 t minus 100 A student says that the function f (x) = x 9 has the x-intercepts (-3,0) and (3,0). Is the student correct? If not, expl.why. There are 937 entries for a talent show.What is the value of the 3? solve show all steps what is 7x-28-7 Which nation did Iroquois confederancy side with and why? A bag contains 6 red marbles, 3 blue marbles and 1 green marble. What is the probability that a randomly selected marble is not blue? What improves the structured approach in design?A team is adopting a structured approach in design which helps them to improve the ___ of the design.