What is the value of x in this equation?
Х/2 - x = x/4 + 6

Answer:

The first one

Step-by-step explanation:

She cant buy anything over $15, but she can buy something thats $15 :))

Answer:

y+2 = (-1/2)(x-3)

Step-by-step explanation:

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Answer:

x = 11

Step-by-step explanation:

The two angles measuring (7x + 14)° and (9x - 8)° are corresponding angles, which are always congruent to each other and thus equal to each other.  

Step 1:  Thus, we can find the value of x by setting the two angles equal to each other:

7x + 14 = 9x - 8

7x + 22 = 9x

22 = 2x

11 = x

Optional Step 2:  We can check that we've found the correct answer by plugging in 11 for x in both (7x + 14) and (9x - 8) and checking that we get the same number:

7(11) + 14 = 9(11) - 8

77 + 14 = 99 - 8

91 = 91

(a) Since all values are greater than 10, the sampling distribution is normally distributed.

(b) The mean of the sampling distribution is 0.23.

(c) The standard deviation of the sampling distribution is 0.1288.

(d) The probability that the difference in sample proportions (senior - junior) of students with parking passes is greater than 30% is -0.56.

In the given question, at Westville High School there are 315 seniors and 389 juniors.

65% of the seniors have parking passes and 42% of the juniors have parking passes.

The statistics teacher selects a SRS of 30 seniors and a separate SRS of 30 juniors.

Let be the difference in the sample proportions of seniors and juniors that have parking passes.

(a) We have to find the shape of the sampling distribution.

n1*p1 = 0.65*30 = 19.5 > 10

n1*(1 - p1) = (1 - 0.65)*30 = 10.5 > 10

n2*p2 = 0.42*30 = 12.6 > 10

n2*(1 - p2) = (1 - 0.42)*30 = 17.4 > 10

Since all values are greater than 10, the sampling distribution is normally distributed.

(b) We have to find the mean of the sampling distribution.

Mean = p1 - p2

Mean = 0.65 - 0.42

Mean = 0.23

(c) We have to calculate and interpret the standard deviation of the sampling distribution.

Pooled proportion, P' = (x1 + x2)/(n1 + n2)

P' = (0.65*30 + 0.42*30)/(30 + 30)

P' = 0.535

Standard deviation = √P'(1-P')*(1/n1 + 1/n2)

Standard deviation = √0.535(1- 0.535)*(1/30 + 1/30)

Standard deviation = 0.1288

(d) We have to find the probability that the difference in sample proportions (senior - junior) of students with parking passes is greater than 30%.

The test statistic, z = Mean - delta/√P'(1- P')*(1/n1 + 1/n2)

z = 0.23 - 0.30/0.1288

z = -0.56

The p-value is 0.7118. [Using NORMSDIST(z-value)]

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Answer:

m=8

Step-by-step explanation:

To find m divide both sides by 4

4m/4=32/4, then simplify

m=8

Answer:

43.6 has 3 significant figures.

Based on the Law of Cosines; it was proven that:

Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.

Based on the unshaded triangle, we can find that:

cos Θ = x/a

Next, we will prove that: cos (180 - C) = x/a

Remember that:

cos (A + B) = cos A cos B - sin A sin B

Law of Cosines: c² = a² + b² - 2ab. cos C

cos C = - [c² - (a² + b²)] /2ab ... (i)

Then:

cos Θ = cos (180 - C)

cos (180 - C) = cos 180 . cos C - sin 180 . sin  C

We subtitute equation (i):

cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C

cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)

If we focus on the unshaded triangle, we can find an equation of a, where:

a² = h² + x² ... (iii)

And if we combine both triangle into a giant triangle, we can make another equation of c. where:

c² = (x + b)² + h² ... (iv)

We will subtitute equation (iv) into equation (ii):

cos (180 - C) =  [c² - (a² + b²)]/ 2ab

cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab

cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)

We subtitute equation (iii) into equation (v):

cos (180 - C) = [x² + 2bx + h² - a²] / 2ab

cos (180 - C) = [a² + 2bx - a²] / 2ab

cos (180 - C) = 2bx / 2ab

cos (180 - C) = x/a --> PROVEN!

Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.

We know that:

a² + b² - 2ab cos C = c²

c² = (x + b)² + h²

We will try to find the value of cos C:

a² + b² - 2ab cos C = (x + b)² + h²

a² + b² - 2ab cos C = x² + b² + 2bx + h²

a² - 2ab cos C = a² + 2bx

- 2 ab cos C = 2bx

cos C = - x/a

We will subtitute the value of cos C under the Law of Cosines:

c² = a² + b² - 2ab cos C

c² = a² + b² - 2ab (- x/a)

c² = a² + b² + 2bx --> PROVEN!

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Answer:

12

Step-by-step explanation:

Answer:

The answer is -5x<-10 because the equation is equal to X>2 and answer-5x<-10  is also equal to X>2

Step-by-step explanation:

Answer:

i think the answer is C

The number of standard deviations from the mean that include all

data values is two.

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that\(\overline x $\color \ - a\cdot\sigma \le 19.95}\) and   \(\overline x $\color \ +a\cdot\sigma \geq 29.95}\)

Use the given values of mean  \(\overline x\) and normal deviation (σ) to notice the worth of "a".

         \(\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a\)

On rounding off we get a = 2

Checking another inequality

         \(\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95\)

Thus , 2 standard deviation include the all values from the given set of data .

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Let x be the mass of the liquid itself, and y the mass of the empty bottle. Then

x + y = 1  1/2 kg

x = y + 3/4 kg

Substitute x into the first equation and solve for y :

(y + 3/4 kg) + y = 1  1/2 kg

(y + 3/4 kg) + y = 3/2 kg

2y + 3/4 kg = 3/2 kg

2y = 3/2 kg - 3/4 kg

2y = 6/4 kg - 3/4 kg

2y = (6 - 3)/4 kg

2y = 3/4 kg

y = 3/8 kg

Now solve for x :

x = 3/8 kg + 3/4 kg

x = 3/8 kg + 6/8 kg

x = (3 + 6)/8 kg

x = 9/8 kg

That is, the empty bottle weighs 3/8 kg, and the liquid that fills the bottle 3/4 of the way weighs 9/8 kg.

If the bottle is completely filled, then it contains an amount of liquid weighing z such that 3/4 of z weighs 9/8 kg. Solve for z :

3/4 z = 9/8 kg

z = (9/8)/(3/4) kg

z = (9/8)•(4/3) kg

z = (9•4)/(8•3) kg

z = 36/24 kg

z = 3/2 kg

So, the total weight of the completely filled bottle is

y + z = 3/8 kg + 3/2 kg

y + z = 3/8 kg + 12/8 kg

y + z = (3 + 12)/8 kg

y + z = 15/8 kg

For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

y^2 - 28/7

Step-by-step explanation:

Answer:

The solutions to the given system of equations are:

Step-by-step explanation:

Given system of equations:

\(\begin{cases}y=-x^2+4\\y=2x+1\end{cases}\)

To solve the given system of equations, substitute the second equation into the first equation:

\(\implies 2x+1=-x^2+4\)

Add x² to both sides:

\(\implies x^2+2x+1=4\)

Subtract 4 from both sides:

\(\implies x^2+2x-3=0\)

Factor the quadratic equation:

\(\implies x^2+3x-x-3=0\)

\(\implies x(x+3)-1(x+3)=0\)

\(\implies (x-1)(x+3)=0\)

Apply the zero product property:

\((x-1)=0 \implies x=1\)

\((x+3)=0 \implies x=-3\)

Substitute the found values of x into the second equation and solve for y:

\(x=1 \implies y=2(1)+1=3\)

\(x=-3 \implies y=2(-3)+1=-5\)

Therefore, the solutions to the given system of equations are:

Answer:

jdtttttttttttttttttttjjfjyk

Step-by-step explanation:

thanks.

To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:

1/2 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

1/2 and 4/8

Now, the fractions are equivalent.

---

4/12 and __/60

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:

4/12 and 20/60

Now, the fractions are equivalent.

---

2/3 and __/12

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:

2/3 and 8/12

Now, the fractions are equivalent.

---

4/4 and __/8

To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:

4/4 and 8/8

Now, the fractions are equivalent.

The predicted population in the year 2030 is 10 people

From the question, we have the following parameters that can be used in our computation:

Population function, P(t)= 15е⁻⁰.⁰¹²⁺

Also from the question, we have

The variable t represents the number of years since 2020

This means that the value of t in 2030 is

t = 2030 - 2020

t = 10

So, we have

P(10)= 15е⁻⁰.⁰¹² ˣ ¹⁰

Evaluate the above products

P(10)= 15е⁻⁰.¹²

Evaluate the exponents

P(10)= 13.30

Approximate the above expression

P(10) = 13

This means that the number of people is 13

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Answer:

58,93.

Step-by-step explanation:

1. the rule is:

AB:AC=BD:CD, then

2. according  to  the rule above:

5.5:AC=2.8:3, then

AC=55*15/14≈58.93.

Answer:

The answer is below

Step-by-step explanation:

Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.

Solution:

a) Let x represent model pump A and let y represent model pump B.

Since There are 63 lbs of stainless steel available, hence:

4.5x + 3y ≤ 63

Both pumps must be at least 12 pumps. Therefore:

x + y ≤ 12

There are orders for at least 6 of the lightweight Model B:

y ≥ 6

Also,  no more than 15 Model B pumps be produced:

y ≤ 15

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:

Minimize Cost = 150x + 210y

b)

Hence the LP formation is:

Minimize Cost = 150x + 210y

4.5x + 3y ≤ 63

x + y ≤ 12

y ≥ 6

y ≤ 15

x ≥ 0.

c) The LP problem was solved using geogebra online graphing tool.

The points that satisfy the problem are:

(0, 6), (0,12), (6, 6)

At (0,6); cost = 150(0) + 210(6) = 1260

At (0,6); cost = 150(0) + 210(12) = 2520

At (6,6); cost = 150(6) + 210(6) = 2160

Hence the minimum cost is at (0, 6)

Answer:

Step-by-step explanation:

Simplifying

1.4x + 3.5y = 0

Solving

1.4x + 3.5y = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3.5y' to each side of the equation.

1.4x + 3.5y + -3.5y = 0 + -3.5y

Combine like terms: 3.5y + -3.5y = 0.0

1.4x + 0.0 = 0 + -3.5y

1.4x = 0 + -3.5y

Remove the zero:

1.4x = -3.5y

Divide each side by '1.4'.

x = -2.5y

Simplifying

x = -2.5y

Let a (n) denote the n-th term in the progression. Consecutive terms in the sequence differ by a fixed constant - call it c - such that

a (n) = a (n - 1) + c

Let a = a (1) be the first term in the sequence. We can solve for a (n) in terms of a alone:

a (n) = a (n - 1) + c

a (n) = (a (n - 2) + c) + c = a (n - 2) + 2c

a (n) = (a (n - 3) + c) + c = a (n - 3) + 3c

and so on, down to

a (n) = a + (n - 1) c

The sum of the first n terms is then

\(\displaystyle\sum_{k=1}^n a(k)=\sum_{k=1}^n(a+(k-1)c)=a\sum_{k=1}^n1+c\sum_{k=1}^n(k-1)=an+\frac{cn(n-1)}2=\frac c2n^2+\left(a-\frac c2\right)n\)

Since this is equal to 3n ^2 + 5n, it follows that

c/2 = 3   =>   c = 6

a - c/2 = 5   =>   a = 8

So the sequence is

a (n) = 8 + (n - 1) 6 = 6n + 2

Answer:

-6x + 21

Step-by-step explanation:

9 - 3(2x - 4)

9 - 6x + 12

-6x + 21

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

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The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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SOLUTION:

Step 1:

In this question, we are given the following:

Barbara has a bunny that weighs 2 pounds and gains 3 pounds

per year which means:

Her cat weighs 6 pounds and gains 1 pound per year which means:

When will the bunny and the cat weigh the same amount means:

collecting like terms, we have that:

CONCLUSION:

The bunny and the cat will weigh the same amount in 2 years' time.