a rectangle has a side length 2x+9 and side width x. If the perimeter is 36 cm, what is the value of x?

The exponential equation, 2ˣ = 1/2, has a value of -1.

Exponential equations are equations in which variables occur as exponents.

Given is an exponential equation, 2ˣ = 1/2, we need to solve it,

2ˣ = 1/2

Taking ㏒ both the side,

㏒ 2ˣ = ㏒ 1/2

x ㏒ 2 = ㏒ 0.5

x = -0.301029996 / 0.301029996

x = -1

Hence, the exponential equation, 2ˣ = 1/2, has a value of -1.

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The average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex]

Average speed is the ratio of the total distance traveled by a body to the total time taken by the body to cover the total distance.

Here, ying zyiyu covered the first [tex]200\;\rm miles[/tex] of the trip at [tex]50\;\rm mph[/tex] so,

Total time taken by ying zyiyu to cover [tex]200\;\rm miles[/tex] is calculated as-

[tex]t_1=\dfrac{200}{50}\\t_1=4\;\rm hour[/tex]

Similarly, ying zyiyu covered the first [tex]100\;\rm miles[/tex] of the trip at [tex]40\;\rm mph[/tex] so,

Total time taken by ying zyiyu to cover [tex]100\;\rm miles[/tex] is calculated as-

[tex]t_2=\dfrac{100}{40}\\t_2=2.5\;\rm hour[/tex]

So, the total time taken by ying zyiyu to travel [tex]300\;\rm miles[/tex] is [tex]4+2.5=6.5\;\rm hours[/tex]

Now, the average spped is calculated as-

[tex]\rm{Average\;Speed}=\dfrac{Total\;Distance}{Total\;Time}\\\rm{Average\;Speed}=\dfrac{300}{6.5}\\\rm{Average\;Speed}=46.15\;\rm mph[/tex]

Hence, the average speed of ying zyiyu is [tex]46.15\;\rm{mph}[/tex].

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Answer: Option 'd' is correct.

Step-by-step explanation:

Since we have given the exponential growth.

Properties of exponential growth are as follows:

1) The graph should pass through (0,1).

2) Domain of exponential growth function is the set of real numbers.

3) Range of exponential growth is greater than 0.

4) The graph is always increasing for the case of exponential growth.

Hence, Option 'd' is correct.

Answer:

$9828.44

Step-by-step explanation:

The semi annual payment is such that the future value of the annuity due is equal to the desired amount when he retires.

The formula to calculate future value of an annuity due periodic payment of M  for time period T for given periodic return r,

A=[tex]\frac{M(1+r)^{T+1}-(1+r)}{r}[/tex]

in this question there are 30*2= 60 payments and the semi annual rate= 4.5/2= 2.25%

putting values we get

1250675= [tex]\frac{M(1+2.25%)^{60+1}-(1+2.25%)}{2.25%}[/tex]

on solving we get M= $9828.44

Alex needs to invest $9828.44 semiannually in his IRA

The value of x on solving the equation 5/6 (3/8 - x) = 16 is - 251 / 5.

In other terms, it is a mathematical statement stating that "this is equivalent to that." It appears to be a mathematical expression on the left, an equal sign in the center, and a mathematical expression on the right.

Given:

5/6 (3/8 - x) = 16

Solve the above equation as shown below,

Use the distributive property to solve the equation,

5 / 6 × 3 / 8 - 5 / 6 x = 16

15 / 48 - 5 / 6 x = 16

5 / 16 - 5 / 6 x = 16

5 / 6 x = 5 / 16 - 16

5 / 6x = -251 / 16

x = -251 / 16 × 6 / 5

x = - 251 / 5

Thus, the value of x is - 251 / 5.

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The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].

Further explanation:

Concept used:

The probability of an event [tex]E[/tex] is calculated as follows:

[tex]\boxed{P(E)=\dfrac{n(E)}{n(S)}}[/tex]  

Here, [tex]n(E)[/tex] is the number of favorable outcomes in an event [tex]E[/tex] and [tex]n(S)[/tex] is the number of element in sample space [tex]S[/tex].

The probability of exactly [tex]r[/tex] success in [tex]n[/tex] trial is expressed as follows:

[tex]\boxed{P(F)=^{n}C_{r}p^{r}q^{n-r}}[/tex]

Here, [tex]r[/tex] is the probability of success in an event and [tex]q[/tex] is the probability of failure.

Calculation:

Consider [tex]A[/tex] as an event of having a girl in first birth and [tex]P(A)[/tex] as the probability of event [tex]A[/tex].

The probability of having a girl is [tex]P(A)=\frac{1}{2}[/tex].

Assume that [tex]A'[/tex] is the complement event of an event [tex]A[/tex] and [tex]P(A')[/tex] is the probability of complementary event [tex]A'[/tex].

The event is the event of not having a girl in the first birth.

The probability of event [tex]A'[/tex] is calculated as follows:

[tex]\boxed{P(A')=1-P(A)}[/tex]   …… (1)

Substitute [tex]P(A)=\frac{1}{2}[/tex] in the equation (1) to obtain the probability of event [tex]A'[/tex].

[tex]\begin{aligned}P(A')&=1-\dfrac{1}{2}\\&=\dfrac{1}{2}\end{aligned}[/tex]

The probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is calculated as follows:

[tex]\begin{aligned}P(F&)=^{8}C_{6}\left(\dfrac{1}{2}\right)^{6}\left(\dfrac{1}{2}\right)^{8-6}\\&=\dfrac{8!}{6!\cdot 2!}\cdot (0.5)^{6}\cdot (0.5)^{2}\\&=28(0.5)^{8}\\&=0.10937\end{aligned}[/tex]  

Thus, the probability of having exactly [tex]6[/tex] girls in [tex]8[/tex] birth is [tex]\boxed{\bf 0.10937}[/tex].

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Answer details:

Grade: Senior school

Subject: Mathematics

Chapter: Probability

Keywords: Probability, exact event, sample space, number of element, complement event, success, failure, favorable, trial, P(E)=n(E)/n(S), P(A')=1-P(A).

Final answer:

To find the probability of getting exactly 6 girls in 8 births, we use the binomial probability formula. In this case, the probability is approximately 0.01.

Explanation:

To find the probability of getting exactly 6 girls in 8 births, we can use the binomial probability formula:

P(x = 6) = C(n, x) * pˣ * (1-p)(n-x)

Where:

In this particular case, P(x = 6) = C(8, 6) * (0.5)⁶ * (0.5)(8-6) = 28 * 0.015625 * 0.015625 = 0.009765625, or approximately 0.01.

To find the unknown factor in the equation 9Xp = 45, divide both sides by 9 to isolate X, resulting in Xp = 5. Therefore, the value of X is 5 when multiplied by the variable p.

To solve the equation 9Xp = 45, we need to find the value of an unknown variable X. The equation indicates that 9 times some number X equals 45. By dividing both sides of the equation by 9, we can isolate X to find its value.

Step 1: Write down the equation: 9Xp = 45.

Step 2: Divide both sides by 9: Xp = 45 ÷ 9.

Step 3: Simplify the right side: Xp = 5.

Therefore, the value of the variable X that makes the equation true when multiplied by p is 5.

Answer: The price today = $250

Step-by-step explanation:

Given : The original price of apple was  $200.

The price of a new apple ipod has increased by 1/4.

Then , the new price =(Original price)  +([tex]\dfrac{1}{4}[/tex]) x (Original price)

= (Original price) ( [tex]1+\dfrac{1}{4}[/tex] )

[tex](\$200)(\dfrac{5}{4})=\$250[/tex]

Hence, the price of ipod today = $250

To write the equation for this line in slope-intercept form, substitute the given values into the formula and solve for the y-intercept.

To write an equation in slope-intercept form, we need to use the formula y = mx + b, where m is the slope and b is the y-intercept.

Given that the line passes through the point (-8,5) and has a slope of 3/2, we can substitute these values into the equation.

So, the equation of the line in slope-intercept form is y = (3/2)x + b. To find the y-intercept, we substitute the coordinates of the point (-8,5) into the equation and solve for b.

5 = (3/2)(-8) + b

5 = -12 + b

b = 17

Therefore, the equation in slope-intercept form is y = (3/2)x + 17.

we know that

If two lines are parallel, then their slopes are the same

Step 1

Find the slope of the given line

we know that

the formula to calculate the slope between two points is equal to

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

in this problem we have

[tex](x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)[/tex]

substitute in the formula

[tex]m=\frac{(-3+4)}{(0+5)}[/tex]

[tex]m=\frac{(1)}{(5)}[/tex]

[tex]m=\frac{1}{5}[/tex]

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{1}{5}[/tex]

[tex](x1,y1)=(-2,2)[/tex]

substitute

[tex]y-2=\frac{1}{5}(x+2)[/tex]

[tex]y=\frac{1}{5}x+\frac{2}{5}+2[/tex]

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

therefore

the answer is

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Answer:

2210

Step-by-step explanation:

Given that a store sold a total of 21,650 balls.

No of baseballs sold =11795

There were baseballs, basketballs and footballs in the store

No of basketballs sold = 4150 fewer than baseballs = [tex]11795-4150\\=7645[/tex]

Total sales =          [tex]21650[/tex]

Baseballs sold =    [tex]11795\\[/tex]

Basketballs sold =[tex]7645[/tex]

No of footballs sold = [tex]21650-11795-7645\\=2210[/tex]

m = monkeys

e = elephants

 there are 5 times as many monkeys as elephants so to find the number of monkeys the equation would be:

m = 5e

The area of the rectangular field is 120,000 square meters.

We shall multiply the length by its width, to find the area of the rectangular field.

We can calculate like this:

Area = Length x Width

Area = 0.4 kilometers x 0.3 kilometers

Next, we convert the measurements to square meters, recalling that 1 kilometer = 1000 meters:

Area = (0.4 km * 1000 m/km) x (0.3 km * 1000 m/km)

Area = (400 m) x (300 m)

Then, multiplying the values, we have:

Area = 120,000 square meters

Hence, the area of the rectangular field is 120,000 square meters.

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To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.

To estimate p(x < 1.5), we can use the concept of probability. Given the information provided, we can assume a uniform distribution between 1.5 and 4. The shaded area in Figure 5.20 represents the shortest 30 percent of repair times. Since we want to estimate the proportion of values less than 1.5, we can estimate it as the shaded area to the left of 1.5. This shaded area is equivalent to the shortest 30 percent of repair times, which is 0.30. Therefore, we can estimate that p(x < 1.5) is approximately 0.30.

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The actual probability is 0.159

To estimate the probability P(X < 1.5) without knowing the exact values of the mean (μ) and standard deviation (σ), we can use the empirical rule (also known as the 68-95-99.7 rule). This rule states that for a normally distributed variable:

Approximately 68% of the data falls within 1 standard deviation (σ) of the mean (μ).

Approximately 95% of the data falls within 2 standard deviations (2σ) of the mean.

Approximately 99.7% of the data falls within 3 standard deviations (3σ) of the mean.

Since the exact values of μ and σ are not available, we can estimate them using the sample mean (X) and sample standard deviation (s) of the data.

In this case, let's assume we have a sample of thickness values {x1, x2, ..., xn}. The sample mean (X) is the average of all the sample values:

X = (∑xi) / n

The sample standard deviation (s) is the square root of the variance (s^2), which is the average of the squared deviations from the mean:

s^2 = ∑(xi - X)^2 / n

Once you have the estimated values of μ (approximately equal to X) and σ (approximately equal to s), you can use the empirical rule to estimate P(X < 1.5).

For example, if you estimate that μ = 2 and σ = 0.5, then:

P(X < 1.5) = P(X < μ - σ) ≈ P(X < 2 - 0.5) ≈ P(X < 1.5) ≈ 0.159

Remember that this is just an estimate, and the actual probability may be slightly different.

Answer:

260 %

Step-by-step explanation:

1) Since, the percentage formula is,

[tex]\text{Percent Increase}=\frac{\text{Amount of Increase}}{\text{Original Amount}}[/tex]

2) Given,

Original amount = 250,

New amount = 900

So, the amount of increase = New amount - Original amount = 900 - 250 = 650

By substituting the values,

[tex]\text{Percentage increase}=\frac{650}{250}[/tex]

3) Now, for expressing the ratio into percentage we need to multiply by 100,

[tex]\frac{650}{250}\times 100=\frac{65000}{250}= 260\%[/tex]