Write 0.0000509 in standard form.

The diagonal of the rectangle is 14.87 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of rectangle = 110 square units

Length = 11 units

Area of a rectangle = Length x Wide.

110 square units = Length x Wide

110 = 11 x Wide

Wide = 110/11

Wide = 10

Now,

The diagonal of a rectangle.

Using the Pythagorean theorem we get,

Diagonal² = Wide² + Length²

Diagonal² = 10² + 11²

Diagonal² = 100 + 121

Diagonal² = 221

Diagonal = √221

Diagonal = 14.87 units.

Thus,

The diagonal of the rectangle is 14.87 units.

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Answer:

Y-int = -45, X-int =-11.25

Step-by-step explanation:

Please read this before moving on :)

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+b, where m is slope and b is the y-intercept.

We know that equation of a line is y=mx+b. To find the value of the x-intercept of the line we simply need to put the value of the y as 0.

Using the Slope Equation : Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

2 points; (0,-40), (-10,0)

0-(-40)/(-10)-0 = 40/-10 = -4

Y=MX+B

Y=MX+(-45)

Y=MX-45

Y-int = -45

Y=MX+B

0=(-4)x+-45

45=-4x

X-int =-11.25

The probability that the retailer sells no more than one house in a month is 0.60.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes and how likely they are to happen. The analysis of events governed by probability is called statistics.

The given is a probability distribution. The probability density function or PDF of the probability is defined for the random variable x, where x ranges from 0 less than or equal to x less than or equal to 2 ie the range of x is from 0 to 2 with 0 and 2 inclusive.

x    :      0          1           2

p(x):   0.20    0.40     0.40

The probability that the retailer sells no more than one house in a month is given by

P(x less than or equal to one) = P(0) + P(1)

=0.20 + 0.40 = 0.60.

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Using the simplification of power, [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex] and [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex].

In the given question,

We have to simplify the given expression.

Before simplifying the expression we first learn that the negative power can be positive after changing their position from numerator to denominator.

We use the method of adding the power of expression to solve the expression.

(1) The given expression is [tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}[/tex].

We firstly simplifying the power after the bracket by multiplying the power to each variable.

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-\frac{1}{4})^{-3}(w^{-1})^{-3}(z^{-2})^{-3}[/tex]

Simplifying the expression.

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1)^{-3}(\frac{1}{4})^{-3}(w^{-3})(z^{6})[/tex]

Now we make the power positive by changing their position

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=(-1){4}^{3}(w^{-3})(z^{6})[/tex]

Simplifying

[tex](-\frac{1}{4}w^{-1}z^{-2})^{-3}=-64w^{-3}z^{6}[/tex]

(2) The given expression is [tex]\frac{g^{-6}h^8}{h^2}[/tex].

Simplifying the expression.

As we know that the power with same base get subtracted when they are in division.

So [tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{8-2}[/tex]

[tex]\frac{g^{-6}h^8}{h^2}=g^{-6}h^{6}[/tex]

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Answer:

It's either 1:3 or 1:3

Step-by-step explanation:

A scale factor is times, calculate and, a reinduced PEMDAS

The expression that equals 2B+C in standard form is 4x² + 6

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

B = x² + 2

C = 2 + 2x²

The expression to calculate is given as

2B + C

Substitute the known values in the above equation, so, we have the following representation

2B + C = 2x² + 4 + 2 + 2x²

Evaluate the like terms

2B + C = 4x² + 6

Hence, the expression is 4x² + 6

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The probability that it toys will be shipped is option b ) 0.6691 .

Hypergeometric Distribution will be used

P ( X = x ) = h ( x , N , n , k ) = [tex]C_{k,x}[/tex][tex]C_{N-k,n-x}[/tex] / [tex]C_{N,n}[/tex]

[tex]C_{n,x}[/tex] = n! / [ x! ( n - x ) !

According to question,

N = 17

k = 2

n = 3

To find : P ( X = 0 ) ,

P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )

                = [tex]C_{2,0} C_{15,3} / C_{17,3}[/tex]

                 = 455 / 680

         = 0.6691

So there is 66.91 % probability that toys will be shipped .

Hence , option b ) 0.6691 is the correct answer .

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There are 6 pennies in a total of 150 coins.

Given that,

Ninety of the 150 coins are quarters. 40 percent of the remaining coins are nickels, with the remainder being dimes and pennies.

and also,

For every penny, there are five dime.

Total = 150 coins

Out of it, 90 are quarters so the remaining coins are 60

It is said that,

In that 60 coins 40% are nickels which means

40% of 60 is 24

So remaining coins are 36 (by subtracting 24 from 60)

It is said that there are 5 dimes for every penny which means

Using Algebra,

x + 5x = 36

6x= 36

x= 6

Therefore, there are 6 pennies in a total of 150 coins.

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A) Yes it is a function and f(x)=2.80+3.50x so 2.80 is an independent function and 3.50x is dependent function

B) Domain x = (0,20] and Range y = (2.8,72.8]

A dependent function is what?

A dependent function type is one whose outcome depends on the parameters of the function.

Independent function: What is it?

Independent function (plural independent functions) as a noun (mathematics) any one of a group of functions whose value cannot be inferred from the values of all the others.

Given: The expression y = 3.5x + 2.8 calculates the y (in dollars) cost of an x-mile taxi fare. You have enough cash to take a cab for a maximum of 20 kilometres.

Domain and range to find

Solution:

y = 3.5x + 2.8

cost y (in dollars)

miles, in.

You have enough cash to take a cab for a maximum of 20 kilometres.

0 < x ≤ 20

Therefore, x = [0, 20].

Domain x = [0, 20]

y = 3.5x + 2.8

x = 0

=> y = 0 + 2.8 = 2.8

x = 20

=> y = 3.5(20) + 2.8

=> y = 70 + 2.8

=> y = 72.8

2.8 < y ≤ 72.8

y = (2.8 , 72.8 ]

Range = (2.8 , 72.8 ]

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Find the domain and range of the function f(x)= √9-x² . OR. Let f ...

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Consider this function. f(x) = |x – 4| + 6 If the domain is restricted to

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Using One way ANOVA and Randomized block design, the sum of squares between groups (ssb) is equal to the sum of sum of sum of explantary variable A's sum of squares and errors sum of square.

Statistics uses one-way ANOVA to compare the means of three or more independent groups to determine if there is a statistically significant difference between the corresponding population means. It is constructed using the sum of squares measure of total variability used in the numerator of the standard deviation, subtracting the mean, squaring the difference, and adding all observations to obtain the total variability Generate a scale. For multiple groups, we focus on decomposing this total variability (total sum of squares) into the variability between means (the sum of squares of the explanatory variable A) and the variability of the residuals or errors (the error sum of squares).

SSTotal = sum of squares = ∑( yᵢ - Y )²

Total variation is assessed by the total mean (the estimated mean of all observations, available from mean-only models).

SSA = Sum of Squares of Explanatory Variable A

Also called treatment, regression, or model sum of squares. ∑∑(yᵢⱼ - Y' )²

SSE = error (residual) sum of squares

Variation of response around group mean.

Also called the sum of squared residuals.

SSE = ∑∑( Y - Y')²

The total sum of squares is always equal to the sum of the sum of the squares of the explanatory variable A and the sum of the squared errors, SST (total) = SSA + SSE. This equation means that if SSA increases, SSE must decrease if SSTotal remains the same. This result is called the sum of squares decomposition formula.

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The equation which represents the sentence given; Half the difference of a number and 5 is−2 is; 1/2(x - 5) = -2; 1 half left parenthesis x minus 5 right parenthesis equals negative 2.

It follows from the task content that the expression which best represents the given algebraic expression is to be determined.

First, the difference of a number, x and t is represented as; (x - 5).

Hence, the word phrase; Half the difference of a number and 5; is best represented algebraically as; 1/2(x - 5).

Ultimately, the whole word phrase; Half the difference of a number and 5 is -2 can best be represented as; 1/2(x - 5) = -2.

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A minimum of 71 observations must fall inside the interval (20, 40).

It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Given,

The data set has 80 observations and has mean 30 and standard deviation 5.

Chebyshev's theorem states that for each data set, the proportion (or percentage) of values ​​that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.

x = 30

s = 5

Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).

(30 - 3.5, 30 + 3.5) = (10, 40)

According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of  80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.

A minimum of 71 observations must fall inside the interval (20, 40).

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The calculation that is not a way to find a fraction of 5/8 is:

1 - 0.125.

A fraction is a numerical representation of the division of the two terms x and y, as follows:

Fraction = x/y.

The terms are classified as follows:

Hence the numeric value of the fraction 5/8 presented in this problem is given as follows:

5/8 = 0.625.

The calculation that is not a way to find the fraction of 5/8 is the only expression that has a different value than 5/8.

The expression with a different value is of:

1 - 0.125 = 0.875.

As the value of 0.875 is different than the value of 0.625 equivalent to the fraction of 5/8.

The complete problem is given by the image at the end of the answer.

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The function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

The function is  

f(x) =[tex]2(\frac{1}{2})^x[/tex]

The function is defined as the expression that represents the relationship between one variable and another variable.

The function is in the form of

f(x) = a × [tex]b^x[/tex]

Such functions are called exponential function

Here  

The value of a = 2

The value of b = 1/2

If the value of b > 1, the function is called exponential growth function.

If the value of b < 1, the function is called exponential decay function.

Here b < 1

Therefore it is exponential decay function

Hence, the function represented by the f(x) =[tex]2(\frac{1}{2})^x[/tex] is an exponential decay function

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If now he uses a 30 frame beehive. It has the same ratios of frames to honey as a smaller beehive. The amount of  honey that Bert’s new beehive hold is 200.

Given data:

Number of frame beehive = 6

Pound of honey = 40

Current Frame beehive = 30

First step is to formulate an equation and then use the formulated equation to find  the number of honey

40 × 30 ÷ 6

Hence,

40 × 5

= 200 honey

Therefore the number of honey is 200.

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We can use both regular and strong induction.

The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).

In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.

Regular Induction form

N>6 = n=7 in basic case

3n = 37 = 2187

N! = 7! = 5040

For n= 7 3n<n! is true

Induction hypothesis

Let for n= k and k>6

Assume 3k<k! is true

We prove that for k = k+1 the assumption holds true then the assumption must be true for k

K = k+1

3k+1 < (k+1)!

3k. 3 < (k+1) k!

3k < (k+1)/3.k!

For k>6

(k+1)/3 >1 and let (k+1)/3 = p

3k < P.k!

But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1

Therefore 3k<k! for k>6

3n < n! for all integers n greater than 6.

Therefore we can use both regular and strong induction

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If 9 seeds are planted, what is the probability that exactly 3 don't grow will be 1/5832000 as 5% chance are there that plant will not grow.

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The chances of seed to be not growing is 1–0.95 =0.05.

For 3 seeds not to grow being simultaneous occurring events have the probability = 0.05×0.05x0.05=0.000125

As 9 seeds being planted the probability of selecting 1 out of 9 is (1/9).

So for 3 mutual occurring case is (1/9)×(1/9)x(1/9)= 1/729

So the probability will be (1/729)×1/8000=1/58,32,000

The likelihood that exactly 3 seeds out of 9 will not germinate is 1/5832000, or 5%, so there is a chance that the plant won't grow.

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Answer:

Step-by-step explanation:

there is probably a way to do this w/o calculus,  but I cheated and used that.

A = Length * Width

A = x * ( 650 -2x)

A = 650x -2[tex]x^{2}[/tex]

d/dx ( A = 650x -2[tex]x^{2}[/tex])

0=650 -4x

4x = 650

x = 135 m

A= 650*135 -2*[tex]135^{2}[/tex]

A = 51,300  [tex]m^{2}[/tex]

There are 2 different bad arrangements possible.

We see that there are 5! absolute ways of orchestrating the numbers. Nonetheless, we can constantly turn these numbers so that, for instance, the number 1 is dependably at the highest point of the circle. Consequently, there are just 4! ways under turn, which is easy to drill down. We methodically list out every one of the 24 cases.

Presently, we should inspect assuming they fulfill the circumstances. We can see that by selecting each number, in turn, we can continuously acquire subsets with aggregates 1, 2, 3, 4, and 5. By picking the round trip, we can get 15. By selecting everything aside from 1, 2, 3, 4, and 5, we can get subsets with amounts of 10, 11, 12, 13, and 14.

This implies that we presently just have to check for 6, 7, 8, and 9. Be that as it may, whenever we have found a set adding to 6, we can pick all the other things and get a set adding to 9, and comparably for 7 and 8. Hence, we just have to check each case for whether we can acquire 6 or 7.

We observe that there are just 4 arrangements that fulfill these circumstances. In any case, each of these is an impression of another. We divide by 2 for these reflections to get the final answer of B = 2.

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About [0.7479, 0.8091] of medical malpractice cases are abandoned or dismissed, according to the estimate with a 95% confidence level.

A confidence interval is a method for estimating a population parameter, such as the population proportion, at a given level of confidence, using the sample statistic, such as the sample proportion, and the confidence coefficient, such as the critical value.

arbitrary sample size, n = 1228

number of those who were dropped or dismissed, x = 856

The sample percentage of later discarded or dropped, p = 956 / 1228 ≅ 0.7785

Level of confidence = 0.99

Level of significance α = 0.01

The population proportion's 99% confidence interval estimate is calculated as follows:

p ± [tex]z_{a/2}[/tex] * [tex]\sqrt\frac{p (1 - p)}{n}[/tex]

Using the Excel function or the z-distribution table for calculation

[tex]z_{a/2} = z_{0.01/2} = z_{0.005}[/tex]

=NORMSINV(0.05)

[tex]z_{0.01/2}[/tex] ≅ ±2.58

The interval's computation is as follows:

0.7785 ± 2.58 * [tex]\sqrt\frac{0.7785 (1 - 0.7785)}{1228}[/tex]

= 0.7785 ± 2.58 * 0.0118

= = 0.7785 ± 0.0306

(0.7479, 0.8091)

As a result, the estimate of the proportion of medical malpractice claims that are withdrawn or dismissed at a 99 percent confidence interval is roughly [0.7479, 0.8091].

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Sarah can purchase 8 mangoes with all her remaining money

Given that:

Sarah has 21.50 to go grocery shopping

She donates 3.00 to a canvasser for a charity (that is subtraction).

Thus, the remaining money = 21.50 - 3.00 = 18.50

If mangoes cost 2.25. In order to know how many mangoes she can purchase if she uses up all of her remaining money, you have to divide the remaining money (18.50) by the cost of the mangoes (2.25). Thus:

Number mangoes = remaining money /cost of mangoes

Number mangoes = 18.50 / 2.25 = 8

Therefore, she can purchase 8 mangoes if she uses up all of her remaining money

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The angle of x in the triangle is 75 degrees.

The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Therefore, the base angles are equal.

The third angle of the triangle is 30 degrees(vertically opposite angles)

Hence,

x + x + 30 = 180

2x + 30 = 180

2x = 180 - 30

2x = 150

x = 150 / 2

x = 75 degrees

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Answer x = 19/24

Step-by-step explanation:

Using the linear function, the depth of the dive at 5 seconds is 60.95 feet

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable.

In this question, we can represent the problem using a linear function or equation and plug in the value of our unknown.

y = 4.8 + 11.23t

Using this function, we can find the depth at 5 seconds;

y = 4.8 + 11.23(5)

y = 60.95ft

The depth of the whale at 5 seconds is 60.95 feet

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Answer:

Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.

Step-by-step explanation:

Assume the triangular sail is a right triangle.

The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]

If A = 4.8, B = 2.5, and C = 7.5, then [tex]4.8^{2} + 2.5^{2} = 7.5^{2}[/tex].

[tex]4.8^{2} + 2.5^{2} = 23.04 + 6.25 = 29.29[/tex]

[tex]7.5^{2} = 56.25[/tex]

In conclusion, [tex]29.29 \neq 56.25[/tex], so there is a problem with the sail.

Answer:

It will take 37.5 minutes for both containers to reach the same amount of water which is 1050 mL

Step-by-step explanation:

1500 - (12 × 37.5) = 1050

600 + (12 × 37.5) = 1050

Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

The equations are

3(x+2) = 18

x + 2 = 6

Part A

Consider the first equation

3(x + 2) = 18

Divide both side of the equation by 3

3(x+2) / 2 = 18/3

x + 2 = 6

We will get equation B from equation A, if we divide both side of the equation by 3

Part 2

The first equation

3(x+2) = 18

x + 2 = 6

x = 6-2

x = 4

The second equation

x+2 = 6

x = 6-2

x = 4

Both the equation has same solution

Hence,

Part A

We can get equation B from A by Multiply/divide both sides by the same non-zero constant.

Part B

The two equations are equivalent, they have same solution

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Considering the average rate of change, the time periods in which snowshoes are recommended are given as follows:

C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.

The average rate of change of a function is given by the change in the output of the function (change in the numeric value) divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given by the fraction presented as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

The initial amount is of 4 inches, hence, considering the rates, the amounts of snow on the ground are given as follows:

Hence the intervals are given by option c.

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