The measure of an angle is three times the measure of its supplementary angle. What is the measure of each angle?

In Mathematics, if a six-digit code can have each digit repeat there are 10 options (0-9) for each position. Having six positions, we multiply the possibilities together, leading us to a conclusion of 1,000,000 possible codes.

The calculation of different codes for a house's security system is a problem of permutation and combination under the field of Mathematics. The code consists of six digits and each digit can be repeated, meaning that there are 10 possibilities (0-9) for each of the 6 positions in the code.

Therefore, for each of the six positions in the code, there are 10 possibilities. To determine the total number of possible codes, we would multiply the number of possibilities for each digit together: 10*10*10*10*10*10 = 1,000,000. So, there are one million possible combinations for the 6-digit code.

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Answer:

D

Step-by-step explanation:

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:

(6,4) is not a solution of y > -x/2 + 7 because (6,4) is on the line

The answer is D.

Hope this helps!

Answer:

No,because (6,4) is on the line.

Step-by-step explanation:

We are given that an inequality equation

[tex]y>-\frac{1}{2}x+7[/tex]

We have to find that the ordered pair (6,4) is a solution of given inequality or not.

[tex]y>-\frac{x}{2}+7[/tex]

Substitute x=6

[tex]y>-\frac{6}{2}+7[/tex]

[tex]y>-3+7[/tex]

[tex]y>4[/tex]

The value of y is greater than 4 not equal to 4.

Therefore, (6,4) is not a solution of given inequality.

No,because (6,4) is on the line.

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)

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.

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:

The correct answer is 333  1/ 3 ml 30% solution and 166  2/ 3 ml of 45% solution.  

step-by-step explanation:

Set up 2 equations. Let x be the 30% solution and y be the 45% solution. Then you have x + y =500 and .3x +.45y = .35*500. Then solve the system.

Answer:

A is your correct answer.

Step-by-step explanation:

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:

Line c ║ line d, applying the converse of the alternate exterior angles theorem.

Step-by-step explanation:

See the given diagram attached.

It is given that ∠ 11 = ∠ 13.

Hence, from this we can conclude that line c ║ line d, applying the converse of the alternate exterior angles theorem.

The alternate exterior angle theorem says that if one line is the transverse line of any two other parallel lines then the alternate exterior angles so generated will be equal. (Answer)

Answer:

c∥d, Converse of the Alternate Exterior Angles Theorem

Step-by-step explanation:

I took the test other answer is right

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:

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.

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:

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:

5.8m

Step-by-step explanation:

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:

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:75%

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

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 67

Step-by-step explanation:65:&:8/&/&&:

Average rate of change in height will be 0.59 inch per day.

Experiment with plants started with,

Let the variable defining change in the height per day of the plant = x

Change in the height of plant A after 2 weeks or 14 days = 14x cm

Height of the plant A initially = 2.5 cm

Height of the plant after 2 weeks = 14x + 2.5

If height of the plant A after 2 weeks = y

Linear equation defining the height of the plant after 2 weeks will be,

y = 14x + 2.5

Plant A is 23.5 cm tall after 2 weeks,

23.5 = 14x + 2.5   [Substitution of y = 23.5]

23.5 - 2.5 = 14x + 2.5 - 2.5

21 = 14x

x = 1.5 cm

Since, 1 cm = 0.393701 inches

Therefore, 1.5 cm = 1.5 × 0.393701

                             = 0.591

                             ≈ 0.59 inches per day

      Hence, average rate of change in the height of plant A will be 0.59 inches per day.

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Answer:

21/8

Step-by-step explanation:

3(7/8)=21/8

To multiply a whole number by a fraction, you have to change the whole number (the 3) into a fraction. To do this, simply put the 3 over 1.

3/1 x 7/8. Multiplying fractions is so easy because all you have to do is multiply the numerators together and then the denominators together.

3x7=21

1x8=8

21/8

This fraction cannot be reduced, but it can be rewritten as a mixed number.

21 divided by 8 is 2 with a remainder of 5.

The answer is 21/8 or 2 5/8. (they mean the same thing)

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:

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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1 + 2(4x + 1)​

mutiply the bracket by 2

(2)(4x)= 8x

(2)(1)= 2

1+8x+2

1+2+8x ( rearranging)

answer:

3+8x or 8x+3

Answer:

8x+3

Step-by-step explanation:

1+8x+2

1+2=3

8x+3 or 3+8x

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:

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:

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)

8 Hours.

If you want his debt to be 0, as in he has nothing left to owe, we will set d (his debt) to 0

0 = 100 - 12.5h

Subtract 100 to move it to the other side

-100 = -12.5h

Divide each side by -12.5

8 = h

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