A teacher wants to split 6 decks of cards between 8 students equally. How many decks of cards will each student get?

Answer:

angle B = 78.46°

Step-by-step explanation:

Use the cosine ratio

[tex]cosB=\frac{2}{10} =0.2[/tex]

[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]

Hope this helps

Answer:

4x³ + 4x² + 5

Step-by-step explanation:

3x³ - 2x + 8 + 2x² + 5x + x³ + 2x² - 3x - 3.

4x³ - 2x + 8 + 2x² + 5x + 2x² - 3x - 3

4x³ + 4x² - 2x + 8 + 5x - 3x - 3

4x³ + 4x² + 8 - 3

4x³ + 4x² + 5

Answer:

x² + y² + 8x - 8y + 7 = 0

Step-by-step explanation:

Formula: (x - a)² + (y - b)²= r²

where,

a = -4

b = 4

Substitute a and b

( x - (-4))² + (y - 4)² = 5²

(x + 4)² + (y - 4)² = 25

Open Bracket( )

(x + 4) (x + 4) = x² + 4x + 4x + 16

(y - 4) (y - 4) = y² - 4y - 4y + 16

x² + 4x + 4x + 16 + y² - 4y - 4y + 16= 25

Collect Like Terms

x² + y² + 8x - 8y + 16 + 16 - 25 = 0

x² + y² + 8x - 8y + 7 = 0

Therefore,

x² + y² + 8x - 8y + 7 = 0

Is The Equation Of The Given Circle.

Answer:

x = 52

Step-by-step explanation:

Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.

Since the cost of the renovation or overhauling of the existing line would be recovered in Year 4 and the NPV of the new production line is $-360,000, Crane Manufacturing should renovate.

Renovation restores an old asset to a better state.  Replacement rids the old in preference for a new asset.

When the two investment options are weighed, a better choice can be arrived at.

Year 1 = $93,324 ($280,000 x 33.33%)

Year 2 = $124,460 ($280,000 x 44.45%)

Year 3 = $41,468 ($280,000 x 14.81%)

Year 4 = $20,748  ($280,000 x 7.41%)

Total cost = $280,000

NPV of new production line = $-360,000

Thus, based on the cost recovery of the old production line and the negative NPV of the new production line, Crane Manufacturing should renovate.

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Should Crane replace or renovate the existing line?

Answer:

subtraction

Step-by-step explanation:

If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.

7 - 4

= 3 she has 3sqft of construction paper left.

She needs to lay 11 slabs on each row to make a square

The total number of slabs is given as:

Total = 121 slabs

Let this represent the area of the slab.

The area of a square is calculated as:

Area = Length^2

Substitute the known values in the above equation

Length^2 = 121

Take the square root of both sides

Length = 11

Hence, she needs to lay 11 slabs on each row to make a square

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The value of x in the equation is 26.7

0.75x + 1.5y = 40

−1.5x − 1.5y = −60

add both equation to eliminate y .

Therefore,

−1.5x + 0.75x = -0.75x

1.5y + (- 1.5y) = 0

40 + (-60) = -20

Hence,

-0.75x  = - 20

divide both sides by -0.75

-0.75x / -0/75 = - 20 / -0.75

x = - 20 / -0.75

x = 26.6666666667

x = 26.7

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Answer:

t = 4b

Step-by-step explanation:

Each bag costs 4 dollars.

hope this helps! <3

Answer:

[tex]x^{\frac{1}{2} } + 48[/tex]

Step-by-step explanation:

This is hard to explain, but basically you use exponent rules to switch it to an exponent

[tex](\sqrt[4]{x^{2} +4} )^{3}[/tex]

It's easiest if you calculate [tex]4^{3}[/tex] first

4³ = 4 x 4 x 4 = 48

Then convert the root to a fraction exponent

[tex]\sqrt[4]{x^{2}} = x^{\frac{2}{4}} = x^{\frac{1}{2} }[/tex]

Combine them using addition, since addition was in the problem

[tex]x^{\frac{1}{2} } + 48[/tex]

I hope this helps!

Considering the given function, we have that:

The function is:

f(x) = 4 - 2x + 6x².

When x = a, we have that:

f(a) = 4 - 2a + 6a².

When x = a + h, we have that:

f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.

For the fraction, we have that:

[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h

Hence:

[f(a + h) - f(a)]/h = 12a + 6h - 2.

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angle at y and w are equal

hence, 54°=w

54°+w+x =180°

x=180-(54°+54°)

x=72°

Answer:

-5/9

Step-by-step explanation:

-4x - 1 = 5x +4   Add 4x to both sides

-1 = 9x + 4    Subtract 4 from both sides

-5 = 9x  Divide both sides by 9

-5/9 = x

The answer is |-4 - 1|.

If you solve this absolute value, the answer would be 5 and if you look at the number line, the distance between the two dots is 5 units.

|-4 - 1| --> |-5| --> 5

in an absolute value, there are no negative numbers so the -5 becomes 5.

Answer:

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a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

We have,

(a) To write the number 0.00000896 moles per liter in scientific notation, we move the decimal point to the right until there is one

non-zero digit to the left of the decimal point.

The number of decimal places we moved to the decimal point will be the exponent of 10 in the scientific notation.

So,

= 0.00000896

= 896/100000000

= 896 x 100/100 x [tex]10^{-8}[/tex]

= 896/100 x [tex]10^{-8 + 2}[/tex]

= 8.96 × [tex]10^{-6}[/tex]

(b)

To write the number 1.1105 pounds in standard notation, we simply write the number as it is, without any scientific notation or exponent.

1.1105 pounds is written in standard notation as 1.1105 pounds.

Thus,

a. The decimal number 0.00000896 can be written as 8.96 × [tex]10^{-6}[/tex] in scientific notation.

b. 1.1105 pounds is written in standard notation as 1.1105 pounds.

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Answer:

7.61577310586

Step-by-step explanation:

Pythagoras Theorem 7 squared + 3 squared= 49+9=58

[tex]\sqrt{58}[/tex]

Applying precedence of operations, the result of the expression is of 161.

Power operations are done before multiplication/division, which are also done before addition/subtraction.

Operations inside brackets or parenthesis also take precedence.

In this problem, the operation is:

[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]

First the power:

[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]

Now the multiplications on the first bracket, and the subtraction on the second:

[96 - 26] + 7[8 - (-5)]

Then, applying the parenthesis to the negative number, we have that:

[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]

[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]

[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]

[tex]\mathsf{= 70 + 7\times13}[/tex]

[tex]\mathsf{= 70 + 91}[/tex]

[tex]\mathsf{= 161}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

f(y-2)+f(4-y)=4

Step-by-step explanation:

Assume (let) x=y-2

So: y=x+2

f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)

The value of that expression is 4 from the given.

Answer:

C ≈ 14.18

Step-by-step explanation:

Question Given:

A circle has an area of 16mm². Find it's circumference.

Formula:

C = 2√πA

Solve:

C = 2√πA

C = 2√(3.14 × 16)

C = 2√50.24

C = 14.1760361173

C ≈ 14.18

Hence, Circumference is approximately 14.18.

~Kavinsky

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

Area of Circle :

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} [/tex]

Now, it's given that area of circle is : 16 mm²

Let's calculate Radius ~

[tex]\qquad \sf  \dashrightarrow \: \pi {r}^{2} = 16[/tex]

[tex] \qquad \sf  \dashrightarrow \: {r}^{2} = \cfrac{16}{ \pi} [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = \sqrt{ \cfrac{16}{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: r = { \cfrac{4}{ \sqrt{ \pi} } }[/tex]

Now,

[tex]\qquad \sf  \dashrightarrow \: circumference = 2\pi r[/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 2 \pi \cfrac{4}{ \sqrt{ \pi} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{ \pi} [/tex]

[ for approximate value take pi = 3.14 ]

[tex]\qquad \sf  \dashrightarrow \: c = 8 \sqrt{3.14} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 8 \times 1.77[/tex]

[tex]\qquad \sf  \dashrightarrow \: c \approx 14.18 \: \: mm[/tex]

Answer:

x=-4, x=9

Step-by-step explanation:

We write this into words:

difference = subtraction

square = ^2

a number = x

is equal to = =

5 times that number = 5x

x^2-36 = 5x

write in standard form

x^2-5x-36

what adds to -5 and multiplies to -36?

-9 and 4!

(x-9)(x+4)

x-9 = 0

x= 9

x+4 = 0

x=-4

Answer:

9

Step-by-step explanation:

Let the number = x.

x² - 36 = 5x

x² - 5x - 36 = 0

(x - 9)(x + 4) =0

x = 9 or x = -4

Answer: 9

The level of significance on 0.05 exists at 83%.

The sample size (n) specified by the local cable company exists 300 which exists quite large.

According to the Central limit theorem, the sampling distribution of sample proportion observes a normal distribution with mean p and standard deviation

[tex]$\sqrt{\frac{p(1-p)}{n}}$[/tex]

Since the sampling distribution of sample proportions observes a normal distribution utilize the z-test for one proportion to execute the test.

The hypothesis is:

[tex]$H_{0}$[/tex]: The proportion of U.S. households that owned two or more televisions exists at 83 %, i.e. p = 0.83

[tex]$H_{1}$[/tex]: The proportion of U.S. households that owned two or more televisions exists less than 83 %, i.e. p < 0.83

Decision Rule:

At the level of significance [tex]$\alpha=0.05$[/tex] the critical region for a one-tailed z-test is:

[tex]$Z \leq-1.645[/tex]

By using the z table for the critical values.

So, if [tex]$Z \leq-1.645$[/tex]  the null hypothesis will be rejected.

Test statistic value:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

Here [tex]$\hat{p}$[/tex] exists the sample proportion.

Compute the value of [tex]$\hat{p}$[/tex] as follows:

[tex]$&\hat{p}=\frac{X}{n} \\[/tex] [tex]$&=\frac{240}{300} \\[/tex]

= 0.80

To compute the value of the test statistic as follows:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$=\frac{0.80-0.83}{\sqrt{\frac{0.83 \cdot(1-0.83)}{3000}}}$[/tex]

The test statistic exists at -1.383 which exists more than -1.645.

Therefore, the test statistic lies in the acceptance region.

Thus we fail to reject the null hypothesis.

At a 0.05 level of significance, we fail to reject the null hypothesis noting that the proportion of U.S. households that owned two or more televisions exists at 83%.

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The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

Let x represent the distance travelled, hence:

x² = 14² + 30²

x = 33 miles

tanФ = 14/33

Ф = 23°

The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

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The number of months taken for the toenail to completely regenerate itself is 13 months

It is the quantity of an amount of something at a rate of one of another quantity.

We have,

Toenail grows:

0.05 mm per day

0.05 mm = 1 day

[ 1 inch = 25.4 mm ]

So,

1 mm = 1/25.4 inch

0.05 x 1/25.4 inch = 1 day

0.0019 inch = 1 day

Divide both sides by 0.0019

1 inch = 1/0.0019 day

1 inch = 526.32 days

Multiply 3/4 on both sides.

3/4 inch = 3/4 x 526.32 days

3/4 inch = 395 days _____(1)

We can assume,

1 month = 30 days

Multiply 395/30 on both sides.

395/30 months = 395 days

13 months = 395 days _____(2)

From (1) and (2) we get,

3/4 inch = 13 months

Thus,

The number of months taken for the toenail to completely regenerate itself is 13 months.

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The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the polynomial:

-2x³ - 7x² + 3x - 4

Simplifying:

= -(2x² - x + 1)(x + 4)

Hence:

-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)

(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

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By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:

[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1}      (1)

Where n is the grade of the complex root.

The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:

k = 0

z₁ = 2.997 + i 4.002

k = 1

z₂ = - 4.964 + i 0.595

k = 2

z₃ = 1.967 - i 4.597

By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.

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The time taken for Company B to clear the parcel of land alone is 14.25 hours

1/8 = 1/x + 1/(x + 4)

1/8 = (x+4)+ (x) / (x)(x+4)

1/8 = (x+4+x) / (x² + 4x)

1/8 = 2x+4 / (x² + 4x)

cross product

1(x² + 4x) = 8(2x + 4)

x² + 4x = 16x + 32

x² + 4x - 16x - 32 = 0

x² - 12x - 32 = 0

Using quadratic formula

x = 14.25 or -2.25

The time taken for Company B to clear the parcel of land alone can only be positive,

Therefore, it is 14.25 hours

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If a 1L IV contains 60meq of kcal and the IV was discontinued after 400ml has infused, then the amount of IV received by the patient is 24meq of kcal.

Calculation for the Amount of IV

It is given that,

1L IV contains 60meq of kcal

⇒ 1000 mL of IV contains 60meq of kcal

⇒ 1 mL of IV will contain 60 / 1000 meq of kcal

As per the question,

The amount of IV infused in the patient = 400 mL

⇒ The amount of IV received by the patient in meq of kcal = 400 × (60 / 1000)

= 4 × 6

= 24 meq of kcal

Hence, the patient receives 24meq of kcal amount of IV.

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