What is the solution to the equation below?
3log X= log 32+ log 2
X=-8
X=-4
X= 8​

Answer:

(a) 3118=61*t

(b)  The amount of time the roller coaster is in motion is 51.11 seconds.

Step-by-step explanation:

Speed ​​is a magnitude that expresses the relationship between the space traveled by an object, the time used for it and its direction. In other words, speed is associated with the change in position of a body over time and can be expressed as:

\(speed=\frac{distance}{time}\)

Then the distance traveled can be expressed as:

distance=speed*time

(a) If x represents the total time that the roller coaster is in motion for each ride, the average speed is 61 feet per second and the distance is 3118 feet then the expression to represent the situation is:

3118=61*x

(b)  To calculate the amount of time the roller coaster is moving, you simply need to solve the expression found in (a). Dividing 61 to both sides:

\(\frac{3118}{61} =\frac{61*x}{61}\)

51.11 seconds=x

The amount of time the roller coaster is in motion is 51.11 seconds.

Answer:

x=1 +or- √(1)-(-8)/-2

Step-by-step explanation:

-2=-x+x^2-4

-2+4= x^2-x

2=x^2-x

x^2-x-2=0

Quadratic formula

x=-b +or -√b^2-4ac/2a

from the equation

a=1

b=-1

c=-2

Insert the variables into the quadratic formula

We have

x=-(-1) +or- √(-1)^2 - 4*(1)*(-2)/-2*(1)

x=1 +or- √(1)-(-8)/-2

=1 +or- √1+8/2

=1 +or-√9/2

=1 +or- 3/2

=1+3/2 or 1-3/2

=4/2 or -2/2

x=2 or -1

Answer:

Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel

Step-by-step explanation:

Question;

The equation representing the path of the ball obtained from a similar question posted online are;

h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20

The above equations represent the same path

The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time t

At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level

The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0

The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;

The vertex of the ball = The maximum height reached by the ball  = (h, k) = (2, 36)

The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape

The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached

If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.

Given sample size is 40, sample mean is 20, sample standard deviation is 5.

We have to find whether the distribution is normally distributed or not.

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.

Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.

Signs of normal distribution are:

Hence the sampling distribution is normally distributed.

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Answer:

I think the answer is 255cm squared

Step-by-step explanation:

If you look at the shape it has 2 shapes. A rectangle and a triangle.

17-10 to get the height of the triangle = 7

22-12 to get the base of the triangle = 10

The area to find a triangle is 1/2 * b * h

= (7 *10) / 2

= 35

To find the rectangle =

22 * 10

= 220

To find the area of the whole thing =

35 (triangle) + 220 (rectangle) = 255cm squared

Answer:

255 cm^

Step-by-step explanation:

If you cut your shape into a triangle and rectangle...or a trapezoid and a rectangle, then add the areas together.

Area of a rectangle is just length × width.



Area of a triangle is:

A = 1/2bh

Area of a trapezoid is:

A = 1/2(b1 + b2)

see image to see two different ways to cut the whole shape into two pieces. Then we calculate the total by adding the areas of the parts.

see image.

Answer:

No water

Step-by-step explanation:

Answer:

128degrees

Step-by-step explanation:

180-52=128

Answer:

No

Step-by-step explanation:

Think of the archway as a semicircle with a radius of 28/2 = 14

The diagonal of the truck is like the hypotenuse of a right triangle with legs of 7 and 13

c² = a² + b²

c² = 7² + 13²

c² = 49 + 169

c² = 218

c = 14.76

Since the diagonal of the truck is greater than the radius of the arch the truck will NOT pass without damage

Answer:

which law?

Step-by-step explanation:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Hello there. To solve this question, we have to remember how to graph a function.

First, remember that the logarithm in any base is an injective function (one-to-one).

We have to find its key-features before graphing it.

These key-features includes: x-intercept, y-intercept (if it exists), its vertical asymptote.

Okay. To find the x-intercept, set the function equal to zero:

Adding 1 on both sides, we get

Apply the property:

Hence we have

So the x-intercept happens at x = 3.

To determine whether or not it has an y-intercept, we check if the limit as x goes to zero from both sides exists and are equal:

In this case, this means we cannot evaluate this function at x = 0, so it doesn't have y-intercept(s).

Next, to determine its vertical asymptote, we check the value of x for which the argument goes to zero, that is

Therefore it has a vertical asymptote at x = 0.

The graph is then given by:

This is a sketch of the graph of the function.

The final answer to this question is contained in the last option.

(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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Answer: -5/14

Step-by-step explanation:

I did the work and I rechecked the answer.

Using the standard z table, a 95% confidence interval for p is (0.5327,0.6173).

In the given question,

A poll is taken in which 302 out of 525 randomly selected voters indicated their preference for a certain candidate.

We have to find a 95% confidence interval for p.

From the question, x=302, n=525

So estimation point,

P=x/n

P=302/525

P=0.575

Now the z value of 95% confidence interval is 1.960 using the standard z table.

Margin of Error (E)=z×√{P(1−P)}/n

Now putting the value

E=1.960×√{0.575(1−0.575)}/525

E=1.960×√(0.575×0.425)/525

E=1.960×√0.244/525

E=1.960×√0.000465

E=1.960×0.0216

E=0.0423

At 95% confidence interval for p is

P−E ≤ p ≤ P+E

Now putting the value

0.575−0.0423≤ p ≤0.575+0.0423

0.5327≤ p ≤0.6173

Hence, a 95% confidence interval for p is (0.5327,0.6173).

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2.5 centimeter is approximately equal to 0.9842 inches ( rounded to four decimal places )

To convert 2.5 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

2.5 cm = 2.5 x 0.393701

Multiply the numbers

= 0.9842 inches ( rounded to four decimal places )

Therefore, 2.5 centimeter is 0.9842 inches

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In PQR, PQ || ST. Given that RP=30, RS=9,and RT=12, The length of rq is 12 units..

if pq is parallel to st, then we can use the property of parallel lines to find the value of rq. specifically, we can use the following proportionality theorem:

(1) rp/rq = rs/st

we are given that rp = 30, rs = 9, and rt = 12. we can use these values to solve for st:

st = rs * (rt/rp) = 9 * (12/30) = 3.6

now we can substitute these values into equation (1) and solve for rq:

30/rq = 9/3.6

multiplying both sides by rq and simplifying, we get:

rq = 30 * 3.6 / 9 = 12

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To complete parts a through c, let's consider the given convergent series and the value of n.

The given series is: ∑k=1[infinity] 1/k^5

a) Find the sum of the series up to n terms:

To find the sum of the series up to n terms, we substitute n = 2 into the series and compute the sum:

S = ∑k=1[2] 1/k^5 = 1/1^5 + 1/2^5 = 1/1 + 1/32 = 33/32

Therefore, the sum of the series up to 2 terms is 33/32.

b) Determine the limit as n approaches infinity:

To find the limit of the series as n approaches infinity, we need to evaluate the sum as n becomes larger and larger:

lim(n→∞) ∑k=1[n] 1/k^5

As n approaches infinity, the series converges to a finite value.

c) Find the value the series converges to:

The value that the series converges to is the sum of the series as n approaches infinity.

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Answer:

Check explanation

Step-by-step explanation:

Given:

y = -0.1x + 22

Where,

y = BMI of an individual

x = antioxidant food consumption per day in cups

Equation of a slope

y = mx + c

Where,

m = slope

c = y - intercept

Therefore,

From the equation

y = -0.1x + 22

slope, m = -0.1

y - intercept, c = 22

Answer:

The y-intercept tells us that a person who doesn’t have any antioxidant foods can expect to have a BMI of 26. For every cup of antioxidant food that is consumed one can expect to lower their BMI by 1.2.

Step-by-step explanation:

i used this for test and it was right.

Answer:

83505

Step-by-step explanation:

It's already in the expanded form...

Answer:

f(-6)=4

Step-by-step explanation:

Answer:

3x

7-k

m/4

(5x)+12

Step-by-step explanation:

most of the words like and are just fillers. and basically means together in this instance

The ratio of the height of shape a to shape c is 2 : 5

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

Area A = 4

Area B = 25

Take the square root of both

So, we have

Length A = 2

Length B = 5

So, we have

Ratio = 2 : 5

Hence, the ratio is 2 : 5

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Answer:

-5x³ + 10x² = -5x²(x - 2)

Step-by-step explanation:

Answer:

-5x³ + 10x² = -5x²(x - 2)

Step-by-step explanation:

this is right i fact checked it

happy trails

a) This hypothesis test is that there is sufficient evidence, at a significance level of 0.01, to suggest that coyotes in the specified region tend to live longer than the average age of 1.75 years.

The level of significance in this hypothesis test is α = 0.1. The null hypothesis (H0) is that the population mean age of coyotes in the region is 1.75 years, while the alternative hypothesis (H1) is that the population mean age is less than 1.75 years.

The sampling distribution to be used in this case is the Student's t-distribution, since the sample size is relatively small (n = 51) and the population standard deviation (σ) is unknown.

The value of the sample test statistic can be calculated by using the formula: t = (x - μ) / (s / √n), where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. The calculated value of the test statistic can then be compared to the critical value(s) from the t-distribution to find the p-value. The p-value represents the probability of observing a test statistic as extreme as the calculated value, assuming that the null hypothesis is true.

Based on the calculated p-value and the chosen level of significance, we can determine whether to reject or fail to reject the null hypothesis. If the p-value is less than α, we reject the null hypothesis and conclude that the data are statistically significant. In this case, the statement "At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant" indicates that the data provide evidence to support the claim that coyotes in the specified region tend to live longer than 1.75 years.

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Answer:

sp with vat=9040

d=20%

vat=13%

mp=?

Step-by-step explanation:

sp with vat=9040

sp+vat%of sp=9040

sp(1+13/100)=9040

sp=9040/1.13=8000

If Her pool is 10 m by 5 m and is surrounded by a 1. 5 m border of paving stones. Therefore, Piscine will need a total of 104 square meters of paving stones.

a) The area of the pool plus the surrounding border of paving stones can be calculated as follows:

Total area = (length + 2 x border width) x (width + 2 x border width)

Total area = (10 + 2 x 1.5) x (5 + 2 x 1.5)

Total area = 13 x 8

Total area = 104 square meters

Therefore, Piscine will need a total of 104 square meters of paving stones.

b) We need to convert the dimensions of each paving stone to meters:

25 cm = 0.25 m

40 cm = 0.4 m

The area of each paving stone is:

0.25 m x 0.4 m = 0.1 square metres

The number of paving stones required can be calculated by dividing the total area by the area of each paving stone:

Number of paving stones = Total area / Area of each paving stone

Number of paving stones = 104 / 0.1

Number of paving stones = 1040

In theory, Piscine will need 1040 paving stones.

c) To determine whether the answer in part b) will be enough, we need to see if we can fit the paving stones into the available space without any gaps. We can arrange the paving stones in rows, with each row containing 10 stones (since the width of the pool is 5 m and the width of each paving stone is 0.4 m).

There will be 26 rows of paving stones around the pool (since the length of the pool plus the two borders is 13 m and the length of each paving stone is 0.25 m). Therefore, the total number of paving stones required is: 26 rows x 10 stones per row = 260 stones

Since the number of paving stones required is less than the number calculated in part b), Piscine will have enough paving stones to complete the border around her pool without any waste.

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The control chart limits (3 sigma) for the fertilizer-bag-filling machine can be computed using Table $6.1.

To compute the control chart limits (3 sigma) using Table $6.1 for the fertilizer-bag-filling machine, follow these steps:

Determine the sample size: In this problem, each sample consists of 7 observations.

Calculate the average range (R): For each sample, calculate the range by subtracting the smallest observation from the largest observation. Then, calculate the average range across all 35 samples.

Find the appropriate value from Table $6.1: Locate the row in Table $6.1 corresponding to the sample size (7) and find the factor associated with 3 sigma. This factor represents the number of standard deviations for the control limits.

Compute the control limits: Multiply the average range (R) by the factor obtained from Table $6.1 to determine the width of the control limits. Then, subtract this width from the overall average of the process data to obtain the lower control limit, and add the width to the overall average to obtain the upper control limit.

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The equation of the line is y = 13/6x - 5

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

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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