Julie needs to cut 4 pieces of yarn, each with the same length and a piece of yarn 7.75 inches long. Let x represent the length of each of the equal pieces of yarn that Julie decides to cut what is the equation that can be used to determine the total length of all of the yarn that she ends up, cutting,y? Is the graph of the equation continuous or discrete

1. First, let us write out the formula for the volume of a cylinder:

V = πr^(2)h

Now, given that the cylinder has a volume of 321 cubic units, we can rewrite the above formula with this new information:

321 = πr^(2)h

2. The volume of a cone is given by the following formula:

V = (1/3)πr^(2)h

Now, we can substitute 321 = πr^(2)h into the formula above to find the volume of the cone (this will work as the cone and cylinder have the exact same radius and height). Thus we get:

V = (1/3)πr^(2)h

V = (1/3)*321

= 107 cubic units

Note that there is another method that is perhaps more intuitive and can be used quite effectively in multiple choice questions, where working isn't required. What you should notice from the general formulas for the volume of a cone and a cylinder is that the volume of a cone is actually 1/3 of the volume of a cylinder (given that they have the same radius and height). Thus, if we know that the cone in our situation has the exact same radius and height as the cylinder, we can use this method as such:

Volume of cone = (1/3)*Volume of cylinder

Volume of cone = (1/3)*321

= 107 cubic units

Answer:

-261.85

Step-by-step explanation:

If she lives with probability .996, it cost her - 334.  

If she dies with probability .004, the value is 71150 - 334  

.996*(-334) + .001*(71150 - 334) = -261.85

Final answer:

Sam's expected value from the life insurance policy is calculated by considering both the probability of survival and death. The probability-adjusted outcomes are summed, showing that Sam would, on average, lose $105 with this policy over a year.

Explanation:

Sam is interested in purchasing a single year life insurance policy that has a value of $25,700. According to actuarial tables, the probability of Sam surviving the next year is 0.99. We calculate the expected value of the life insurance policy for him by taking into account both outcomes: survival and death within the next year.

The expected value (EV) is calculated by multiplying the value of the potential outcomes by their respective probabilities and then summing these products together.

To calculate Sam's expected value from the life insurance policy, we account for both scenarios:

If Sam survives (which has a 0.99 probability), he receives nothing from the policy and only loses the premium paid, which is $362.00.

If Sam dies (which has a 0.01 probability), his estate receives the policy worth of $25,700.

Expected Value = (Probability of Surviving) * (Value if Survive) + (Probability of Dying) * (Value if Die) - (Cost of Insurance Premium)

So for Sam's case, it would be:

Expected Value = (0.99 * $0) + (0.01 * $25,700) - $362

Expected Value = ($0) + ($257) - $362

Expected Value = $257 - $362

Expected Value = -$105

Therefore, the expected value of the life insurance policy for Sam is a negative $105, meaning that, on average, Sam would lose $105 over the one year term of the policy.

Check the picture below.

Answer:

A =  137°

Step-by-step explanation:

We are given a figure of a quadrilateral ABCD which is inscribed in a circle and we are to find the measure of angle A.

We know that the opposite angles of the quadrilateral are supplementary which means that they add up to 180 degrees.

Here the opposite angle of A is C which is 43 degrees.

So, A + 43° = 180°

A = 180° - 43°

A =  137°

Answer:

see explanation

Step-by-step explanation:

let y = f(x) then rearrange making x the subject

y = 2x - 10 ( add 10 to both sides )

y + 10 = 2x ( divide both sides by 2 )

[tex]\frac{y+10}{2}[/tex] = x

Change y back into terms of x

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{2}[/tex]

Answer:

∠DFE ≅ ∠DFG

Step-by-step explanation:

we know that

Triangles are congruent by SAS, if any pair of corresponding sides and their included angles are equal in both triangles

In this problem we have that

The pair of corresponding sides that are equal are

EF=GF  and DF (is the same side for both triangles)

The included angle are ∠DFE and ∠DFG

therefore

The additional information needed to prove that triangles DEF and DGF are congruent by SAS is that angles ∠DFE and ∠DFG are equal

so

∠DFE ≅ ∠DFG

Answer:de=dg

Step-by-step explanation:

Answer:

x = 5/7

Step-by-step explanation:

(7^x)^4) = 7^2 * 7^3 / 7^3x

1. Simplify the expression

(7^x)^4) becomes 7^4x

7^2 * 7^3 becomes 7^5

7^5/7^3x becomes 7^5 - 7^3x

Your new equation: 7^4x = 7^5 - 7^3x

2. Since the bases(7) are the same set the exponents equal to each other

4x = 5 - 3x

3. Combine like terms

4x + 3x = 5

7x = 5

4. Divide both sides by 7 to get x by itself

x = 5/7

Answer:

x = [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

[tex](7^{x})^{4}=\frac{7^{2}\times 7^{3}}{7^{3x}}[/tex]

[tex](7^{x})^{4}=\frac{7^{(2+3)}}{7^{3x}}[/tex] [Since [tex]a^{b}\times a^{c}=a^{b+c}[/tex] ]

[tex]7^{4x}=\frac{7^{5}}{7^{3x}}[/tex] [since [tex](a^{b})^{c}=a^{bc}[/tex] ]

[tex]7^{4x}={7^{5}\times{7^{-3x}}[/tex]  [ [tex]\frac{1}{a}=a^{-1}[/tex] ]

[tex]7^{4x}=7^{(5-3x)}[/tex]

4x = 5 - 3x

[tex]4x+3x=5[/tex] ⇒ 7x = 5

x = [tex]\frac{5}{7}[/tex]

Answer:

6x^6y^8z^6

Step-by-step explanation:

(3x^3y^4z^4)(2x^3y^4z^2)

= 6x^(3+3) y^(4+4) z^(4+2)

= 6x^6y^8z^6

Answer:

The simplified form of given expression is [tex]6x^6y^8z^6[/tex].

Step-by-step explanation:

The given expression is

[tex](3x^3y^4z^4)(2x^3y^4z^2)[/tex]

On multiplication of constants, we get

[tex](3\times 2)(x^3y^4z^4)(x^3y^4z^2)[/tex]

[tex]6(x^3y^4z^4)(x^3y^4z^2)[/tex]

It can be written as

[tex]6(x^3x^3)(y^4y^4)(z^4z^2)[/tex]

Using product property of exponent, we get

[tex]6x^{3+3}y^{4+4}z^{4+2}[/tex]          [tex][\becuase a^ma^n=a^{m+n}][/tex]

[tex]6x^6y^8z^6[/tex]

Therefore the simplified form of given expression is [tex]6x^6y^8z^6[/tex].

Answer:

y=8*4^x

Step-by-step explanation:

Let the exponential function be of the form y=A*B^x

We want to find constant A and B.

So I'm going to use (1,32) giving me 32=A*B

I'm going to use (4,2048) giving me 2048=A*B^4

2048/32=64

A*B^4/A*B=B^3

So If you divide the equation 2048=A*B^4 by 32=A*B

we get 64=B^3

which gives us B=4

Since 32=A*B and B=4 then A=8

So the answer is y=8*4^x

Answer:

Translate the circles so they share a common center

point, and dilate circle Y by a scale factor of 3.

Step-by-step explanation:

^^^

Answer:

C) Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

Step-by-step explanation:

Answer:it’s a function

Step-by-step explanation:

By using a graph of f(x), one can establish y-values for corresponding x-values. Graphs are visual representations of the relationship between x and y. The type of graph used depends on the variables and their relationships.

To evaluate the given expression using the graph of f(x), locate the necessary y-values for the suitable x-values from the graph. The values for y are the functional values of f(x) at any given point x. For instance, given the points (1,5), (2,10), (3,7), and (4,14) in your table, these represent the values of f(x) = y at x = 1, 2, 3, and 4 respectively. Therefore, use the graph to find the y-values for the specific x-values required.

Remember that graphs are visual representations of a function and the relationship between variables x and y. In a graph, the rise or fall of the line tells us how the two quantities being compared are changing relative to each other.

The types of graphs largely depends on the types of variables and the relationship between them. For instance, Line graphs are used when both variables are numerical and the data is continuous. Bar graphs are used when comparing the quantity, frequency, or other measure for different categories or groups. Pie chart is used when you are trying to compare parts of a whole.

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Answer:

The boat is 5727.25ft far from the coast

Step-by-step explanation:

Refer the figure given.

We need to find how far is the boat from the coast = AB

Angle of elevation = 2°

The lighthouse on the coast is 200 feet tall, AC = 200 ft

We have

           [tex]tan2=\frac{AC}{AB}=\frac{200}{AB}\\\\AB=\frac{200}{tan2}=5727.25ft[/tex]

The boat is 5727.25ft far from the coast

Answer:

The boat is 5727.25ft far from the coast

Answer:

1x+2

Step-by-step explanation:

1/4*4x=1x

1/4*8=2

1x+2

Answer:

x+2

Step-by-step explanation:

1/4 (4x + 8)

Multiply each term inside the parentheses by 1/4

1/4*4x + 1/4*8

x+2

Answer:

Step-by-step explanation:

[tex]f(x)=x^2\\\\f(-3)\to\text{put x = -3 to the equation of the function}\\\\f(-3)=(-3)^2=(-3)(-3)=9[/tex]

Answer:

y = [tex]\frac{12-2x}{5}[/tex]

Step-by-step explanation:

Given

2x + 5y = 12

Isolate the term in y by subtracting 2x from both sides

5y = 12 - 2x ( divide both sides by 5 )

y = [tex]\frac{12-2x}{5}[/tex]

The equation for y is y = [tex]-\frac{2x}{5}+\frac{12}{5}[/tex]. The given equation is solved for y by applying simple operations like subtraction and division.

To isolate a variable in an equation,

The equation is 2x + 5y =12

Step 1: Subtract 2x from both the sides

⇒ 2x + 5y -2x = 12 - 2x

⇒ 5y = -2x + 12

Step 2: Dividing by 5 on both sides

⇒ 5y/5 = -2x/5 + 12/5

⇒ y = -2x/5 + 12/5

Therefore, the equation is y = -2x/5 + 12/5.

Learn more about the solving for other variables in an equation here:

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Answer:

61% decrease

Step-by-step explanation:

To find the percent decrease, take the original amount and subtract the new amount.  Then divide by the original amount.  Multiply by 100%

original amount :56

New amount :22

original - new = 56-22 = 34

(original - new)/original = 34/56 =.607142857

Multiply by 100% = .607142857* 100% = 60.7142857%

To the nearest percent = 61%

Answer:

61% decrease

Step-by-step explanation:

To solve this you need to find the difference between the original amount and the current amount which is

56- 22= 34

Then you do 34 over the original amount which is

34/56

Then you put x over 100

x/100

Now you have 34/56 and x/100

Now you do cross product property

34*100=3400

56*x=56x

56x=3400

Divide 3400 by 56 which is 60.71

Round to the nearest percent 61%

The formula for compound interest is: A = P(1 +r/n)^nt

Where P is the principal ( starting value)

r is the interest rate

n is the number of compounds

and t is the number of years.

Fill in the letters with the given information:

A = 400(1+0.04/12)^(12*11)

A = 400(1.00333)^132

A = 400*1.551557

A = 620.63

The answer is $620.63

For this case we must solve the following equation:

[tex]3 (x-7) = 42[/tex]

Applying distributive property to the terms within the parenthesis we have:

[tex]3x-21 = 42[/tex]

Adding 21 to both sides of the equation:

[tex]3x = 42 + 21\\3x = 63[/tex]

Dividing between 3 on both sides of the equation:

[tex]x = \frac {63} {3}\\x = 21[/tex]

Answer:

[tex]x = 21[/tex]

Answer:

The correct answer is option A.  21

Step-by-step explanation:

It is given an expression in variable x, 3(x - 7) = 42

To find the value of x

Let  3(x - 7) = 42

3x - (3 * 7) = 42   (Open the bracket)

3x - 21 = 42

3x = 42 + 21

3x = 63

x = 63/3 = 21

Therefore the value of x = 21

The correct answer is option A.  21

ANSWER

[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21}[/tex]

EXPLANATION

The given product is:

[tex]( \sqrt{14} - \sqrt{3} )( \sqrt{12} + \sqrt{7} )[/tex]

We expand using the distributive property to obtain:

[tex]\sqrt{14}( \sqrt{12} + \sqrt{7}) -\sqrt{3}( \sqrt{12} + \sqrt{7} )[/tex]

Extract the perfect squares to get:

[tex]\sqrt{14}(2 \sqrt{3} + \sqrt{7}) -\sqrt{3}( 2\sqrt{3} + \sqrt{7} )[/tex]

Expand further to get;

[tex]2 \sqrt{42} +7 \sqrt{2}- 2(3) - \sqrt{21} [/tex]

This simplifies to,

[tex]2 \sqrt{42} +7 \sqrt{2}- 6- \sqrt{21} [/tex]

Answer:

B, D

Step-by-step explanation:

The types of angles are:

Right angle

Straight angle

Complementary angles

Options A< B< and D are the correct answer.

We have,

The right angle is a 90-degree angle.

When two angles add up to 180 degrees, the angles are called complementary angles.

A straight angle is a 180-degree angle.

Now,

From the figure,

∠JLK = 90

∠KLM = 90

These are 90-degree angles.

And,

∠JLM = ∠JLK + ∠JLM

= 90 + 90

= 180

This can be termed as:

- straight angle (∠JLM)

- complementary angle (∠JLK and ∠JLM)

Thus,

The types of angles are:

Right angle

Straight angle

Complementary angles

Learn more about angles here:

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Hello There!

The temperature at 10 am in the morning was 1 degree below zero.

First, we know at 8 am that the temperature was 3 degrees below zero so that number is -3 and it’s our starting number.

Next, it says an hour later the temperature has gone up 6 degrees so we have -3 + 6 and we get a sum of positive 3.

Finally, at 9 am the temperature dropped again but this time 4 degrees so 3 - 4 = -1

The temperature at 10 am in the morning was 1 degree below zero.

Answer:

The correct answer is:

16˚F

Step-by-step explanation:

The correct answer is:

-14˚F + 10˚F = -4 ˚F

10˚F x 2 = 20˚F

-4˚F + 20˚F = 16˚F

Answer:

Length = 15 inches

Step-by-step explanation:

Here we are given the width and the perimeter of the rectangle and we are required to find out our length. We will use the formula of perimeter in order to find the length.

The formula for perimeter

P=2(l+b)

where

l is length

b is width = 6

P is perimeter = 42

substituting them in formula we get

42=2(l+6)

dividing both sides by 2 we get

21 = l + 6

subtracting 6 from both sides we get

15 = l

Hence length is 15 inches

Answer: 15 inches

Step-by-step explanation: It is 15 inches i had this question and did all the steps and got 15 then i answered 15 and it was correct

Answer:

Part 1) 2.1 cups of cream

Part 2) 4.2 cups of dark chocolate

Step-by-step explanation:

we know that

The recipe for 20 chocolate truffles is:

I cup of cream

2 cups of dark chocolate

step 1

Find how many cups of cream are needed for 42 truffles

using proportion

Let

x-----> the number of cups of cream needed

20/1=42/x

x=42/20=2.1 cups of cream

step 2

Find how many cups of dark chocolate are needed for 42 truffles

using proportion

Let

x-----> the number of cups of dark chocolate needed

20/2=42/x

x=42*2/20=4.2 cups of dark chocolate

[tex]2x(a-2b)+3y(2b-a)=2x(a-2b)-3y(a-2b)=(2x-3y)(a-2b)[/tex]

The probability of not drawing a blue marble from a bag containing four blue and three white marbles is calculated as the number of white marbles divided by the total number of marbles, resulting in 3/7. The marble is replaced after the first draw, so the total number of marbles stays the same for the second draw.

The question is about calculating the probability of not drawing a blue marble from a bag which contains a certain number of blue and white marbles. The probability of an event is calculated as:

P(event) = The number of ways the event can occur / Total number of outcomes

In the given example, there are four blue marbles and three white marbles in the bag, making a total of seven marbles. If James draws one marble, the probability of not drawing a blue marble i.e., drawing a white marble, is the number of white marbles divided by the total number of marbles. Thus:

P(Not Blue) = P(White) = Number of White Marbles / Total Marbles = 3 / 7

It's important to note that the probability is calculated this way because James replaces the marble after drawing it the first time. So, the total number of marbles remains the same for the second draw, keeping the probability the same. This concept is related to probability in Geometric Distribution scenarios.

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The probability is 9/12 which can simplify to D: 3/4

When you draw a marble, there are 12 possible marbles you can draw. There are 3 blue marbles and 9 non-blue marbles. Therefore, the probability of drawing a non-blue marble is 9/12. This can simplify to 3/4.

Another way to solve this problem is to use the concept of complements. The complement of event A is the event that does not occur. In this case, the event A is drawing a blue marble and the complement of event A is not drawing a blue marble.

The probability of event A is 1 - the probability of the complement of event A.

The probability of not drawing a blue marble is 1 - 3/12 = 9/12 = 3/4.

Therefore, the answer is D: 3/4.

Answer: 3z+4x-5d-e=0

Step-by-step explanation:

I’m assuming you were asked to simplify or combine like terms...

I moved the 4d over to combine with -d by changing the sign and I did the same for e

Answer:

[tex]z = \frac{5d}{3} + \frac{e}{3} - \frac{4x}{3} [/tex]

ANSWER

The resulting parabola in vertex form is:

[tex](x - 4) = 4( {y + 3)}^{2}[/tex]

EXPLANATION

The original equation of the parabola is given as

[tex]x = 4 {y}^{2} [/tex]

This parabola has its vertex at the origin.

If the graph of this parabola is shifted four units right and three units down, then the new equation is:

[tex](x - 4) = 4( {y + 3)}^{2}[/tex]

This the equation of the transformed parabola.

Its vertex is now at (4,-3).

Answer:

(x-4)=4(y+3)^2

Step-by-step explanation:

Answer:

4. 2.5

Step-by-step explanation:

Answer:

D) 2.5

Step-by-step explanation:

We are given the graph. We need to find the local maximum.

The local maximum is nothing but the where the curve moves to the maximum in up hill.

Look at the graph, the moves up from the interval [0, 2.5].

At x = 2.5 the graph attains the maximum y = 0.5

Therefore, the local maximum (y =0.5) is at x = 2.5.

The answer is D) 2.5

Answer:

We have the following function:

F(x) = x^2 + 3x - 2

Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)

Then, the solution to the system of equation is:

x1 = -3.562

x2 = 0.562

Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2

F(x - 1) = (x+2.562)(x-1.562)

Then, the solution to the equation is:

x1 = -2.562

x2 = 1.562

answer :  

we have the following function  

F(x) = x^2 + 3x - 2

Factorizing, we have: F(x) = (x+ 3.562)(x -0.562)

Then, the solution to the system of equation is:

x1 = -3.562

x2 = 0.562

Now, let's work with F(x - 1) = (x-1)^2 + 3(x-1) - 2

F(x - 1) = (x+2.562)(x-1.562)

Then, the solution to the equation is:

x1 = -2.562

x2 = 1.562

[tex]P = 2L + 2W\\2L=P-2W\\L=\dfrac{P-2W}{2}[/tex]