⦁ Two times the sum of eight and a number equal twelve.



write as an inequality

Answer:

5.4 = 7.56

1.5 = 2.1

Step-by-step explanation:

Just find the answer for 40% of the given meters.

Answer:

9

Step-by-step explanation:

3 (2²) - 2(2) + 1 =

3 (4) - 4 + 1       =

12 - 4 + 1           =

8 + 1                 = 9

Answer:

\( m\overset{\Large\frown}{EFC} = 237° \)

Answer:

\(P(G_1) = \frac{5}{13}\)

\(P(G_2) = \frac{1}{3}\)

\(P(X \ge 1) = \frac{25}{39}\)

Step-by-step explanation:

Given

\(G = 5\)

\(R = 4\)

\(B = 4\)

\(n = 13\)

Solving (a): \(P(G_1)\)

This is calculated as:

\(P(G_1) = \frac{G}{n}\)

\(P(G_1) = \frac{5}{13}\)

Solving (b): \(P(G_2)\)

This is calculated as:

\(P(G_2) = \frac{G - 1}{n - 1}\) -- this is so because the selection is without replacement

\(P(G_2) = \frac{5 - 1}{13 - 1}\)

\(P(G_2) = \frac{4}{12}\)

\(P(G_2) = \frac{1}{3}\)

Solving (c): \(P(X \ge 1)\)

Using the complement rule, we have:

\(P(X \ge 1) = 1 - P(X = 0)\)

To calculate \(P(X = 0)\), we have:

\(G = 5\) --- Green

\(G' = 8\) ---- Not green

The probability that both selections are not green is:

\(P(X = 0) = P(G'_1) * P(G'_2)\)

So, we have:

\(P(X = 0) = \frac{G'}{n} * \frac{G'-1}{n-1}\)

\(P(X = 0) = \frac{8}{13} * \frac{8-1}{13-1}\)

\(P(X = 0) = \frac{8}{13} * \frac{7}{12}\)

Simplify

\(P(X = 0) = \frac{2}{13} * \frac{7}{3}\)

\(P(X = 0) = \frac{14}{39}\)

Recall that:

\(P(X \ge 1) = 1 - P(X = 0)\)

\(P(X \ge 1) = 1 - \frac{14}{39}\)

Take LCM

\(P(X \ge 1) = \frac{39 -14}{39}\)

\(P(X \ge 1) = \frac{25}{39}\)

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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Answer:

\((y-5)^2=12(x+2)\)

Step-by-step explanation:

Since the focus point is directly right of the vertex, the axis of symmetry will be horizontal, which means that we use the equation \((y-k)^2=4p(x-h)\) where \((h,k)\) is the vertex and \((h+p,k)\) is the focus point.

Since we know our vertex to be \((h,k)\rightarrow(-2,5)\) and our focus point to be \((h+p,k)\rightarrow(1,5)\), the distance from the vertex to the focus point is \(p=3\).

Hence, the equation is:

\((y-5)^2=4(3)(x-(-2))\\\\(y-5)^2=12(x+2)\)

Current trees = 25

trees when workers are finished = 80

Subtract the number of current trees (25) to the number of trees that are when the workers are finished:

80-25 = 55

The workers planted 55 trees today

Answer:

it's prime factors are; 1, 2 ,3, 3, 5, 7, 11, 13, 19, 23

Since the diagonals in a kite intersect creating a right angle, the angles 2x° and (10x - 6)° are complementary angles. So we have:

So the value of x is 8.

Answer:

i don’t know sorry

Step-by-step explanation:

nothing

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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We need to assume that the can of soda can be represented as a cylinder. Then we use the formula for a cylinder volume and that's it.

The volume of a cylinder is given by:

Where r is the radius of the base and h the height of the can.

If we reply the measures in this equation we have:

So we can conclude that the volume of the can of soda is 19.5 in³, thus the correct answer is A.

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

Number of cookies = b

Number of cookies the family ate = 20

number of cookies left = ?

Number of cookies = Number of cookies ate + number of cookies that remained

b = 20 + number of cookies that remained

To get the number of cookies that remained, we'll subtract 20 from both sides:

An expression showing number of cookies remaining:

Answer:

a) Price of admission is $12.50

b) linear equation: 1.25x + 12.5 = y

slope: 1.25

y-intercept: 12.5

The equation above is in slope-intercept form

Here's the work step by step :)

hope it helps!

Step-by-step explanation:

$1.25 is the cost per ticket

Jermaine bought 25 tickets in total

Spent a total of $43.75

y = total cost

x = number of ride tickets

1.25 ( 25 ) = 31.25

31.25 is the total money spent on ONLY tickets.

To find the cost of admission...

43.75 - 31.25 = 12.50

The cost of admission is $12.50

Equation: 1.25x + 12.5 = y

(1.25 is the cost per ticket and 12.5 is the intial charge/admission fee and y is the total cost)

y = mx + b

m= slope and b= y - intercept

1.25x + 12.5 = y

slope: 1.25

y - intercept: 12.5

The solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.

We can solve this exponential equation for x by using logarithms. We can take the logarithm of both sides of the equation, using any base that we prefer. For instance, we can use the natural logarithm, ln:

ln(3^(3x - 2)) = ln(9^(4x - 1))

Now, we can use the properties of logarithms to simplify both sides of the equation. First, recall that ln(a^b) = b ln(a), for any positive value of a and any real value of b. Therefore, we have:

(3x - 2) ln(3) = (4x - 1) ln(9)

Next, we can use another property of logarithms, namely ln(a^b) = b ln(a) = ln(c) → a^b = c, to eliminate the natural logarithms from both sides of the equation. Specifically, we can rewrite ln(9) as ln(3^2), and then use the power rule for logarithms, ln(a^b) = b ln(a), to get:

(3x - 2) ln(3) = (4x - 1) ln(3^2) = 2 (4x - 1) ln(3)

Now, we can simplify the equation by multiplying out the coefficients of ln(3) on the left-hand side:

3x ln(3) - 2 ln(3) = 8x ln(3) - 2 ln(3)

Then, we can collect like terms:

3x ln(3) - 8x ln(3) = -2 ln(3) + 2 ln(3)

Finally, we can solve for x by factoring out ln(3) and dividing both sides by the resulting factor:

(3 ln(3) - 8 ln(3)) x = 0

-5 ln(3) x = 0

x = 0

Therefore, the solution of the exponential equation 3^(3x-2) = 9^(4x-1) is x = 0.

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Initial amount saved = $13

Total amount earned for working h hours at $6 per hour = 6h

Total amount in $ Bob will have = 6h + 13

The required inequality is

The correct option is the last option

Answer:

Step-by-step explanation:

The equation of the supply function is q = 20000p - 10000

Let's use the point-slope form of a linear equation:

slope = (change in quantity) / (change in price) = (10000 - 5000) / (1.50 - 1.00) = 10000 / 0.50 = 20000

Using the point-slope form with the point (1.50, 10000):

q - 10000 = 20000(p - 1.50)

Simplifying:

q = 20000p - 20000 + 10000

q = 20000p - 10000

So the equation of the supply function is q = 20000p - 10000

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Step-by-step explanation:

Total shirts = 19

Probebility of not gray = 19 - 4 = 15

if not gray it should be black and white..

Than probebility of not gray is 15/ 19=0.78

Approx....

The equivalent expression of 4(5+y)  by distributing is 20 + 4y.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

In other words, two mathematical expressions are said to be equivalent if they yield the same result upon solving them.

Therefore, let's find the equivalent expression of 4(5 + y) by distributing it.

Hence,

4(5 + y)  = 20 + 4y

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After 4.5 seconds, the baseball will have dropped approximately 99.35 meters.

To find out how far the baseball will have dropped after 4.5 seconds, we need to use the free fall formula.

The terms involved in this calculation are:
Time (t): 4.5 seconds.

Acceleration due to gravity (g): 9.81 m/s² (approximated)
Distance dropped (d)
The free fall formula is:
\(d = (1/2) \times g \times t^{2}\)
Now, we will plug in the given values and solve for d:
Substitute the values
\(d = (1/2) \times 9.81 \times  (4.5)^{2}\)
Calculate the square of time
\(d = (1/2) \times 9.81 \times 20.25\)
Multiply the values
d = 99.3525.

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Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

18:24

Step-by-step explanation:

There is 18 men and they are at the beginning of the problem so the 18 men go first then the  24 Women.

Answer:

So 900 children went that day and

225 adults went that day

Step-by-step explanation:

1125 divided by 1.25=900 children

so then if you want to find out adults then just subtract

1125-900=225 adults

Hope this helped and Have a great day!!!

The first step in evaluating the expression 3x{9-(4+2)/2 is to simplify the innermost parentheses. By performing operations within parentheses first, we can simplify the expression and make it easier to evaluate.

To begin, we evaluate the expression within the parentheses (4+2), which equals 6. Thus, the original expression becomes 3x{9-6/2}.

The next step is to simplify the division operation. We divide 6 by 2, resulting in 3. Now the expression becomes 3x{9-3}.

The subsequent step is to simplify the subtraction operation. We subtract 3 from 9, giving us 6. The expression now becomes 3x6.

Finally, we multiply 3 by 6, yielding a final result of 18. Therefore, the evaluation of the expression 3x{9-(4+2)/2 is equal to 18.

By simplifying the parentheses, performing the division, and evaluating the subtraction, we systematically reduce the expression to its simplest form. Following the order of operations (also known as PEMDAS or BODMAS), which prioritizes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right), ensures an accurate evaluation of the expression.

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#A

No preliminary values so no y intercept

rate of change =16.5

Equation

#2

4-1/2=4.5hours

Put 4.5 in equation

#3

Let y be 115.5

Now

Answer:

A)  c = 16.5h

B)   $74.25

C)  7 hours

Step-by-step explanation:

Bazinga charges $16.50 per hour to dog sit.

Therefore, to calculate the total charge, multiply the number of hours by the charge per hour:

\(\large \begin{array}{| c | c |}\cline{1-2} \sf number\:of\:hours & \sf charge\:in\:dollars\\\cline{1-2} 1 & 16.50 \\\cline{1-2} 3 & 49.50 \\\cline{1-2} 6 & 99.00 \\\cline{1-2} 8 & 132.00 \\\cline{1-2}\end{array}\)

As explained above, to calculate the total charge, multiply the number of hours worked by the charge per hour of $16.50

⇒ c = 16.5h

where:

To calculate how much Bazinga will earn if they dog sit for 4.5 hours, substitute h = 4.5 into the equation and solve for c:

⇒ c = 16.5h

⇒ c = 16.5(4.5)

⇒ c = $74.25

To calculate how long it will take Bazinga to earn $115.50, substitute c = 115.5 into the equation and solve for h:

⇒ c = 16.5h

⇒ 115.5 = 16.5h

⇒ h = 115.5 ÷ 16.5

⇒ h = 7 hours