A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the 1000-pound legal limit, and the standard deviation to be less than 40. A random sample of 31 helmets was tested and the sample mean and variance were found to be 825 pounds and 2350 pounds2, respectively. The manufacturer wants to know if the data provides sufficient evidence to indicate that the standard deviation is significantly less than 40.
Step 1 of 5: Calculate the test statistic for this problem. Round your answer to two decimal places.
Step 2 of 5: Determine the p-value for a lower one-sided alternative hypothesis (left-tail test). The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 3 of 5: What is the rejection region at the 10% level of significance for the test on the variance for a left-tailed alternative hypothesis? The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 4 of 5: State your conclusion using a significance level of 0.05. The alternative hypothesis for this problem is H1: Ï2 < 1600 lbs2.
Step 5 of 5: Calculate a 90% confidence interval for the variance of force on the helmets. Round your answers to four decimal places.

Answer: The way you can find the area of this shape is by splitting the shape into a triangle and a square find the areas of each shape and then add the values.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Distribute the 10: 30p + 40

If you are solving for p, then subtract 40: 30p = -40

Then divide 30: p = -40/30, simplified to p = -4/3

Answer:

  30p -40

Step-by-step explanation:

You want to simplify the expression -10(-3p +4).

The distributive property tells you the product is ...

  -10(-3p +4)

  = (-10)(-3p) + (-10)(4)

  = 30p +(-40)

  = 30p -40

__

Additional comment

It is easy to get confused by minus signs. For any given numerical product the sign of the result will be negative if (and only if) the number of negative factors is odd.

Here, the first product is (-10)(-3p), which has an even number of minus signs. The result will be the same as with no minus signs:

  (-10)(-3p) = (10)(3p) = 30p

On the other hand, the product (-10)(4) has an odd number of minus signs. That result will be negative:

  (-10)(4) = -40

For this problem, you could start by distributing the minus sign, changing the sign of each term inside the parentheses:

  -10(-3p +4) = 10(3p -4)

Doing this can simplify the mental load of figuring the signs of the product terms.

The measure of the third angle in the triangle is 80 degrees.

The sum of the angles in a triangle is always 180 degrees.

Therefore, to find the measure of the third angle in the triangle with angle measures of 40° and 60°,

We can subtract the sum of these two angles from 180°:

180° - (40° + 60°) = 180° - 100° = 80°

Therefore, the measure of the third angle in the triangle is 80 degrees.

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Answer:

see explanation

Step-by-step explanation:

10

length of side opposite ∠ A is BC = 20

11

length of side adjacent to ∠ A is AC = 21

12

length of hypotenuse is AB = 29

13

sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{20}{29}[/tex]

14

cos A = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{21}{29}[/tex]

15

tan A = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{20}{21}[/tex]

The Surface area of the triangular prism is 26.88 cm².

The Volume of the triangular prism is 7.68 cm³.

The formulas we would used are:

Surface area of triangular prism = (S1 + S2 + S3)(L) + bh

Volume of triangular prism = 1/2 * base * height * length of prism

Perimeter of the triangular face = (S1 + S2 + S3) = 4.0 + 3.2 + 2.4 = 9.6 cm

Length of prism = 2.0 cm

base of triangular face (b) = 3.2 cm

height of triangular face (h) = 2.4 cm

Plug in the values:

Surface area of triangular prism = (9.6)(2.0) + (3.2)(2.4) = 26.88 cm²

Volume of triangular prism = 1/2 * 3.2 * 2.4 * 2.0 = 7.68 cm³

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She needs 74.25 ft² of glass to cover the pyramid.

To obtain the surface area of any prism, we combine the areas of all the parts that compose the prism.

The pyramid in this problem is composed as follows:

The area of the square base is given as follows:

As = 5.5² = 30.25 ft².

The area of the four triangles is given as follows:

At = 4 x 1/2 x 5.5 x 4

At = 44 ft².

Hence the surface area of the pyramid is given as follows:

S = As + At

S = 30.25 + 44

S = 74.25 ft².

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Answer:

true

Step-by-step explanation:

Answer- 24 spins

The probability of getting an E on a single spin is 1/4. The probability of not getting an E on a single spin is 3/4.

To find the expected number of spins before getting 6 E's, we can use the negative binomial distribution.

The formula for the expected value of a negative binomial distribution is:

E(X) = r * (1/p)

where:

- X is the random variable representing the number of spins until the 6th E appears

- r is the number of successes we want (in this case, 6)

- p is the probability of success (in this case, 1/4)

E(X) = 6 * (1/(1/4)) = 24

Therefore, Marcus's prediction for the number of total spins before the letter E appears 6 times is 24.

So the answer is 24 spins.

To discover the probability that the ceramics piece is painted, we basically separate the number of painted pieces by the whole number of pieces: P(painted) = 183/837 ≈ 0.2185

b. To discover the likelihood that the painted ceramics piece is painted in a curvilinear enhancement, we utilize Bayes' hypothesis:

P(curvilinear | painted) = P(painted | curvilinear) * P(curvilinear) / P(painted)

We are given that there are 183 painted pieces, of which 14 are painted in a curvilinear enrichment. In this manner,

P(painted | curvilinear) = 14/183 ≈ 0.0765

We are moreover given that there are 837 pieces in add up, of which 183 are painted.

P(painted) = 183/837 ≈ 0.2185, we ought to discover the likelihood that a painted piece is painted in a curvilinear enrichment, which is given as 14 out of 183 painted pieces. P(curvilinear) = 14/183 ≈ 0.0765

P(curvilinear | painted) = (0.0765) * (0.0765) / (0.2185) ≈ 0.0266

thus, given that the pottery piece is painted, the likelihood that it is painted in a curvilinear enhancement is roughly 0.0266, or 2.66%.

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The value of x after simplifying the given equation is approximately 1295.6.

To solve for x in the equation

(679/1327) + (677-x)/1329 + (675-x)/1331 + (673-x)/1333 = 4

We can start by simplifying the fractions and combining like terms

679/1327 + (3x - 1010)/((1329)(1331)(1333)) = 4

Multiplying both sides by (1327)(1329)(1331)(1333), we get

(679)(1329)(1331)(1333) + (3x - 1010)(1327)(1331)(1333) = 4(1327)(1329)(1331)(1333)

Expanding the products and simplifying, we get

(679)(1329)(1331)(1333) + (3x)(1327)(1331)(1333) - 1010(1327)(1331)(1333) = 4(1327)(1329)(1331)(1333)

Adding 1010(1327)(1331)(1333) to both sides, and dividing both sides by (3)(1327)(1331)(1333), we get

x ≈ 1295.6

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Assume that A and B are independent events. it means that the occurrence of event A does not affect the probability of event B and vice versa.

b. Assume that A and B are independent events. My response is Yes, P(A and B) can be defined as P(B) • P(A|B).

In the event that A and B are independent events, at that point the probability of A happening is one that is influenced by the event of B and vice versa. Hence, P(B) is comparable to P(B|A), showing that the probability of occasion B happening remains unaltered in any case of event A's event. Within the same vein, the likelihood of event A happening remains consistent whether event B has stay put or not, indicated as P(A) = P(A|B).

Therefore in response to question 2, The reason why independent events are not affected  by one another is that the likelihood of one event happening has no effect on the probability of the other event occurring.

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The cumulative frequency of the numbers 6-10 is thus 2 + 0 + 1 + 1 + 0 = 4.

To determine the frequency of the numbers 6-10 in this stem-and-leaf plot, examine the second row, which has a stem of 1 and leaves of 0 0 2 3 6 6. This row displays the digits 10, 10, 12, 13, 16, and 16, which correspond to 6 students who sold between ten and nineteen lollipops.

Because 2 of these 6 pupils sold exactly six lollipops (represented by leaf 06), the frequency of the number six is two.

There are no students who sold 7 lollipops exactly.

Because one kid sold exactly eight lollipops (represented by the leaf 08), the number 8 has a frequency of one.

One student sold exactly nine lollipops (represented by the number 9) As a result, the frequency of the number 9 is 1.

Zero students sold a total of ten lollipops.

The cumulative frequency of the numbers 6-10 is thus 2 + 0 + 1 + 1 + 0 = 4.

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If a pizza with an 18-inch diameter is divided into 10 equal pieces, then each slice will have a surface area of roughly 25.45 square inches.

Diameter is defined as a straight line across the middle of a body or figure, particularly a circle or sphere. Pizza diameter is the length of a straight line that touches two locations on the edge of a pizza pie and passes through its center.

Each sector of the pizza, which is divided into 12 equal sections, has an arc measurement of 360/10= 36 degrees.

As = (360÷Ф) ×X r² where x is the measure of the intercepted wave, yields the area of a sector.

We know that x=36 and

d=18→r=9 in. Thus, r is the radius and A is the area of each intersecting arc of a sector.

A=1/10×81π

then each slice will have a surface area of roughly 25.45 square inches.

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The correct answer is false. A reduced echelon matrix [tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where[tex]b \neq 0[/tex], is not considered one-to-one.

Let's first define what it means for a matrix to be one-to-one.

A matrix is said to be one-to-one if each column of the matrix is linearly independent.

This means that for any given input, there is only one possible output.
Now, let's consider the reduced echelon matrix T(x) = 0. If this matrix has a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], b ≠ 0, it means that one of the variables in the system of equations represented by the matrix is a free variable.

This free v[tex]T(x) = 0.[/tex]ariable can take on any value, and the other variables will adjust accordingly.
If the reduced echelon matrix is [tex][1 0 | 2; 0 0 | 0],[/tex] the system of equations would be [tex]x = 2[/tex] and y can be any value.

This means that the matrix is not one-to-one, because there are multiple outputs for the same input.
the correct answer is false.

A reduced echelon matrix[tex]T(x) = 0[/tex] with a row of [tex][0 . . 0 | 0] or [0 . . . 0 | b][/tex], where [tex]b \neq 0[/tex], is not considered one-to-one.

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The value of x is 3 unit.

The correct option is B.

We have,

P = 3√2/2

Angle= 45

Using Trigonometry

cos 45 = B /H

1/√2 = ( 3√2/2)/ x

x= 3√2/2 . √2

x = 6/2

x= 3 unit

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Answer:

sugger

Step-by-step explanation:

because she bought 34.15 super and 34.144 pepper

Answer:

Quotient=23 and remainder=14

The measure of variability that the charity should use to accurately represent the data is B. The IQR of 13 is the most accurate to use, since the data is skewed.

The charity should use the Interquartile Range (IQR) as the measure of variability since the data is skewed. The IQR measures the range of the middle 50% of the data, which is less affected by outliers or skewed data.

Q1 is the median of the first half of the data: 5, 5, 6, 8, 10, 15 (Q1 = 7)

Q3 is the median of the second half of the data: 15, 18, 20, 20, 20, 20, 20 (Q3 = 20)

Now, we can calculate the IQR:

IQR = Q3 - Q1

IQR = 20 - 7

IQR = 13

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Answer:

1. is (18,4)

2. is (8,10)

3. (-9,-8)

4. (9,-8)

Step-by-step explanation:

i promise its right please give brainliest

Answer:

24 meters

Step-by-step explanation:

We can use Pythagoras' theorem to solve this problem. Let's call the width of the field "w". We know that Ken ran from one corner of the field to the opposite corner, a distance of 85 meters. This distance is equal to the hypotenuse of a right triangle whose legs are the length and width of the field. We also know that Ken ran along its length, a distance of 77 meters. This length is one of the legs of the right triangle.

Using Pythagoras' theorem, we can write:

w^2 + 77^2 = 85^2

Simplifying this equation gives:

w^2 = 85^2 - 77^2

w^2 = 576

Taking the square root of both sides gives:

w = sqrt(576)

w = 24

Therefore, the width of the field is 24 meters 1.

I hope this helps!

The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made

To determine how many diners can be expected to show up at The Orchard Cafe, we can follow these steps:

1. Identify the percentage of diners who actually show up: Since 4% of diners with reservations don't show up, the percentage of diners who do show up is 100% - 4% = 96%.

2. Calculate the expected number of diners who show up: Multiply the total number of reservations (81) by the percentage of diners who show up (96%).

81 reservations x 0.96 (96% as a decimal) = 77.76

Since the number of diners must be a whole number, you can round the result to the nearest whole number.

In this case, 77.76 can be rounded down to 77.

Your answer: The Orchard Cafe can expect approximately 77 diners to show up out of the 81 reservations made.

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The probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 8 + 7 + 6 = 21

probability of picking a blue ball = 7/21

probability of picking a green ball = 6/21

probability of picking a blue or green ball = 7/21 + 6/21

probability of picking a blue or green ball = (7 + 6)/21

probability of picking a blue or green ball = 13/21

probability of picking a blue or green ball = 0.6190

Therefore, the probability that a ball picked at random is blue or green is equal to 0.619 to the nearest thousandth.

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Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

A quadratic equation can be made together into perfect square trinomial simply adding or removing elements from both sides, a technique known as "completing the square."

You can use the square's completion as another mathematical tool to solve a variety of problems:

Given expression:

-3x² - 298 = 60x - 1

isolating the x values:

-3x² - 60x = 298 - 1

-3x² - 60x = 299

Taking -3 common from the left hand side:

-3(x² + 20x) = 299

x² + 20x = - 299/3

This, can be written as:

x² + 2*10x = - 299/3

add both side by 100

x² + 2*10x + 100 = - 299/3 + 100

On simplification:

(x + 10)² = (-299 + 300) /3

(x + 10)² = 1 /3

Comparing obtained expression with the given form: (x+a)²=b

a = 10 and b = 1/3

Thus, the intermediate step in the form (x+a)² = b as a result of completing the square for the given equation is - (x + 10)² = 1 /3.

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The values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

We can use the following formulas to find the variance of X:

Var(X) = E[X^2] - (E[X])^2

E[X] = p1 + 2p2 + 3p3

E[X^2] = p1 + 4p2 + 9p3

Substituting these expressions into the formula for the variance, we get:

Var(X) = p1 + 4p2 + 9p3 - (p1 + 2p2 + 3p3)^2

Simplifying this expression, we get:

Var(X) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex]

To maximize Var(X), we want to maximize this expression subject to the constraint p1 + p2 + p3 = 1. We can use Lagrange multipliers to find the maximum. Let:

L(p1, p2, p3, λ) = -[tex](p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3 + λ(1 - p1 - p2 - p3)[/tex]

Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 2/7, p2 = 3/7, p3 = 2/7, λ = 4/7

Therefore, the values of p1, p2, p3 that maximize Var(X) are p1 = 2/7, p2 = 3/7, and p3 = 2/7.

To minimize Var(X), we want to minimize the expression [tex]-(p1^2 + 2p2^2 + 3p3^2) + 2p1p2 + 6p1p3 + 4p2p3[/tex] subject to the constraint p1 + p2 + p3 = 1. We can use the same Lagrange multiplier method to find the minimum. Taking partial derivatives and setting them equal to zero, we get:

-2p1 + 2p2 + 6p3 - λ = 0

4p1 - 4p2 + 4p3 - λ = 0

6p1 + 8p2 - 6p3 - λ = 0

p1 + p2 + p3 = 1

Solving these equations, we get:

p1 = 0, p2 = 1/3, p3 = 2/3, λ = 2/3

Therefore, the values of p1, p2, p3 that minimize Var(X) are p1 = 0, p2 = 1/3, and p3 = 2/3.

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The equation represents a linear function.

What is quadratic equation?

A quadratic equation is a polynomial equation of degree two which can be written in the form: ax² + bx + c = 0, where x is the variable and a, b, and c are constants with 'a' not equal to 0. The term 'quadratic' comes from the Latin word 'quadratus', which means 'square'.

The equation given in the image is a quadratic equation in standard form, which means it is written in the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

To determine which statement is true about this equation, we need to analyze its discriminant, which is given by the expression b^2 - 4ac. The discriminant tells us about the nature of the solutions of the quadratic equation.

If the discriminant is positive, then the equation has two distinct real roots.

If the discriminant is zero, then the equation has one real root (also known as a double root).

If the discriminant is negative, then the equation has two complex roots (conjugate pairs).

In the given equation, a = 3, b = -4, and c = 1. Substituting these values into the discriminant formula, we get:

b^2 - 4ac = (-4)^2 - 4(3)(1) = 16 - 12 = 4

Since the discriminant is positive, we know that the quadratic equation has two distinct real roots. Therefore, statement (A) is true.

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Answer:

B. Mixed numbers with unlike denominators can be subtracted from each other.

Step-by-step explanation:

Mixed numbers are numbers that have a whole part and a fractional part, such as 2 1/4 or 3 3/5. Unlike denominators are fractions that have different numbers in the bottom, such as 1/4 and 3/5. They are also called unlikeable denominators because they make math harder and more annoying. Who likes to deal with fractions anyway?

Mixed numbers with unlike denominators can be subtracted from each other, but only if you follow some tedious steps. First, you have to find a common denominator for the fractions, which is the smallest number that both denominators can divide into. This is like finding a common enemy for two rival gangs. For example, to subtract 2 1/4 from 3 3/5, we need to find a common denominator for 1/4 and 3/5. The least common denominator is 20, because both 4 and 5 can divide into it. Then, we have to multiply both fractions by the same factor to get equivalent fractions with the same denominator. This is like dressing up both gangs in the same uniform to make them look alike. For example, we multiply 1/4 by 5/5 and 3/5 by 4/4 to get:

2 1/4 = 2 5/20

3 3/5 = 3 12/20

Now we can subtract the fractions by subtracting the numerators and keeping the denominators the same. This is like taking away some members from each gang and seeing who has more left. For example, we subtract 5/20 from 12/20 and get 7/20. Then we subtract 2 from 3 and get 1. Finally, we add the whole part and the fractional part together to get the final answer. This is like adding up the remaining members of one gang and giving them a name. For example, we get:

3 12/20 - 2 5/20 = (3 - 2) + (12/20 - 5/20) = 1 + 7/20 = 1 7/20

Therefore, the correct answer is B. Mixed numbers with unlike denominators can be subtracted from each other. But why would you want to do that? It's much easier to use decimals or percentages instead. Fractions are so last century.

Answer:

156

Step-by-step explanation:

Use the system of PEMDAS.
6*3 = 18
6*4 = 24
6*5 = 30
6*8 = 48
2[3*4+1/2(3*4)] = 36
Add all.
18+24+30+48+36 = 156

A graph which is that of the inequality shown include the following: D. Graph D.

In order to to graph the solution to the given linear inequality on a coordinate plane, we would use an online graphing calculator to plot the given linear inequality and then take note of the points that lie on its line;

y ≥ -3x + 1

Next, we would use an online graphing calculator to plot the given linear inequality as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that a possible solution for the linear equation is the ordered pairs (0, 1) and (1, -2), with a solid line that is shaded above to indicate the solution, and this must be represented with the greater than or equal to (>) inequality symbol.

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