The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3 cm radius and
6 cm height. What is the depth of the ice-cream, correct to two decimal places?
m
3 cm
Ice-cream
6 cm
depth of
ice-cream
5cm

Answers

Answer 1

Answer:

h = 5 cm

Step-by-step explanation:

Given that,

The volume of ice-cream in the cone is half the volume of the cone.

Volume of cone is given by :

[tex]V_c=\dfrac{1}{3}\pi r^2h[/tex]

r is radius of cone, r = 3 cm

h is height of cone, h = 6 cm

So,

[tex]V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3[/tex]

Let [tex]V_i[/tex] is the volume of icecream in the cone. So,

[tex]V_i=\dfrac{18\pi}{2}=9\pi\ cm^3[/tex]

Let H be the depth of the icecream.

Two triangles formed by the cone and the icecream will be similiar. SO,

[tex]\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}[/tex]

So, volume of icecream in the cone is :

[tex]V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm[/tex]

or

h = 5 cm

So, the depth of the ice-cream is 5 cm.


Related Questions

PLEASE HELP!
Suppose there is a strong positive correlation between mand n. Which of the
following must be true?
A. An increase in m causes n to increase.
B. When m increases, n tends to decrease.
C. When m increases, n tends to increase.
D. An increase in m causes n to decrease.

Answers

Answer:

A an increase in m cause n to increase

Step-by-step explanation:

a positive correlation means they will travel in the same direction when one is affected.

Answer:

Option A: An increase in m causes n to increase.

Step-by-step explanation:

A Positive correlation is a relationship between two variables in which both variables move with the same ratio. A positive correlation exists when one variable increases as the other variable increases, or vice-versa.

A perfect positive correlation means that both variables move by the exact same percentage.

Therefore, if there is a strong positive correlation between m and n then  V increases and, w tends to increase.

     

                           Hope this helped :)

What is the sign of -1.69+(-1.69)

Answers

Answer: Negative sign

Adding two negative values results in another negative value.

-1.69 + (-1.69) = -3.38

It's like starting $1.69 in debt and then adding 1.69 dollars of more debt. You'll slide further into debt being $3.38 in debt total.

The sign is negative as the value of -1.69 + (-1.69) is -3.38.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

-1.69 + (-1.69)

= -1.69 - 1.69

= -3.38

This means,

The sign is negative.

Thus,

The value of -1.69 + (-1.69) is -3.38.

Learn more about expressions here:

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Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41

Answers

Answer:

[tex]a\cdot b[/tex] = 1

Step-by-step explanation:

Given that,

Vector [tex]a=5i+7j[/tex]

Vector [tex]b=-4i+3j[/tex]

We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]

We know that,

[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]

So,

[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]

So, the value of [tex]a\cdot b[/tex] is 1.

Answer:

1

Step-by-step explanation:

1.
The ratio of the numbers of sides of two regular polygons is 1:2 .If each interior angle of the first
polygon is 1200 then the measure of each interior angle of the second polygon
is
(1)1400
(2)1350
(3)1500
(4)1600

Answers

first polygon

ext. angle=180°-120°

=60°

[tex]ext \: ang = \frac{360}{n} [/tex]

n=360°/60°

n=6

second polygon

n=2(6)=12

ext. ang= 360°/n = 360°/12° = 30°

int. ang = 180°-30°= 150°

answer is C

If the ratio of the numbers of sides of two regular polygons is 1:2 and each interior angle of first angle is 120° then the measure of each interior angle of the second polygon is 150° which is option 3).

What is regular polygon?

A regular polygon is a polygon whose all sides are equal to each other.

How to find interior angle?

We have been given ratio of sides of two polygon that is 1:2 and the interior angle of first polygon that is 120 degrees.

Exterior angle will be 180-120=60°

We know that exterior angle =360/n where n is the sides of the polygon.

60=360/n

n=360/60

n=6

Number of sides of other polygon=2*6=12

Exterior angle=360/n

=360/12

=30

Interior angle=180-30=150°

Hence the interior angle of the second polygon is 150 degrees.

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savanah solved the equation 3+4 multiplied by the absolute value of x/2+3=11 for one solution. her work is shown below. what is the other solution to the given absolute value equation: savanah's solution was x= -2

Answers

Answer:

-10

Step-by-step explanation:

Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.

Note that the expression in modulus can be expressed as a positive expression and negative expression.

For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;

[tex]3+4(\frac{x}{2} + 3) = 11[/tex]

On simplification;

[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]

For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;

[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]

On simplifying;

[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]

Hence her other solution of x is -10

domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)

Answers

Answer:

[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]

Step-by-step explanation:

The domain is the set of all possible x values.

The range is the set of all possible y values.

For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.

[tex]\mathrm{D= (-7,3] }[/tex]

For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.

[tex]\mathrm{R= (-10,9.2] }[/tex]

The first side of a triangle measures 3 in. less than the second side, the third side is 2 in. more than the first side, and the perimeter is 20 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.

Answers

Answer:

P = 3x - 4

Step-by-step explanation:

Side 1 = x - 3

Side 2 = x

Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1

Perimeter = 20 in

Perimeter = Side 1 + Side 2 + Side 3

Perimeter = (x - 3) + (x) + (x - 1)

Perimeter = x - 3 + x + x - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 3 - 1

Perimeter = 3x - 4

P = 3x - 4

Solve for x (x+4)/3 = 2.

a. x = -2

b. x=2

c. x = 2/3

d. x= -10/3​

Answers

Answer:

The answer is option B

Step-by-step explanation:

[tex] \frac{x + 4}{3} = 2[/tex]

To solve it first of all cross multiply

That's

x + 4 = 6

Move 4 to the right side of the equation

The sign changes to negative

That's

x = 6 - 4

We have the final answer as

x = 2

Hope this helps you

What are the zeros of the quadratic function represented by this graph?
У
A
6
2
X
-6
- 2
6
2-
-6-
A.
1 and 3
OB.
-3 and -1
C.
-3 and 1
D. -1 and 3

Answers

Answer: C.  -3 and 1

Look where the parabola crosses the x axis. This is where the x intercepts are located. The term "x intercept" is the same as "root" and also the term "zero".

15 POINTS AND BRAINLIEST JUST HELP ME PLZZZZZ 4x^2 + 28x + 49 = 0 Rewrite equation (x + __ )^2 = __

Answers

Answer:

[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]

Step-by-step explanation:

[tex]4x^2 + 28x + 49 = 0[/tex]

[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]

[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]

[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]

[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]

[tex](x+7)^2 =-3x^2-14x[/tex]

Answer:

(x+7)² = -3x² -14x

Step-by-step explanation:

4x^2 + 28x + 49 = 0

Subtract 3x² and 14x from each sides.

x^2 + 14x + 49 = -3x² -14x

Next step will be factoring.

(x+7)² = -3x² -14x

A political candidate has asked his/her assistant to conduct a poll to determine the percentage of people in the community that supports him/her. If the candidate wants a 10% margin of error at a 95% confidence level, what size of sample is needed

Answers

Answer:

The desired sample size is 97.

Step-by-step explanation:

Assume that 50% people in the community that supports the political candidate.

It is provided that the candidate wants a 10% margin of error (MOE) at a 95% confidence level.

The confidence interval for the population proportion is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Then the margin of error is:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Compute the critical value of z as follows:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table.

Compute the sample size as follows:

[tex]MOE= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

       [tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]

          [tex]=[\frac{1.96\times \sqrt{0.50(1-0.50)} }{0.10}^{2}\\\\=[9.8]^{2}\\\\=96.04\\\\\approx 97[/tex]

Thus, the desired sample size is 97.

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = x2 − 4x y = 3x

Answers

Answer:

Hello your question is incomplete attached is the missing part the second curve ; y = 3x is incomplete so i would solve the problem taking the second curve as ; y = 3x + 8 ( giving you the general methodology )

answer : y = ( 5,32) , x = ( -1,8 )

area of shaded region = 90.673

Step-by-step explanation:

The given curves ; [tex]y = x^2 - 4x\\y = 3x +8[/tex]

solving the above curves simultaneously

[tex]x^2-4x = 3x + 8[/tex]

x^2 - 7x - 8 = 0

( x + 1 )(x - 8 ) = 0

hence  X = ( -1 , 8 )

Therefore y = 3x + 8

when x = -1 ,  y = -3 + 8 = 5

when x = 8 ,  y = 24 + 8 = 32

hence y = ( 5, 32 )

attached below is the sketched region

Integrating the curves to determine the shaded area in respect to x = ( -1, 8)

∫ [( 3x +8 ) - ( x^2 - 4x ) ] dx

∫ ( -x^2 +7x + 8 ) dx

= { - x^3/3  + 3x^2 + 8x }

= { - 8^3/3 + 3(64) + 64} - { -1^3/3 + 3 - 8 }

= {-170.66 + 192 + 64 } - { -1/3 - 5 }

= -170.66 + 192 + 64 + 5.333 = 90.673 ( area of the shaded region )

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped10 times and the man is asked to predict the outcome in advance. He gets 7 out of10 correct. What is the probability that he would have done at least this well if hehad no ESP?

Answers

Answer:

I would say 70%

Step-by-step explanation:

He got 7 of of 10 (7/10 = 70%) right so I  would say he would do just as well without ESP since it doesn't exist.

bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab

Answers

Answer:

4b + .60a

Step-by-step explanation:

b represents the number of bunches of bananas

a represents the number of apple

Multiply the cost by the number purchased of each item and add them together

4b + .60a

Answer:

[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]

Step-by-step explanation:

Bananas represented by b

1 banana costs $4 so b bananas will cost $ 4 b

Apples represented  by a

1 apples costs 0.60 $ so a apples will cost $ 0.60 a

Totally, they will cost:

=> $ (4 b + 0.60 a)

find out what's wrong with this graph

Answers

Answer:

The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.

Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit

Answers

Answer:

A. 10%

B. Lower limit= 21

Upper limit = 39

Step-by-step explanation:

Mean = 30

SD = 3

a. COV = SD/|x| × 100

= 3/30 × 100

= 10%

= 0.1

B. For 88.9 chevbychev interval:

= (1 - 1/K²) = 0.889

= 1/K² = 1 - 0.889

= 1/K² = 0.111

= K² = 1/0.111

= K² = 9

= K = √9

K = 3

Lower limit = 30 - 3(3)

Lower limit = 21

Upper limit = 30 + 3(3)

Upper limit = 39

Therefore lower limit is 21 and upper limit is 39

In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=2, what is the area of the shaded region? Answer as a decimal, if necessary. Little confused on this one.

Answers

Answer:

10 units²

Step-by-step explanation:

Consider the unshaded region to consists of 2 triangles, ∆AED and ∆BEC, which are both of equal dimensions. Their bases and heights are both the same. Both triangles are embedded inside a rectangle ABCD.

Area of the shaded region = Area of rectangle - area of the 2 triangles.

Area of rectangle = l*w

l = 10

w = 2

[tex] Area_R = 10*2 = 20 units^2 [/tex]

Area of the 2 triangles = 2(½*b*h)

b = 2

h = 5

[tex]Area_T = 2(\frac{1}{2}*2*5)[/tex]

[tex] Area_T = 1*2*5 = 10 units^2 [/tex]

Area of shaded region = 20 - 10 = 10 units²

point a is at (6,-6) and point c is at (-6, -2)
Find the cooridantes of point b on AC such that AB=3/4 AC

Answers

Answer:

(-3,-3)

B=(6-9,6+3)

3
Select the correct answer.
Which equation represents the line that is parallel to y= 2 and passes through (-1,-6)?
OA x=-1
OB
X= 2
OCy= -6
OD. y= 2x - 4
Reset
Next

Answers

Hey there! I'm happy to help!

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

I hope that this helps! Have a wonderful day!

Answer:

Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.

We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.

If the line we are looking for is flat; it stays at the same y-value the entire time. We see that  the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.

Step-by-step explanation:

; ) BELIEVE IN YOURSELF!!!!!!!!!!!!!!!!!

The Bookstall Inc. is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are $1.35 each, and hardcover books are $3.50. Of the 60 books sold last Tuesday morning, 55 were paperback and the rest were hardcover. What was the weighted mean price of a book? (Round your answer to 2 decimal places.)

Answers

Answer:

dddddd okaksy ogvurn

Step-by-step explanation:

d

in the diagram, find the values of a and b.​

Answers

Answer:

           m∠a = 67° ,   m∠b = 42°

Step-by-step explanation:

∠a is alternate interior angle to ∠ECD

∠b is alternate interior angle to ∠BCD

so:

If AB || CD then:

m∠a = m∠ECD = 25° + 42° = 67°

m∠b = 42°

State the correct polar coordinate for the graph shown:

Answers

Answer:

Solution : ( - 8, - 5π/3 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).

Find the first five terms of the sequence of partial sums. (Round your answers to four decimal places.) [infinity] (−5)n + 1 n!

Answers

Answer:

25.0000 + -37.5000 + 66.6667 + -63.5416 + 66.6667

Step-by-step explanation:

The actual formatting of the question has been attached to this response.

From the question,

Let the sequence of terms be [tex]b_{n}[/tex] i.e

[tex]b_{n}[/tex] = [tex]\frac{(-5)^{n+1} }{n!}[/tex]

Let the sequence of partial sums be [tex]S_{n}[/tex] i.e

[tex]S_{n}[/tex] = s₁ + s₂ + s₃ + . . . + sₙ

Therefore the first five terms of the sequence of partial sums will be S₅ i.e

S₅ =  s₁ + s₂ + s₃ + s₄ + s₅

Where;

s₁ = b₁

s₂ = b₁ + b₂ = s₁ + b₂

s₃ = b₁ + b₂ + b₃ = s₂ + b₃

s₄ = b₁ + b₂ + b₃ + b₄ = s₃ + b₄

s₅ = b₁ + b₂ + b₃ + b₄ + b₅ = s₄ + b₅

Where;

b₁ can be found by substituting n = 1 into equation (i) as follows;

[tex]b_{1}[/tex] = [tex]\frac{(-5)^{1+1} }{1!}[/tex]

[tex]b_{1}[/tex] = 25

[tex]b_{1}[/tex] = 25.0000

Recall that

s₁ = b₁

∴ s₁ = 25.0000 to 4 decimal places

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

b₂ can be found by substituting n = 2 into equation (i) as follows;

[tex]b_{2}[/tex] = [tex]\frac{(-5)^{2+1} }{2!}[/tex]

[tex]b_{2}[/tex] = -62.5

[tex]b_{2}[/tex] = -62.5000

Recall that

s₂ = s₁ + b₂

∴ s₂ = 25.000 + -62.5000 = -37.5000

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

b₃ can be found by substituting n = 3 into equation (i) as follows;

[tex]b_{3}[/tex] = [tex]\frac{(-5)^{3+1} }{3!}[/tex]

[tex]b_{3}[/tex] = 104.1667

Recall that

s₃ = s₂ + b₃

∴ s₃ = -37.5000 + 104.1667 = 66.6667

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

b₄ can be found by substituting n = 4 into equation (i) as follows;

[tex]b_{4}[/tex] = [tex]\frac{(-5)^{4+1} }{4!}[/tex]

[tex]b_{4}[/tex] = -130.2083

Recall that

s₄ =  s₃ + b₄

∴ s₄ = 66.6667 + -130.2083 = -63.5416

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

b₅ can be found by substituting n = 5 into equation (i) as follows;

[tex]b_{5}[/tex] = [tex]\frac{(-5)^{5+1} }{5!}[/tex]

[tex]b_{5}[/tex] = 130.2083

Recall that

s₅ = s₄ + b₅

∴ s₅ = -63.5416 + 130.2083 = 66.6667

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

Therefore, the first five terms of the partial sum is:

25.0000 + -37.5000 + 66.6667 + -63.5416 + 66.6667

What is the lateral area of the drawing is it a 200 km.b. 425.c.114d.1021km

Answers

Answer:

114 km

Step-by-step explanation:

Each side is an isosceles trapezoid, so ED=2 since you would need to add 2 to each end of the bottom line to get the top line. Now use Pythagorean Theorem to get ED^2+AD^2=AE^2. Plug in your numbers to solve for AE. This is the height of each trapezoid. Then use your formula for the area of a trapezoid, (B1+B2)h/2, to get the area of each side, then multiply by 4 to get the lateral area since there are 4 sides. Remember lateral area is just the sides, then surface area is when you include the area of the two bases.

A researcher reports a 98% confidence interval for the proportion of Drosophila in a population with mutation Adh-F to be [0.34, 0.38]. Therefore, there is a probability of 0.98 that the proportion of Drosophola with this mutation is between 0.34 and 0.38. True or False

Answers

Answer:

False

Step-by-step explanation:

The 98% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 98% confidence that the proportion of Drosophola with his mutation is between 0.34 and 0.38.

A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.

Answers

Answer:

1/5

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event /total outcome

Since the population consists of 100 elements, the total outcome of event = 100.

If random sample of 20 element is drawn from the population, the expected outcome = 20

On the first selection, the probability of any particular element being selected = 20/100 = 1/5

On the maturity date of a $10,800, 6-month, 8% note, the borrower sends a check that includes the principal and all of the interest due on the note. What is the amount of the borrower's check?​

Answers

Answer: $ 11,232.00

Step-by-step explanation:

Given:  Amount = $ 10,800

Interest Rate = 8%   =0.08

Time in Months= 6.00

Formula :

Interest on Note = (Amount)× (Interest Rate) × ((Time in Months) /12)

= (10800)× (0.08)× (6/12)

= $432

The amount of the borrower's check =(Amount + Interest on Note)

= $ (10,800+432)

= $ 11,232.00

Hence, The amount of the borrower's check = $ 11,232.00

{4.OA.A.3} There are 1,492 chairs in the auditorium. Ms. Jones wants to put them into 10 rows. If she splits the chairs evenly into 10 rows, how many chairs will Ms. Jones have left over?

Answers

Answer:

2 chairs will be left over.

Step-by-step explanation:

Given that

There are a total of 1492 chairs.

which are to divided in 10 rows evenly.

To find:

Number of chairs left ?

Solution:

Let the number of chairs in each row = [tex]x[/tex]

There are 10 rows so number of chairs in rows = 10[tex]x[/tex]

Let the number of chairs left = [tex]y[/tex]

Total number of chairs =10[tex]x[/tex] + [tex]y[/tex]  = 1492

The above equation is like:

Divisor [tex]\times[/tex] Quotient + Remainder = Dividend

So, we have to find the remainder in this question where we are given Divisor and Dividend.

10 [tex]\times[/tex] 149 + 2 = 1492

So, dividing 1492 with 10, we get remainder as 2.

Hence, 2 chairs will be left.

Solve the equation for solutions in the interval [0, 2 π). Use algebraic methods and give exact values. Support your solution graphically. cos2x = 0

Answers

Answer:

45° or 135°

Step-by-step explanation:

Cos 2x = 0

2x = cos^-1 0

2x = 90° or 270°

x= 45° or 135°

Answer:

Step-by-step explanation:

● cos 2x = 0

We khow that Pi/2 equals 0.

So

● 2x = Pi/2 or 2x= -Pi/2

Then:

● x = Pi/4 or x = -Pi/2

So the solutions are:

● x = Pi/4 + 2×k×Pi

● or x = -Pi/4 + 2×k×Pi

Where k is an integer

The picture below has a graphical solution

● Pi/4 is approximatively 0.785 and -Pi/4 is approximatively -0.785

● the output of both Pi/4 and -Pi/4 is 0

So our answer was righr

Suppose you have read two different books on world war 2 and each book has different arguments about how the war started which of the following sources provides the best support for the authors arguments

Answers

Answer:

Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.

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