Length 10 cm and width 7 cm

Answer:

Part 1) The domain is the interval (-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) The domain is the interval (-∞,0) ∪ (0,2) (2,∞)

Part 3) The domain is the interval (-∞,-6) ∪ (-6,6) ∪ (6,∞)

Step-by-step explanation:

Part 1) we have

[tex]\frac{32}{y}-\frac{y+1}{y+7}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 0 or cannot be equal to -7

The domain for y is all real numbers except the number -7 and the number 0

The domain in interval notation is

(-∞,-7) ∪ (-7,0) ∪ (0,∞)

Part 2) we have

[tex]\frac{y^2+1}{y^2-2y}[/tex]

we know that

The denominator cannot be equal to zero

[tex]y^2-2y=0\\y^2=2y\\y=2[/tex]

so

The value of y cannot be equal to 0 or 2

The domain for y is all real numbers except the number 0 and 2

The domain in interval notation is

(-∞,0) ∪ (0,2) (2,∞)

Part 3) we have

[tex]\frac{y}{y-6}+\frac{15}{y+6}[/tex]

we know that

The denominator cannot be equal to zero

so

The value of y cannot be equal to 6 or cannot be equal to -6

The domain for y is all real numbers except the number -6 and the number 6

The domain in interval notation is

(-∞,-6) ∪ (-6,6) ∪ (6,∞)

Answer:

B

Step-by-step explanation:

20% is 20 out of 100

and that's how you find out how much of a tip you should leave.

The proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100

Let the amount of tip h left be expressed as x

Given the following parameters

To find the amount of tip Jennifer dropped;

Price of tip = 20% of 15

x = 20/100 * 15

x/15 = 20/100

Hence the proportion that would BEST represent how to find how much tip she should leave is x/15 = 20/100

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Final answer:

The missing value in the ratio table is 16.

Explanation:

To find the missing value in the ratio table, we can look at the relationship between the given values. In this case, we have the ratios of towels to blankets. We can see that the ratio of towels to blankets is the same for each pair of values. So, we need to find a value that, when divided by 8, gives the same result as when 14 is divided by 7.

Let x be the missing value. We can set up the equation 14/7 = x/8. To solve for x, we can cross multiply: 14 * 8 = 7 * x. This gives us 112 = 7x. Dividing both sides by 7, we find that x = 16.

Therefore, the missing value in the ratio table is 16.

Answer:

Answer is A (-3p^8/4q^3)

Step-by-step explanation:

We want to simplify a fraction. The simplification is:

[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{-3*p^8}{4*q^3}[/tex]

So we start with the fraction:

[tex]\frac{15*p^{-4}q^{-6}}{-20*p^{-12}*q^{-3}}[/tex]

Where:

Now, remember the rule:

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

Then we can rewrite:

[tex]\frac{15*p^{-4}*q^{-6}}{-20*p^{-12}*q^{-3}} = \frac{15}{-20}*\frac{p^{-4}}{p^{-12}}*\frac{q^{-6}}{q^{-3}} \\\\= -\frac{-3}{4}*p^{-4 - (-12)}*q^{-6 - (-3)}\\\\= -\frac{-3}{4}*p^{8}*q^{-3}\\\\= \frac{-3*p^8}{4*q^3}[/tex]

And we can't keep simplifying this, so this is the correct answer.

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The question lacks enough information to provide a definitive answer. If we know the width of a cart, we can divide 43 by the cart width to find out how many carts fit in a row.

Unfortunately, we can't definitively answer this question as it doesn't specify the width of each cart. The number of carts that fit in a row greatly depends on the width of each cart. To calculate this, you would need to divide the total row width (43 feet) by the width of each individual cart. For example, if each cart was assumed to be 1 foot wide, then a total of 43 carts would fit in a row. However, if each cart was assumed to be 2 feet wide, then only 21 carts (with 1 foot left over) would fit in a row.

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Answer:

Number of  children's tickets sold  =  150

Number of adult's tickets sold = 250

Step-by-step explanation:

The total number of tickets sold  = 400

Let us assume the number of children's tickets   = m

So, the number of adult's ticket's sold  = 400 - m

Here, the cost of 1 movie ticket for adult  = $8.00

So, the cost of (400 -m) adult tickets = (400 - m) ( Cost of 1 adult ticket)

= (400 - m) ($8) = 3200 - 8 m

The cost of each ticket for child = $5.00

The cost of m children  tickets = m ( Cost of 1 children ticket)

= m($5) = 5 m

Now, total cost of tickets = Money spend on (Adult's + children's) Ticket

⇒ 2750 =  (3200 - 8 m) +  (5 m)

or,  2750 - 3200 = -8 m + 5 m

or, -450 = -3 m

or, m = 450/3 = 150

or, m = 150

Hence, the number of  children's tickets = m = 150

The number of adult's tickets sold =  400 - m = 400 -150 = 250

Answer:

[tex]67\dfrac{1}{2}[/tex] sq, units.

Step-by-step explanation:

See the diagram of the parallelogram with given dimensions.

We know, the area of a parallelogram = Length of any side × Perpendicular distance of this side from the opposite parallel side.

Here, it is given that the length of a pair of parallel sides is 9 units and the perpendicular distance between those parallel lines is 7.5 units.

Therefore, the area of the parallelogram is (9 × 7.5) = 67.5 square units. (Answer)

Hence, in fraction the area can be expressed as [tex]67\dfrac{1}{2}[/tex] sq, units. (Answer)

Answer:

17 × 12 = 204 teddy bears

Step-by-step explanation:

17 cases, 12 bears in each case

Answer: A. g+2g =352

Step-by-step explanation:

Let points : g

If molly has half of George then let

Let molly : 1

Let George: 2

Therefore g*1 =g

And g*2 = 2g

So, g+2g = 352

Final answer:

The solution to the given system of equations is x=3 and x=-7. To find the solution, set the expressions for y equal to each other, combine like terms, and solve for x. Substitute the values of x back into one of the original equations to find the corresponding y value.

Explanation:

The solution to the given system of equations is x = 3 and x = -7.

To find the solution, we can set the expressions for y equal to each other:

2x + 3 = -3x + 3

Combine like terms:

5x = 0

Divide both sides by 5:

x = 0/5

x = 0

Substitute x = 0 back into either of the original equations to find the corresponding y value:

y = 2(0) + 3

y = 0 + 3

y = 3

The solution to the system of equations is (0, 3).

Answer:6.7

Step-by-step explanation:5.2+6.3=11.5 then you do -12 divided by 2.5 and get -4.8 then you add the answers together but that won’t work because different signs subtract and you get positive 6.7

To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, you first perform the division. Then, substitute the result and add the numbers inside the parentheses. Finally, subtract the result from the addition.

To evaluate the expression (5.2+6.3) - 12 ÷ 2.5, we start by performing the division. 12 ÷ 2.5 equals 4.8. Now, we substitute this result into the expression, so the expression becomes (5.2+6.3) - 4.8. Next, we add the numbers inside the parentheses together, giving us 11.5. Finally, we subtract 4.8 from 11.5, resulting in 6.7.

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Final answer:

The slope of the line passing through (0, 5) and (-12, 2) is calculated using the slope formula and is found to be 1/4.

Explanation:

The slope of the line passing through the points (0, 5) and (-12, 2) can be calculated using the formula slope (m) = (rise)/(run), where 'rise' is the change in the y-values and 'run' is the change in the x-values. To find the slope, we subtract the y-value of the second point from the y-value of the first point and divide by the subtraction of the x-value of the second point from the x-value of the first point: m = (5 - 2) / (0 - (-12)) = 3 / 12 = 1/4. Therefore, the slope of the line is 1/4.

Answer:

7.88

Step-by-step explanation:

Answer: 7,88

Explanation

Answer:

The equation of the hyperbola in standard form is [tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]

Step-by-step explanation:

Given:

Centre of the hyperbola=(−2,4)

one vertex of the hyperbola= (−2,7) .

slope of the asymptote = 12

To Find:

The equation of the hyperbola in standard form=?

Solution:

W know that the  standard form of hyper bola is

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

where

(h,k) is the centre

(x,y) is the vertex of the parabola

a is the length between the centre and the vertices of the hyperbola

b is  the distance perpendicular to the transverse axis from the vertex to the asymptotic line

Now the length of a is given by

a=|k-y|

a=|4-7|

a=|-3|

a=3

Also we know that,

Slope =[tex]\frac{a}{b}[/tex]= 2

=>[tex]\frac{3}{b}=2[/tex]

=>[tex]\frac{3}{2}=b[/tex]

=>b=1.5

Now substituting the known values in equation(1)

[tex]\frac{(x - 4)^2 }{ 3^2} - \frac{(y - (-2)^2}{  1.5^2} = 1[/tex]

[tex]\frac{(x - 4)^2 }{ 9} - \frac{(y +2)^2}{2.25} = 1[/tex]

Answer:

[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]

Step-by-step explanation:

The standard form of a hyperbola centered at a point distinct from origin has the following form:

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

The distance between the center and the vertex is:

[tex]b = \sqrt{[(-2)-(-2)]^{2}+(7-4)^{2}}[/tex]

[tex]b = 3[/tex]

The value of the other semiaxis is:

[tex]\frac{a}{b} = 12[/tex]

[tex]a = 12\cdot b[/tex]

[tex]a = 36[/tex]

The standard equation of the hyperbola is:

[tex]\frac{(x+2)^{2}}{1296} - \frac{(y-4)^{2}}{9} = 1[/tex]

Answer:

The probability of getting 12 successes out of 15 trials is [tex]P(12) = 0.2501[/tex].

Step-by-step explanation:

Given:

The probability distribution is binomial distribution.

Number of trials are, [tex]n=15[/tex]

Number of successes are, [tex]x=12[/tex]

Probability of success is, [tex]p=0.8[/tex]

Therefore, probability of failure is, [tex]q=1-p=1-0.8=0.2[/tex]

Now, probability of getting 12 successes out of 15 trials is given as:

[tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}\\P(12)=_{12}^{15}\textrm{C}(0.8)^{12}(0.2)^{15-12}\\P(12)=455\times 0.8^{12}\times 0.2^{3}\\P(12)=0.2501[/tex]

Therefore, the probability of getting 12 successes out of 15 trials is 0.2501.

Applying the binomial distribution, we get that P(X = 12) = 0.2501.

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

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, given by:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, defined by the formula below.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Considering that p is the probability of a success on a single trial.

For this problem, the parameters are [tex]n = 15, p = 0.8[/tex], and we want to find P(X = 12). Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 12) = C_{15,12}.(0.8)^{12}.(0.2)^{3} = 0.2501[/tex]

Thus P(X = 12) = 0.2501.

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Answer:

see explanation

Step-by-step explanation:

Given that the the difference of  cubes is

a³ - b³ = (a - b)(a² + ab + b²)

Given

64[tex]x^{6}[/tex] - 27 ← a difference of cubes

with a = 4x² and b = 3, thus

= (4x²)³ - 3³

= (4x² - 3)(16[tex]x^{4}[/tex] + 12x² + 9) ← in factored form

The required expression (4x^2-3)(16x^4+12x^2+9).

To evaluate 64x^6-27 as a^3-b^3=(a-b)(a^2+ab+b^2).

Cubic identity is given as [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].

Here,
=64x^6-27
=(4x^2)^3-3^3

Such that, a =4x^2 and b = 3.
Put a and b in  [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].

[tex](4x^2)^3-3^3=(4x^2-3)(16x^4+12x^2+9).[/tex]

Thus, the required expression (4x^2-3)(16x^4+12x^2+9).

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Answer:

27

Step-by-step explanation:

square root of 9 is 3, so you multiply 3 by 9.

Answer:

27

Step-by-step explanation:

Answer:

Yes,two planes descending at the same angle

Explanation:

Given the angle of deviation as seen by the pilot is equal to 15 degrees,

i.e the angle made by the line of sight with the ground is 15 degrees also the angle of elevation from a person at ground to the other plane is given to be equal to 15 degrees

which means the angle made by line of sight to plane and ground is equal to 15 degrees hence both of these situations refer to the same angle at a point and hence both planes are descending at the same angle.

There are 2 answers: Choice 1, Choice 4

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

Why is this? Because we use the rule

P(A & B) = P(A) * P(B)

which only works if events A and B are independent

----

For the first answer choice,

P(A) * P(B) = 0.6*0.4 = 0.24 = P(A & B)

so that matches.

The same applies to the fourth answer choice as well

P(A) * P(B) = 0.3*0.2= 0.06 = P(A & B)

----

The other answer choices don't match up.

The second answer choice has

P(A) * P(B) = 0.3*0.4 = 0.12 but that doesn't match with the 0.70 given

Similarly for the third answer choice,

P(A) * P(B) = 0.5*0.1 = 0.05 which doesn't match with the 0.60

Answer:

Yes

Step-by-step explanation:

Answer:

f(-1) = -6

f(0) = -5

f(1) = -4

f(2) = -3

f(5) = 0

f(8) = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[Function] f(x) = x - 5

f(-1) is x = -1 for function f(x)

f(0) is x = 0 for function f(x)

f(1) is x = 1 for function f(x)

f(2) is x = 2 for function f(x)

f(5) is x = 5 for function f(x)

f(8) is x = 8 for function f(x)

Step 2: Evaluate

f(-1)

f(0)

f(1)

f(2)

f(5)

f(8)

Answer:

The cabinet is longer by 1/12 foot.

Step-by-step explanation:

3/4 x 3/3 = 9/12

2/3 x 4/4 = 8/12

Answer:

5.8m

Step-by-step explanation:

Answer:

Step-by-step explanation:

see attached to identify which is the tenth's place

How you round the tenth's place depends on the digit in the hundredths place.

If the hundredths digit is less than 5, then you keep the tenths place the same (i.e round down)

If the hundredths digit is greater or equal than 5, then you increase the tenths place by 1 (i.e round up)

The mean absolute deviation is a measure of variation in a dataset, not its center. It helps indicates how spread out the data is from the mean value.

The mean absolute deviation is not a measure of center,instead, it is a measure of variation. The center of a data set is typically represented by measures like the mean, median, or mode. These describe the common, central value in the dataset.

Conversely, the mean absolute deviation is a statistical tool used for understanding the dispersion or variation in a set of values. It gives an average of the absolute differences between each data point and the mean of the data set. This helps identify how spread out the data is from the mean.

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Multiply the number of hours worked by how much is made per hour:

7 hours x $10.25 per hour = $71.75 total

so it's 71.76  all i did was multiply 7 x 10.25 which equals 71.76

Answer:

The total cost is $95.32.

Step-by-step explanation:

Given:

Total came to $76.75. There is an 8% sales tax and 15% tip.

Now, to find the total cost.

8% sales tax is there so we calculate the amount after adding sales tax:

$76.75 + 8% of $76.75

[tex]76.75+\frac{8}{100}\times 76.75[/tex]

[tex]76.75+0.08\times 76.75[/tex]

[tex]76.75+6.14[/tex]

[tex]82.89[/tex]

The cost after sales tax is $82.89.

Now, the cost after 15% tip:

$82.89 + 15% of $82.89

[tex]82.89+\frac{15}{100}\times 82.89[/tex]

[tex]82.89+0.15\times 82.89[/tex]

[tex]82.89+12.43[/tex]

[tex]95.32[/tex]

The cost after the tip is $95.32.

Therefore, the total cost is $95.32.

Answer:

(c)  For p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).

Step-by-step explanation:

Here,  The dividend expression is  [tex]4x^2-p(x)+7[/tex] = E(x)

The Divisor = (x-3)

Remainder  = -2

Now, by REMAINDER THEOREM:

Dividend  = (Divisor x Quotient)  + Remainder

If ( x -3 ) divides the given polynomial with a remainder -2.

⇒  x = 3  is a  solution of given polynomial E(x)  - (-2) =  

[tex]E(x)  - (-2)  = 4x^2-p(x)+7 -(-2)  = 4x^2-p(x)+9[/tex] =  S(x)

Now, S(3) = 0

⇒[tex]4x^2-p(x)+9 = 4(3)^2 - p(3) + 9 = 0\\\implies 36 - 3p + 9 = 0\\\implies 45= 3p , \\or p  =15[/tex]

or, p =1 5

Hence, for p = 15,  [tex]4x^2-p(x)+7[/tex] leaves a remainder of -2 when divided by (x-3).

Answer:75%

Step-by-step explanation:im sorry I can't get it out in words but you have the answer

Answer:

D

Step-by-step explanation: