7. Defects in poured metal caused by contamination follows a Poisson distribution with average number of occurrences being 2 per cubic millimeter. What is the probability that there will be at least three defects in a randomly selected cubic millimeter of this metal

Answer:you can make around 3

Step-by-step explanation:

john can make 3 different patterns because he has 3 colors for example...

pattern 1:green,red,blue

pattern 2:red,blue,green

pattern 3:blue,red,green

A fraction is a number that represents part of a whole, and therefore, it is not a whole number

The correct option for the fraction of the adverts Carlos did sell is option A.

A. 1/9

Reason:

Known parameter are;

Number of 1/4 page advertisement Mary sold = Twice the number of page advertisement Carlos sold

The number of 1/4 page adverts James sold = 3 times the number  Mary sold

Let x represent the number of adverts Mary sold, ley y represent the number of adverts Carlos sold, and let z represent the number of adverts James sold, we have;

z = 3·x

Therefore, we have;

z = 2 × 3·y = 6·y

Substituting x = 2·y, and z = 6·y, gives;

The total number of adverts sold = 9·y

The number of adverts Carlos sold = y

The correct option is A. 1/9

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On solving the provided question, we got to know that he can bake 200/57 loaves or 3 29/57 loafs.

Mathematically speaking, fractions are represented by integers that indicate a portion of a whole. In the same way that a whole can be any quantity, value, or object, a fraction can be a portion or subset of any quantity of a whole. As an example, let's try to comprehend this idea. The pizza in the picture below is cut into 8 equally sized pieces. The chosen slice of pizza might now be expressed as 1/8 if we wanted to. This indicates that we are talking about one of eight equally sized sections. It denotes a ratio of 1/8. Reading options include: One-eighth, or

1 by 8

13 1/3 divided by 3 4/5

Let's first convert these mixed numbers to incorrect fractions.

13  1/3 =  13(3) + 1 = 39 + 1 = 40/3

3 4/5 = 3(5) + 4= 19/5

Now that we have divided 40/3 by 19/5, we can just switch the operation to multiplication and flip the second fraction because we know how to divide fractions.

40/3 x 5/19 = 200/57

he can bake 200/57 loaves or 3 29/57 loafs.

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Answer:

42

Step-by-step explanation:

20/100*210

20/100=1/5 or 0.2

1/5 or 0.2*210= 42

For finding a 95% confidence interval:

a) The sample mean is x = 16.13.

The sample standard deviation is s = 6.948.

The degrees of freedom are df = 10.

The critical value of t for a 95% confidence interval is t = 2.228.

The margin of error is ME = t × s/√n = 2.228(6.948)/√11 = 4.263.

The 95% confidence interval is x ± ME = 16.13 ± 4.263 = (11.867, 20.393).

b) The 95% confidence interval is (11.867, 20.393).

This means that we are 95% confident that the true population mean number of visits per physical therapy patient is between 11.867 and 20.393 visits.

c) This is because the confidence interval is a range of values that is likely to contain the true population mean. If many samples of the same size are taken from the same population, then about 95% of the confidence intervals from these samples will contain the true population mean.

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The graph of the system of the inequalities is attached.

To graph the inequalities y < -x - 4 and y ≥ (3/5)x + 4, we can start by graphing the corresponding equations and then shade the appropriate regions based on the inequality signs.

Let's begin with the equation y = -x - 4:

Choose a range of x-values to plot.

For simplicity, let's use x-values from -10 to 10.

Substitute different x-values into the equation to find corresponding y-values.

For example:

When x = -10, y = -(-10) - 4 = 10 - 4 = 6.

When x = 0, y = -(0) - 4 = -4.

When x = 10, y = -(10) - 4 = -10 - 4 = -14.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = -x - 4.

Next, let's graph the equation y = (3/5)x + 4:

Again, choose a range of x-values to plot. Let's use the same range of -10 to 10.

Substitute different x-values into the equation to find corresponding y-values. For example:

When x = -10, y = (3/5)(-10) + 4 = -6 + 4 = -2.

When x = 0, y = (3/5)(0) + 4 = 0 + 4 = 4.

When x = 10, y = (3/5)(10) + 4 = 6 + 4 = 10.

Plot these points on the coordinate plane and draw a straight line passing through them.

This line represents the equation y = (3/5)x + 4.

Now, let's shade the regions based on the inequalities:

For y < -x - 4, we need to shade the region below the line y = -x - 4.

For y ≥ (3/5)x + 4, we need to shade the region above or on the line y = (3/5)x + 4.

Hence, the region where the shaded regions overlap represents the solution to both inequalities.

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Answer:

B-80

Step-by-step explanation:

All angles add up to 180 subtract the 20 from 180 get 160, subtract the 80 from 160 and your left with 80

180-20-80=80

Answer:

80 degrees

Step-by-step explanation:

All the angles add up to 180 degrees

20 degrees plus x degrees + 80 degrees = 180

Answer:

a=3√700b210b

Step-by-step explanation:

Answer:

(4, 7/2)

Step-by-step explanation:

midpoint = x values/2, y values/2

Answer:

I am confident the answer is H.

Answer:87.86

Step-by-step explanation:

110x75/100=82.50

82.50x106.5/100=87.86

Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

Answer:

The answer is It is between 0 and 1

Step-by-step explanation:

If you solve the problem step by step as (-2^3)^-2<1 then it comes out as true so it would be less than 1 but more then 0.

Answer:

5 %

Step-by-step explanation:

1000 g = 1 kg

50 kg = 0.05 kg

0.05 = 5%

Therefore, 50 g as a percentage of 1kg is 5%.

Answer:

Don't see any graphs

Step-by-step explanation:

Answer:

its A

Step-by-step explanation:

The given statement "If data set A has a larger standard deviation than data set B, data set A is more spread out than data set B" is true.

The standard deviation is a measure of a data set's dispersion. It tells us how far the data values are from the mean.

A larger standard deviation means that the data points are more spread out, i.e., they are farther from the mean.

Therefore, if data set A has a standard deviation that is greater than data set B, it means that the values in data set A are more spread apart.

Hence, the given statement is true.

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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The number 842 is the number whose digit 4 is ten times larger than in the number 384

To solve the problem, we need to find a number in which the digit 4 is ten times larger than in the number 384.

In the number 384, the digit 4 is in the ones place, which means that its value is 4.

To find a number in which the digit 4 is ten times larger, we need to find a number in which the digit 4 is in the tens place and its value is 10 times larger than 4, which is 40.

The only answer option that fits this description is 842. In this number, the digit 4 is in the tens place and its value is 40, which is ten times larger than its value in the number 384.

Therefore, the correct answer is 842.

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Answer:

x = 145

Step-by-step explanation:

x and 35° lie on a straight line and are supplementary angles , sum to 180°

x + 35 = 180 ( subtract 35 from both sides )

x = 145

Answer: i don’t know

Step-by-step explanation:

Answer:34

Step-by-step explanation:

Answer:

4/3

Step-by-step explanation:

12/9 is equivalent to 4/3, because you can divide both the numerator and denominator by the common factor of 3 and that will give you the correct fraction: 4/3.

Hope this helped.

Therefore, the school spent $28.36 on a pass and lunch for each student.

The term "cost" typically refers to the amount of resources, usually money, time, or effort, that is required to produce or obtain something. It is the expense incurred in order to achieve a particular goal or outcome.

cost can be further classified into different types, such as fixed costs (expenses that do not change regardless of the level of production), variable costs (expenses that change depending on the level of production), and opportunity costs (the cost of the next best alternative that is forgone when choosing a particular course of action).

First, we need to find the total number of people who need passes for the zoo.

30 students + 2 teachers = 32 people in total

The cost of the passes for 32 people is $634.24, so the cost per person is:

$634.24 ÷ 32 = $19.82 per person

Next, we need to find the cost of lunch per student. We know that the school spent $256.20 on lunch for just the students, so:

$256.20 ÷ 30 students = $8.54 per student

Finally, we can add the cost of the pass and the cost of lunch together to find the total cost per student:

$19.82 (pass) + $8.54 (lunch) = $28.36

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The total cash due at signing is $3,700 at the local dealership..

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

The total cash due is calculated as:

Down payment: $1,800

Security deposit: $400

Acquisition fee: $300

Total: $1,800 + $400 + $300

Apply the addition operation, and we get

= $3,700

Thus, the total cash due at signing is $3,700.

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\(\begin{array}{|c|ll}\cline{1-1}\textit{a\% of b}\\\cline{1-1}\\\left( \cfrac{a}{100} \right)\cdot b\\\\\cline{1-1}\end{array}~\hspace{5em}\implies \stackrel{\textit{6.25\% of 859.99}}{\cfrac{6.25}{100}\cdot 859.99} ~~\approx ~~53.75\\\\\\~\hfill \stackrel{\textit{total cost for the bike}}{859.99+53.75 ~~\approx~~ 913.74}~\hfill\)

Therefore the value of function f(g(x)) comes out to be x\(e^{2}\) +\(e^{2}\)-3

An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. If anything is entered for x, there is just one output for y. Since x is the input value, we can state that y is a function of x.

Here,

Given: f(x)=x\(e^{2}\)-3  and g(x)=x+1

To find the value of f(g(x))

we put g(x) in f(x)

So,

=> f(g(x))= g(x)\(e^{2}\)-3

=>f(g(x))= (x+1)\(e^{2}\)-3

=> f(g(x))= x\(e^{2}\) +\(e^{2}\)-3

Therefore the value of function f(g(x)) comes out to be x\(e^{2}\) +\(e^{2}\)-3

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If the average is 85 minutes, then on the seventh day he skated for 115 minutes.

For a set of N values {x₁, x₂, ..., xₙ} we define the average as:

A = (x₁ + ... + xₙ)/N

Here we know that for four days, he skated for 1hr + 25min = 85 min

Then for 2 days he skated for 1hr + 10min = 70 min

And the seventh day he skated x minutes.

We know that the average is 85 min, then we can write the equation:

(4*85 + 2*70 + x)/7 = 85

x = 85*7 - 2*70 - 4*85

x = 115

He scated for 115 minutes.

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Answer:

Step-by-step explanation:

-4/5, -11/10, -5/2, 9/5

Answer:

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Step-by-step explanation:

Before solving the question, we need to understand the central limit theorem, and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Test if a lower proportion of men favor stricter gun control than women:

At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So

\(H_0: p_M - p_W = 0\)

At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So

\(H_1: p_M - p_W < 0\)

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.

This means that:

\(p_W = \frac{313}{564} = 0.555\)

\(s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209\)

In a random sample of 588 men, 307 favored stricter gun control laws.

This means that:

\(p_M = \frac{307}{588} = 0.522\)

\(s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206\)

0 is tested at the null hypothesis:

This means that \(\mu = 0\)

From the samples:

\(X = p_M - p_W = 0.522 - 0.555 = -0.033\)

\(s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029\)

Value of the test statistic:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.033 - 0}{0.029}\)

\(z = -1.12\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.

Looking at the z-table, z = -1.12 has a p-value of 0.1314.

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Answer:

3y(-5y^3+4y-3)

Step-by-step explanation: