please I need help with all my spring packet
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You can find two irrational numbers [tex]r,s[/tex] between 0 and 1.

Then, you'll have

[tex]2016 < 2016+r < 2017,\quad 2016 < 2016+s < 2017[/tex]

And both [tex]2016+r[/tex] and [tex]2016+s[/tex] will be irrational, because they are the sum of a rational number (2016) and an irrational number (r or s).

Finally, in order to find two such numbers, you can start with any irrational number, and scale it down until it lies between 0 and 1.

For example, you can start from [tex]\sqrt{2}\approx 1.4142[/tex] and divide it by any integer greater than 2, say that we choose

[tex]r = \dfrac{\sqrt{2}}{7}[/tex]

[tex]s = \dfrac{\sqrt{2}}{4}[/tex]

So, the two irrational numbers between 2016 and 2017 are

[tex]2016 + \dfrac{\sqrt{2}}{7},\quad 2016 + \dfrac{\sqrt{2}}{4}[/tex]

Two irrational numbers between 2016 and 2017 can be found by adding non-repeating, non-terminating decimals to 2016. Examples include 2016.172 and 2016.399.

Finding irrational numbers between two given numbers involves knowing that irrational numbers are those which cannot be expressed as a quotient of two integers and have non-repeating, non-terminating decimal expansions. Examples of irrational numbers include the square root of non-perfect squares, pi (π), and 'e' (the base of natural logarithms).

Between two such close numbers (like 2016 and 2017), an easy way to find irrational numbers is to add a non-repeating, non-terminating decimal to the smaller number. For instance, let's use 0.172 and 0.399 (which are derived from the reference numbers provided) and add these to 2016:

Both 2016.172 and 2016.399 are irrational numbers that lie between 2016 and 2017.

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Answer:

[tex]\large\boxed{(4^3)^5=4^{15}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (a^n)^m=a^{nm}\\\\(4^3)^5=4^{(3)(5)}=4^{15}[/tex]

Step-by-step explanation: Here we have the number  (4^3)^5.

We can use the relationship: [tex](x^{a} )^{b} = x^{a*b}[/tex]

so our number can be written as: [tex](4^{3}) ^{5} = 4^{3*5} = 4^{15}[/tex].

But you can simplify it further!

we know that [tex]4 = 2^{2}[/tex], then [tex]4^{15} = (2^{2}) ^{15} = 2^{2*15} = 2^{30}[/tex]

ANSWER

b>1

EXPLANATION

The given inequality is;

2 (b - 4) > -6

Expand the parenthesis to get,

2b-8>-6

2b>-6+8

Simplify the right hand side.

2b>2

Divide both sides by:

b>1

Answer:

A, B and D.

Step-by-step explanation:

A:  because 5* 5^(x-1) = 5^(x - 1 + 1) = 5^x.

B. 15^x / 3 = 5^x

D. (15/3)^x = 5^x.

( Note C = 5 , E = 5^(x+2) and x^5 not = 5^x.)

Final answer:

The equivalent expressions to 5^x are 5*5^(x-1), 15^x/3^x, and (15/3)^x. These follow the rules of adding exponents when multiplying with the same base and raising an entire factor to a power.

Explanation:

The student has asked which expression is equivalent to 5x. To find expressions equivalent to exponents, we use rules such as the product of powers, which states that when multiplying expressions that have the same base, we can add their exponents (e.g., 5a  imes 5b = 5a+b). Similarly, to raise an exponential factor to a power, we multiply the exponent by the power.

Looking at the given options:

Therefore, the correct answers are options A, C, and D, each demonstrating different properties of exponents.

Answer: 6w+9=4 and w=-5/6

6w+9=4 now solve for w

6w+9-9=4-9

6w=-5

w=-5/6

Putting back into equation to check our answer;

6(-5/6)+9=4

-5+9=4

4=4 correct, our answer checks out.

Any questions please just ask. Cheers

The equation of the translated sentence Nine more than the product of a number and 6 is equal to 4 is 6w + 9 = 4.

A numerical expression can be formed from statements it is represented i the form of numbers and their operations.

According to the given sequence Nine more than the product of a number and 6 is equal to 4 we have to convert it in numerical form.

Let the number be w.

∴ 6w + 9 = 4

6w = 4 - 9

6w = -5

w = -5/6.

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Answer:

1. F

2. T

3. T

4. T

Step-by-step explanation:

Let's break down the definitions.

Quadrilateral - A polygon with 4 sides

Square - A quadrilateral with 4 equal sides and 90 degree angles

Rectangle - A quadrilateral with 4 sides with opposite sides that are congruent and have 90 degree angles

Parallelogram - A quadrilateral with 4 sides with opposite sides that are congruent and do not have 90 degree angles

Rhombus - A quadrilateral with 4 equal sides but does not have 90 degree angles

Now let's look at the questions.

Does every 4 sided figure have equal sides? - No

Is a rectangle with 4 equal sides a square? - Yes

Is every parallelogram with 4 equal sides a parallelogram? - Yes

Is every 4 equal sided figure a figure with opposite sides that are equal? - Yes

Question 1 - False, rectangle is not a square if it has a different length or width

Question 2 - True, square can also be a rectangle as long as there are four congruent sides

Question 3 - True, rhombus is a parallelogram

Question 4 - True, square can be also known as a rectangle

Answer:

SA = 250 pi

SA = 785 in^2

Step-by-step explanation:

Givens

d = 10

h = 20

r = d/2

Formula

r = d/2

r = 10/2

r = 5

SA = 2*pi*r^2 + pi*d*h

Solution

SA = 2 * pi * 5^2 + pi * 10 * 20

SA = 2 * 25 *pi  + pi * 200

SA = 50 pi + 200 pi

SA = 250*pi

This is one answer.

The second is 250 * 3.14

SA = 785 in^2

Answer:

Yes, she has enough paint, since she does not need to paint the window. The area that needs to be painted is only 87 ft², and she has enough paint for 90 ft².

Step-by-step explanation:

Area of the wall (including window)

= 12 x 8

= 96 ft²

Area of the window

= 3 x 3

= 9 ft²

Area of the wall that needs to be covered with paint

= 96 - 9

= 87 ft²

Answer:

Yes, she has enough paint. The area to be painted is the area of the wall minus the area of the window. A = (12)(8) = 96; A = (3)(3) = 9; area to be painted: 96 – 9 = 87 square feet.

Answer:

105 degrees

Step-by-step explanation:

The measure of angle H from the given figure is 67.5 degree.

Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.

Given that measure of angle F is 67.5°

The angles formed when two lines cross each other are known as vertical angles. Vertically opposite angles are the opposing angles created by these lines.

In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines.

From the given figure,

∠F=∠H (Vertically opposite angles are equal)

Angle F= Angle H=67.5°

So, angle H is 67.5 degree

Therefore, the measure of angle H is 67.5 degree.

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"Your question is incomplete, probably the complete question/missing part is:"

The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠H?

$15,822 is the correct answer, you multiply 36 by $419 and add the down payment of $738

$15,822. first you multiply $419 x 36 to get 15,084. then you add the down payment

Answer:

Step-by-step explanation:

Moving from (0, 4) to (2, 3), we see x increasing by 2 from 0 to 2 and y decreasing by 1 from 4 to 3.

Thus, the slope of this line is m = rise / run = -1/2.

Starting with y = mx + b, we substitute 0 for x, 4 for y and -1/2 for b, obtaining:

4 = (-1/2)(0) + b.  Therefore, b = 4, and the desired equation is:

y = (-1/2)x + 4

The answer would -9/10

If you need the work just let me know!

Answer:

-9/10

Step-by-step explanation:

7/10 = r - (- 8/5)

7/10 = r + 8/5

r = 7/10 - 8/5

r = -9/10

Answer:

13

Step-by-step explanation:

If you said one side was 5 inches long anf the other side was 8 add thoes up u get 13

ANSWER

x=3

EXPLANATION

The given equation is:

[tex] {x}^{3} - 27 = 0[/tex]

We add 27 to both sides of the equation to get:

[tex] {x}^{3} = 27[/tex]

We write 27 as number to exponent 3.

[tex]{x}^{3} = {3}^{3} [/tex]

The exponents are the same.

This implies that, the bases are also the same.

Therefore

[tex]x = 3[/tex]

The answer is:

The equation has only one root (zero) and its's equal to 3.

[tex]x=3[/tex]

We are working with a cubic equation, it means that there will be three roots (zeroes) for the equation.

To solve the problem, we need to remember the following exponents and roots property:

[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]

[tex](a^{b})^{c}=a^{b*c}[/tex]

So, we are given the equation:

[tex]x^{3}-27=0[/tex]

Isolating x we have:

[tex]x^{3}=27\\\\\sqrt[3]{x^{3}}=\sqrt[3]{27}\\\\x^{\frac{3}{3} }=\sqrt[3]{(3)^{3} }\\\\x^{\frac{3}{3} }=3^{\frac{3}{3} }\\\\x=3[/tex]

Hence, we have that the equation has only one root (zero) and its's equal to 3.

Have a nice day!

Answer:

36/39

Step-by-step explanation:

Answer:

The correct option is C.

Step-by-step explanation:

Given information: In DEF, sin D= 36/39.

In a right angled triangle,

[tex]\sin \theta=\frac{perpendicular}{hypotenuse}[/tex]

[tex]\sin D=\frac{EF}{DE}[/tex]

[tex]\frac{36}{39}=\frac{EF}{39}[/tex]

[tex]EF=36[/tex]

[tex]\cos \theta=\frac{base}{hypotenuse}[/tex]

[tex]\cos E=\frac{EF}{DE}[/tex]

[tex]\cos E=\frac{36}{39}[/tex]

The value of cos E is [tex]\frac{36}{39}[/tex]. Therefore the correct option is C.

Answer:

see explanation

Step-by-step explanation:

The ratio received = 9 : 13 : 18

Sum the parts of the ratio 9 + 13 + 18 = 40

Divide the amount by 40 to find the value of one part of the ratio

[tex]\frac{800}{40}[/tex] = £20 ← value of 1 part of ratio

Eli gets 9 × £20 = £180

Freda gets 13 × £20 = £260

Geoff gets 18 × £20 = £360

To divide £800 between Eli, Freda and Geoff based on their ages, we need to find the ratio of their ages and divide the total amount by this ratio. Eli will get £180, Freda will get £260, and Geoff will get £360.

To find out how much each person will get, we need to divide the total amount of money by the sum of their ages in the given ratio.

The sum of their ages is 9 + 13 + 18 = 40.

The ratio is 9:13:18.

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mean: 14.5

median: 15.5

innerquartile: 17.5

Answer:

mean = 14.5 ; median = 15.5 ; interquartile = 7.5

Step-by-step explanation:

Given : 17,23,8,5,9,16,22,11,13,15,17,18.

To find : Find the mean median and interquartile for the data set .

Solution : We have given 17,23,8,5,9,16,22,11,13,15,17,18.

First we arrange in ascending order 5 , 8 ,9 ,11, 13, 15, 16 , 17, 17,18, 22, 23,

Mean : [tex]\frac{Sum\ of\ all\ number}{total\ number}[/tex].

Mean :  [tex]\frac{5+8+9 +11 +13+ 15+16+17+17+18+ 22+23,}{12}[/tex].

Mean : 14.5

Median : Average of middle two numbers

Median :  [tex]\frac{15 + 16}{2}[/tex].

Median :  [tex]\frac{31}{2}[/tex].

Median : 15 .5

Interquartile  : median of lower half  - median of upper half.

Interquartile  : [tex]\frac{17 +18}{2}[/tex]  - [tex]\frac{9 + 11}{2}[/tex].

Interquartile  :  17.5 - 10= 7.5

Therefore, mean = 14.5 ; median = 15.5 ; interquartile = 7.5

The answer is:

The volume of the cylinder is equal to:

[tex]Volume=3096.8cm^{3}[/tex]

To find the volume of the cylinder, first, we need to use the equation to calculate its area to find its diameter, and then, calculate its volume since we know that the height of the cylinder is equal to its diameter.

So,  using the  equation to calculate the area of its base, we have:

[tex]BaseArea=\pi *r^{2}\\\\r=\sqrt{\frac{BaseArea}{\pi } }=\sqrt{\frac{196cm^{2} }{\pi }}\\\\r=\sqrt{\frac{196cm^{2} }{\pi }}=\sqrt{62.4cm^{2}}=7.9cm[/tex]

Therefore, we have that the radius of the cylinder is equal to 7.9 cm, it means that its diameter is equal to:

[tex]diameter=2*radius=7.9cm*2=15.8cm[/tex]

Now that we know the diameter, let's calcule the volume of the cylinder:

[tex]Volume=BaseArea*height=BaseArea*Diameter\\\\Volume=196cm^{2}*15.8cm=3096.8cm^{3}[/tex]

Hence, we have that the volume of the cylinder is equal to:

[tex]Volume=3096.8cm^{3}[/tex]

Have a nice day!

The volume of a cylinder with a base area of 196 cm² and a height equal to the diameter is approximately 2145.74 cm³.

To find the volume of a cylinder with a given base area and a height equal to the diameter, you can use the formula V = πr²h, where π is Pi (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder. The base area of the cylinder (A) is given as 196 cm², which is also equal to πr². Given that the height is equal to the diameter, we can express the height as 2r.

First, you need to solve for the radius (r) using the base area:

A = πr² → r = √(A/π) = √(196 / 3.14159) ≈ 7 cm

Now plug this value into the volume formula:

V = πr²h = π * (7 cm)² * (2 * 7 cm) = π * 49 cm² * 14 cm

Finally, calculate the volume:

V ≈ 3.14159 * 49 cm² * 14 cm ≈ 2145.74 cm³

The volume of the cylinder is approximately 2145.74 cm³.

To find the original price of a discounted item, divide the price paid by the percentage paid, in decimal form. In this case, $55.25 divided by 0.65 gives $85, which is the original price of the skateboard.

If a skateboard was purchased for $55.25 with a 35% off coupon, then that price represents 65% of the original price (100% - 35% = 65%).

To find the original price, you would take the price paid and divide it by the percentage you paid, in decimal form. In this case, that's 0.65 (65%).

So, the calculation would be $55.25 ÷ 0.65 which gives you approximately $85. This means the original price was $85.

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Answer:ddd

lol

Step-by-step explanation:

Answer:

laptop/phone

As the computer advanced, transistors were invented. They were smaller and allowed the computers to become smaller than ever. Slowly, the size of the computers decreased as more and more pieces were invented.

Step-by-step explanation:

The invention of transistors allowed computers to be smaller.

A computer is a device that accepts information (in the form of digitalized data) and manipulates it to some result based on a program, software, or sequence of instructions on how the data is to be processed.

The invention of transistors or the computer chips made computers to work smarter than previously.

These computers also were more efficient and more reliable than the computers of the first generation.

The transistor replaced the cumbersome vacuum tube in televisions, radios and computers.

Hence, the invention of transistors allowed computers to be smaller.

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Answer:

Step-by-step explanation:

[tex]f(x)=x^4-3x^3+5x=1x^4-3x^3+0x^2+5x+0[/tex]

The Remainder Theorem states that when we divide a polynomial f(x)

by x − a the remainder R equals f(a).

a = -2

Syntetic substitution.

1. Write only the coefficients of x in the dividend inside an upside-down division symbol.

[tex]\underline{\begin{array}{c|ccccccc}\ &1&-3&0&5&0\\\ \end{array}}[/tex]

2. Put the divisor at the left.

[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ \end{array}}[/tex]

3. Drop the first coefficient of the dividend below the division symbol.

[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ \end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1\end{array}[/tex]

4. Multiply the drop-down by the divisor, and put the result in the next column.

[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1\end{array}[/tex]

5. Add down the column.

[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1&-5\end{array}[/tex]

6. Repeat 4 and 5 until you can go no farther

[tex]\underline{\begin{array}{c|ccccccc}-2&1&-3&0&5&0\\\ &&-2&10&-20&30\end{array}}\\\begin{array}{ccccccccc}\ \ \ \ &1&-5&10&-15&30\end{array}[/tex]

The remainder is 30, so f(-2) = 30.

Check:

[tex]f(x)=x^4-3x^3+5x\\\\f(-2)=(-2)^4-3(-2)^3+5(-2)=16-3(-8)-10=16+24-10=30[/tex]

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

Given the vector < a, b > then the magnitude is

[tex]\sqrt{a^2+b^2}[/tex], thus

| (- 3, 2) | = [tex]\sqrt{(-3)^2+2^2}[/tex] = [tex]\sqrt{9+4}[/tex] = [tex]\sqrt{13}[/tex]

The length of the magnitude of the given vector <-3,2> is:

                        [tex]\sqrt{13}[/tex]

We know that for any vector of the type: <a,b>

The magnitude of the length of the vector is given by the formula:

[tex]|<a,b>|=\sqrt{a^2+b^2}[/tex] [tex]\sqrt{13}[/tex]

Here we are given the vector as: <-3,2>

i.e. a= -3

and  b=2.

This means that the length of the magnotude of the vector is given by:

[tex]|<-3,2>|=\sqrt{(-3)^2+(2)^2}\\\\i.e.\\\\|<-3,2>|=\sqrt{9+4}\\\\i.e.\\\\|<-3,2>|=\sqrt{13}[/tex]

Hence, the answer is:  [tex]\sqrt{13}[/tex]

height(h) = 7x

base(b) = 4x

Since you know the value of x, you can plug it in

h = 7(10) = 70in

b = 4(10) = 40in

[tex]A = \frac{1}{2}bh[/tex]

[tex]A=\frac{1}{2} (40)(70)[/tex]

[tex]A=\frac{1}{2} (2800)[/tex]

A = 1400in²

Answer:

[tex]-3k^3 - 24k^2 + 15k[/tex]

Step-by-step explanation:

In this question we need to solve the equation

[tex]3k(-k^2-8k+5)[/tex]

For solving it, we need to multiply 3k with each number inside the bracket and find the results.

In finding products, we add the power having same bases and coefficients are multiplied.

[tex]3k(-k^2-8k+5)\\=3k(-k^2) +3k(-8k) +3k(5)\\= -3k^3 - 24k^2 + 15k[/tex]

3(x^2 + 1) + 2

So the last option

Answer:

50

Step-by-step explanation:

In the expression [tex]n=10p+20,[/tex] p represents the yearly gross profit in millions of dollars and n represents the total number of employees.

When the yearly gross profit was 20 million dollars, then the number of employees was

[tex]n=10\cdot 20+20=200+20=220.[/tex]

When the yearly gross profit was 15 million dollars, then the number of employees was

[tex]n=10\cdot 15+20=150+20=170.[/tex]

Hence, the decrease in the number of employees is

[tex]220-170=50.[/tex]

To determine how far Michael will hike in 2 hours, we calculate his hiking rate which is 1.5 miles per hour and then multiply by the total time, resulting in a distance of 3 miles hiked in 2 hours.

To find out how far Michael will hike in 2 hours, we need to set up a proportion based on the information that he hikes 1/4 of a mile every 1/6 of an hour. First, we find the rate at which Michael hikes by dividing the distance by the time:

Rate = 1/4 mile / 1/6 hour = (1/4) * (6/1) = 6/4 = 1.5 miles per hour.

Now, to find out how far he will hike in 2 hours, we simply multiply the rate by the total time:

Distance in 2 hours = 1.5 miles/hour * 2 hours = 3 miles.

Therefore, Michael will hike 3 miles in 2 hours.

Answer:

$1.75

Step-by-step explanation:

1 pound of carrot and 1.5 pounds of squash cost $7.00.

1c + 1.5s = 7 ----------------- [ 1 ]

4.5 pounds of carrot and 1.75 pound of squash cost $14.00.

4.5c + 1.75s = 14 ----------------- [ 2 ]

[ 1 ] x 4.5:

4.5c + 6.75s = 31.5 ----------------- [ 1a ]

[1a] - [2]:

5s = 17.5

s = $3.50

Sub s = 3.5 into [ 1 ]:

1c + 1.5 (3.5)  = 7

1c + 5.25 = 7

1c = $1.75

By setting up and solving a system of linear equations based on the purchases made by two customers, we calculated the price of carrots to be $2.00 per pound.

To determine the price per pound for carrots, we can set up a system of linear equations based on the provided information and solve it. Let 'c' represent the cost per pound of carrots and 's' represent the cost per pound of squash.

Multiplying Equation 1 by 3 gives us:

Now, let's subtract Equation 2 from this new equation to eliminate 's' and solve for 'c'.

After calculating, we find that c = $2.00 per pound for carrots.

Answer:

Proportional

Step-by-step explanation:

If the function is proportional, it will have the following relationship:

f(x) = kx

Let's look at the first one:

-14 = -7k

k = 2

Now let's see if k=2 is true for the rest:

0 = 2(0) True

10 = 2(5) True

16 = 2(8) True

f(x) = 2x.  So this is indeed proportional.