Solve (x - 5)^2 = 3

Answer:

The sixth term;

= 16 + (6-1)4 = 16 +20 = 36

Sixth term = 36

Pattern; a = 16, d = 4

16,20,24,28,32,36...

Completed question;

Chairs for an orchestra are positioned in a curved form with the conductor at the center. The front row has 16 chairs, the second has 20 and the third has 24, and so on. describe the pattern of the sequence. How many chairs are in the 6th row?

Step-by-step explanation:

This scenario can be represented by an arithmetic progression sequence.

nth term of an AP = a + (n-1)d

Where;

a = first term

d = common difference

n = term number

Given;

First term a = 16

Second term = a + d = 20

since a = 16

a+d = 16+d = 20

d = 20-16 = 4

The sixth term;

= 16 + (6-1)4 = 16 +20 = 36

Sixth term = 36

Pattern; a = 16, d = 4

16,20,24,28,32,36...

To calculate the surface area of a rectangular pyramid, you need to find the base area and the areas of the triangular faces, then sum them up. In this case, the surface area of the given rectangular pyramid is 65 square millimeters.

The surface area of a rectangular pyramid is calculated by adding the base area to the sum of the areas of the four triangular faces.

Answer:

x = [tex]x = \frac{2+r}{p-8}[/tex]

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

(2+r)/(p-8) = x

Step-by-step explanation:

-px+r=-8x-2

Add px to each side

-px+r+px=-8x+px-2

r = -8x+px -2

Add 2 to each side

2+r = px-8x

Factor out an x

(2+r) = x(p-8)

Divide each side by (p-8)

(2+r)/(p-8) = x(p-8)/(p-8)

(2+r)/(p-8) = x

Answer:

P(t) = 100e^[(ln2.4/lne)t]

or

P(t) = 100e^0.87546t

Step-by-step explanation:

see attached picture

Answer:

$1,968.6

Step-by-step explanation:

Compound Interest = [P * (1 + i)ⁿ] - P

P = principal = $7,500

i = annual interest rate = 6%

n = number of periods = 4 years

Compound Interest = [$7,500 * (1 + 0.06)⁴] - $7,500

Compound Interest = [$7,500 * (1.06)⁴] - $7,500

Compound Interest = [$7,500 * (1.06)⁴] - $7,500

Compound Interest = [$7,500 * 1.26247696] - $7,500

Compound Interest = $9,468.5772 - $7,500

Compound Interest = $1,968.5772

Answer:

^C

Step-by-step explanation:

The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

y = 1/8x²

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The vertex of parabola = (0, 0)

And, The focus of parabola = (0, 2)

Hence, We get;

a = 2

So, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

x² = 4ay

x² = 4 × 2y

x² = 8y

y = 1/8x²

Thus, The equation of a parabola with Vertex (0, 0) and focus (0, 2) is,

y = 1/8x²

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Answer:

14.19

Step-by-step explanation:

The equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]  and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm

We have a wooden plaque in the shape of an ellipse with height 26 centimeters and width 16 centimeters.

We have to find equation for the ellipse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point.

The general form of the equation of ellipse is -

[tex]\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } =1[/tex]

Where -

a is the length of semi major axis.

b is the length of semi minor axis.

In the question given to us -

height of ellipse = length of major axis = 2a =26

width of ellipse = length of minor axis = 2b = 16

Therefore -

a = 13 cm  

and

b = 8 cm

Substituting the values in the equation of ellipse, we get -

[tex]\frac{x^{2} }{(13)^{2} } +\frac{y^{2} }{(8)^{2} } =1[/tex]

[tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]

Now, at y = 6 cm above the center -

[tex]\frac{x^{2} }{169 } = 1 - \frac{36 }{64} }\\\\\frac{x^{2} }{169 } = 0.57\\x^{2} = 169\times0.57\\x = 9.81 cm[/tex]

Hence, the equation of the ellipse with height = 26 cm and width = 16 cm is - [tex]\frac{x^{2} }{169 } +\frac{y^{2} }{64} } =1[/tex]  and the horizontal width, in centimeters, of the plaque at a distance of 6 centimeters above the center point is 9.81cm

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Answer:

7 fishes

Step-by-step explanation:

Given the growth of the population of fish which is modeled by the exponential function:

[tex]P(t)=7 \cdot b^t[/tex]

Where:

t=time in weeks after release

b=growth rate of the fish

At t=0

[tex]P(0)=7 \cdot b^0\\P_0=7 \cdot 1 \\P_0=7[/tex]

The initial number, [tex]P_0[/tex] of fish which was released into the lake is 7.

Answer:

818.87

Step-by-step explanation:

£650 = $710.76

$1.00 = £0.91

Answer:

y=2x+4

y=-1/2x+4

linear quations

both have the same y intercept (=4).

y=2x+4  is positive straight line, slope = 2

y=-1/2x+4 is negative straight line, slope=-1/2

Step-by-step explanation:

You times 40 by $8:50 to get what he earned for the 40 hours. This will get you $340. To get the overtime pay, it's 1.5 times $8.50. This will get you $12.75, so times it by 10 to get the overtime pay. You end up with $127.50. You add both pays together (340 + 127.5) to get $467.50.

Answer:

a) 0.65

b) 0.1581

Step-by-step explanation:

We are given the following in the question:

Distribution of X:

Mean = 0.125

Standard deviation = 0.05

Distribution of Y:

Mean = 0.350

Standard deviation = 0.10

Solution:

[tex]M = X + 1.5Y[/tex]

a) mean of M

[tex]\mu_M = \mu_X + 1.5(\mu_Y) = 0.125 + 1.5(0.350) = 0.65[/tex]

b) standard deviation of M

If X and Y are independent then,

[tex]Var(X+Y) = Var(X) + Var(Y)\\Var)aX) = a^2Var(X)[/tex]

[tex]Var(M) = Var(X+1.5Y)\\Var(M) =Var(X) + (1.5)^2Var(Y)\\Var(M) = (0.05)^2 + (1.5)^2(0.10)^2 = 0.025[/tex]

Standard deviation of M =

[tex]=\sqrt{Var(M)} = \sqrt{0.025} = 0.1581[/tex]

The mean of M is 0.650. The standard deviation of M is approximately 0.1581.

To find the mean of M, we need to substitute the mean values of X and Y into the equation M = X + 1.5Y. Given that X has a mean of 0.125 and Y has a mean of 0.350, we can calculate the mean of M as follows:

Therefore, the mean of M is 0.650.

To find the standard deviation of M, we can use the fact that X and Y are independent. The formula for the standard deviation of the sum of independent random variables is given by:

σM = √(σX2 + (1.5σY)2)

Given that X has a standard deviation of 0.05 and Y has a standard deviation of 0.10, we can substitute these values into the formula to calculate the standard deviation of M:

Therefore, the standard deviation of M is approximately 0.1581.

Answer:

2 feet

Step-by-step explanation:

We are given that

[tex]b_1=21 feet[/tex]

[tex]b_2=5feet[/tex]

Area of trapezoid=26 square ft

We have to find the height of the cross section.

We know that

Area  of trapezoid=[tex]\frac{1}{2}(b_1+b_2)h[/tex]

Using the formula

[tex]26=\frac{1}{2}(21+5)[/tex]

[tex]26=\frac{1}{2}(26)h[/tex]

[tex]h=\frac{26\times 2}{26}=2 feet[/tex]

Hence, the height of cross section =2 feet

Answer:

  5.1

Step-by-step explanation:

Since there is no diagram provided here, we assume that c is the length of the hypotenuse, so we have ...

  c² = a² +b² . . . . . . Pythagorean theorem

  c² = 2.7² +4.3² = 25.78

  c = √25.78 ≈ 5.0774

  c ≈ 5.1

Answer:

"90% confidence" means there is a probabilty of 90% that the population mean (average compensation for the population of party clowns) lies within the confidence interval.

Step-by-step explanation:

The confidence interval is a range of values in which, according to the level of confidence that is calculated, is likely to include a parameter of the population. In this case, this parameter is the population mean compensation of party clowns.

The level of confidence is 90%, so there is 90% of confidence (or probability) that the population mean compensation for party clowns lie within $9394 and $9926.

None of the options below is correct.

Answer:

Probability that a student will score more than 1700 points is 0.50.

Step-by-step explanation:

We are given that the mean score for a standardized test is 1700 points. The results are normally distributed with a standard deviation of 75 points.

Let X = Scores results on a test

So, X ~ N([tex]\mu=1700,\sigma^{2} =75^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean score = 1700 points

            [tex]\sigma[/tex] = standard deviation = 75 points

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that a student will score more than 1700 points is given by = P(X > 1700 points)

  P(X > 1700) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{1700-1700}{75}[/tex] ) = P(Z > 0) = 1 - P(Z [tex]\leq[/tex] 0)

                                                        = 1 - 0.50 = 0.50

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0 in the z table which has an area of 0.50.

Hence, the probability that a student will score more than 1700 points is 50%.

Answer:

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

Step-by-step explanation:

Probability of a teacher being certified in Cardio-Pulmonary Resuscitation (CPR).

36 of 80

So

[tex]p = \frac{36}{80} = 0.45[/tex]

In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR?

45% of the days

0.45*180 = 81

In about 81 days we can expect that the teacher on bus duty will likely be certified in CPR

To calculate the number of days a teacher certified in CPR will be on bus duty, use the ratio of certified teachers (9/20) multiplied by the total number of school days (180), resulting in an expectation of 81 days.

The student is asking to calculate the number of days one can expect a teacher certified in CPR to be on bus duty at a local intermediate school. Given that 36 out of 80 teachers are certified in CPR, the ratio of certified to non-certified teachers is 36/80, which can be simplified to 9/20. To find out how many days a teacher on bus duty will likely be certified in CPR, we apply this ratio to the total number of school days, which is 180.

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Answer:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Step-by-step explanation:

For this case we define the random variable X as the annual income for people at certain city. And we know the following properties:

[tex] E(X) = 42, Sd(X) =42[/tex]

They select a sample size of n = 90>30. So then we can assume that the central limit can be applied.

From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

We want to calculate this probability:

[tex]P(\bar X <38)[/tex]

And we can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 38 we got:

[tex] z = \frac{38-42}{\frac{30}{\sqrt{90}}}= -1.265[/tex]

So then we want to find this probability:

[tex] P(z<-1.265)[/tex]

And we can use the normal standard distribution or excel and we got:

[tex] P(z<-1.265)=0.103[/tex]

Answer:

56

Step-by-step explanation:

The product of 2 numbers is what you get multiplying them together:

12x4 = 48

Now we need 8 more of that product so:

48 + 8 = 56

Answer:

  Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.

Step-by-step explanation:

The unit rate is the change in y for a 1-unit change in x. Since the graph of a proportion will go through the origin, it is appropriate to look at the y-value for x = 1 (one unit from the origin).

___

The ratio of units up to units to the right is also the unit rate when the fraction is reduced to lowest terms. It is a "unit" rate when the denominator of the fraction is 1 unit.

Answer:

A

Step-by-step explanation:

Answer: The correct answer is an UNFILLED CIRCLE

Step-by-step explanation: An organism can be homozygous dominant, if it carries two copies of the same dominant allele, or homozygous recessive, if it carries two copies of the same recessive allele.

A homozygous dominant is represented by an UNFILLED CIRCLE.

Answer:

The right question that describes what we need to examine is that:

If we examine the proportion of students at their campus who still live at home with their parents, how likely is that proportion to be more than 36%?

Step-by-step explanation:

For hypthesis testing, it is the p-value that needs to be obtained, to know the significance of the result. It is in the definition of what the p-value stands for that one would be able to pick which question best describes what we need to determine?

The p-value is actually defined as the probability of obtaining results as extreme as the observed results in the statistical analysis provided that the null hypothesis is true.

It is the probability of obtaining the claim to be tested that is usually contained in the alternative hypothesis, provided the null hypothesis is true.

So, since the null hypothesis states that the proportion of Millennial students at their campus, that live at home with their parents = 36%

The p-value is how likely it is or the probability that more than 36% of Millennial students at their campus live at home with their parents.

Hope this Helps!!!

The answer is: No. The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

Answer:

The answer is C.

Step-by-step explanation:

Answer:

D. Apothem

Step-by-step explanation:

An Apothem is a line from the center of a regular polygon at right angles to any of its sides.

The correct describes the line the arrow is pointing to in the regular pentagon below is,

⇒ Apothem

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

A regular pentagon is shown in figure.

Now, The line is vertical line.

Hence, From the center of the pentagon to the edge is called ''Apothem.''

Therefore, The correct describes the line the arrow is pointing to in the regular pentagon below is,

⇒ Apothem

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Answer:

False, there are infinite solutions

Step-by-step explanation:

Try solving this

3y - 6x = 24

8 + 2x = y

3(8 + 2x) - 6x = 24

24 + 6x - 6x = 24

24 = 24  true

Answer:

C

Step-by-step explanation:

Edge Trust

The value of the h(2), in the given graphed function, is determined as: C. 0.

The value of a function is the corresponding x-value of the function at that particular point or given y-value.

On the given function graph, when h(2), which is y = 2, the corresponding value of x is 0.

Therefore, the value of h(2) is: C. 0.

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Answer:

a. True

Question 13 of the attached image;

Step-by-step explanation:

Confidence interval, in statistics can be defined as the probability that a population parameter will fall between two set values( upper and lower bound) for a certain proportion of times. Therefore, there's 99% chance that the true difference in RDI levels between men and women is contained within the 99% Confidence interval shown in the previous questions.

The statement is a matter of statistical inference and would be true if the interval was correctly computed using appropriate methods. While the 99% confidence level suggests we are highly confident the true value lies within the interval, it is not a direct measure of probability.

The statement 'There is a 99% chance that the true difference in RDI levels between men and women is contained in the interval already computed' is an assertion relating to statistical inference, specifically, confidence intervals. If this interval was correctly computed using appropriate statistical methods, then it would be true that we are 99% confident that the true difference in RDI levels between mean and women is within this interval. However, it's worth noting that a 99% confidence interval does not necessarily mean there is a 99% probability that the value lies within the interval, it rather suggests that if we were to repeat this study 100 times, we would expect the true mean difference to be within the computed confidence interval 99 times.

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Answer:

3 schools did

Step-by-step explanation: