The greyed letters are the question. The blackened letters is the solution. How do I get there?

False. It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are

While the information states that there is a moderate positive correlation between the speed of the motor vehicle and the severity of injuries, correlation does not imply causation. Therefore, it cannot be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are. Correlation simply indicates that there is a relationship between the two variables, but other factors may also be influencing the severity of injuries.

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Approximately 32% of students scored above 86 on the university exam.

To determine the percentage of students who score above 86, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule, in a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Given that the mean is 78 and the standard deviation is 8, we can calculate the z-score for 86 using the formula:

z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

z = (86 - 78) / 8 = 1

Since 86 is one standard deviation above the mean, we know that approximately 68% of students scored below 86. Therefore, the percentage of students who score above 86 can be estimated as 100% - 68% = 32%.

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The combination formula  C(8, 5) is calculated as: 56

Combinations in probability theory and even other areas of mathematics tell us about a sequence of outcomes where the order does not matter. For example, when we order a pizza, it doesn't matter whether we order it with ham, mushrooms, and olives or olives, mushrooms, and ham.

Now, we want to find the combination given as C(8, 5)

The formula for combination is:

nCr = n!/(r!(n - r)!)

Thus;

8C5 = 8!/(5!(8 - 5)!)

= 56

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The  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Matrix multiplication is a binary operation that produces a matrix from two matricesThe given matrices are [tex]A=\left[\begin{array}{ccc}1\\2\end{array}\right][/tex] and [tex]B=\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

To perform product of two matrices, we should make sure that the number of columns in the 1st matrix is equal to the rows in the 2nd matrix

AB=[tex]\left[\begin{array}{ccc}1\\2\end{array}\right].\left[\begin{array}{ccc}4&5\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}4+5\\8+10\end{array}\right][/tex]

[tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

Hence, the  product of the given matrices is [tex]AB=\left[\begin{array}{ccc}9\\18\end{array}\right][/tex]

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By using the formula of final amount, The future value is,

Future value = 29,640

We have to given that;

Present value = 12,000

Time = 8 years

And, interest rate = 12%

Now, For Calculate a future value for present value of 12,000 term of 8 years interest rate 12%, we can use the formula for present amount.

Since, We know that;

Future value = P (1 + r)ⁿ

Where, P is present amount.

r is interest rate.

n is number of years.

Hence, We can substitute all the given values, we get;

Future value = P (1 + r)ⁿ

Future value = 12,000 (1 + 12%)⁸

Future value = 12,000 (1 + 0.12)⁸

Future value = 12,000 (1.12)⁸

Future value = 12,000 x 2.47

Future value = 29,640

Therefore, The future value for present value of 12,000 term of 8 years interest rate 12% is,

Future value = 29,640

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The correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

To solve the inequality x^2 - 9x < -18, you can follow these steps:

Move all terms to one side of the inequality to form a quadratic expression: x^2 - 9x + 18 < 0.

Factorize the quadratic expression: (x - 6)(x - 3) < 0.

Determine the sign of the expression for different intervals of x. To do this, you can create a sign chart:

Interval | (x - 6) | (x - 3) | (x - 6)(x - 3) |

x < 3 | - | - | + |

3 < x < 6 | - | + | - |

x > 6 | + | + | + |

Analyze the sign chart to determine when the expression (x - 6)(x - 3) is less than zero (negative).

The expression is negative when x is between 3 and 6, i.e., 3 < x < 6.

Write the solution in interval notation:

x < 3 or x > 6

Therefore, the correct solution to the inequality x^2 - 9x < -18 is x < 3 or x > 6.

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The equation that shows how to find p, the total amount of Alex's paycheck, is:

35/p = 70/100.

This equation represents the fact that 70% of Alex's paycheck (0.7p) was automatically deposited into her savings account, and that amount is given as $35. To solve for p, we can divide both sides of the equation by 0.7:

p = 35 / 0.7

p = 35/70 x 1/100

35/p = 70/100.

Therefore, the total amount of Alex's paycheck this week is $50.

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Therefore, the degrees of freedom for the treatment source of variation is 3.

In ANOVA (Analysis of Variance), the total variability of a dataset is divided into different sources of variation, such as treatment, error, and total. The treatment source of variation represents the differences between the means of the groups being compared. The degrees of freedom for the treatment source of variation refer to the number of independent pieces of information used to estimate the variability due to treatment. It is calculated as the number of groups minus one. In this case, with four groups, the degrees of freedom for the treatment source of variation is 3. This value is used in calculating the F-statistic and determining if there are significant differences between the group means.

The degrees of freedom for the treatment source of variation can be calculated using the formula:

Degrees of freedom (treatment) = number of groups - 1

In this case, there are 4 groups, so the degrees of freedom for the treatment source of variation would be:

Degrees of freedom (treatment) = 4 - 1 = 3

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The correct explanation about the rectangle is No, the adjacent sides are not perpendicular. Option D

A rectangle is defined as a quadrilateral with four right angles (90 degrees).

The shape provided in the diagram is not a rectangle because its four sides are not right angles.

Given that the coordinates for each point is a (3.9, -1)  b(2, 4)  c. (-2, -2)  d. (-1, -3).

Slope of AB = (4 - (-1)) / (2 - 3.9) = 5 / (-1.9) =-2.63

Slope of BC = (4 - 2) / (2 - (-2)) = 2 / 4 = 0.5

Slope of CD = (-2 - (-3)) / (-2 - (-1)) = 1 / -1 = -1

Slope of DA = (-1 - (-2)) / (3.9 - (-1)) = 1 / 4.9 = 0.20

The slopes of AB and CD are not equal, and the slopes of BC and DA are not equal either. Therefore, the opposite sides are not parallel.

the product of the slopes of adjacent sides (AB and BC) is not -1, which indicates that the angle between them is not a right angle

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Answer:

(-5, 2)

Step-by-step explanation:

2x + 3y = -4

x + 9y = 13

We can solve this by substituting or using elimination.

Substituting:

2x + 3y = -4

-2x     = -2x     Subtract 2 from both sides.

3y = -2x - 4

3    =   3              Divide both sides by 3.

y = -2/3x - 4/3

x + 9(-2/3x - 4/3) = 13  Replace the y with -2/3x - 4/3.

x - 6x - 12 = 13     use the distributive property.

-5x - 12 = 13

     +12 = + 12           Add 12 to both sides.

-5x = 25

-5  = -5                  Divide both sides by -5.

x = -5

Now that we know what x is, we substitute -5 for the variable x in any of the two equations.

x + 9y = 13

-5 + 9y = 13  Replaced x with -5

+5       = +5   Add 5 to both sides.

9y = 18

Divide both sides by 9 to get:

y = 2

The other way to solve:

Elimination:

2x + 3y = -4

x + 9y = 13

Make the variable y cancel out.

-3(2x + 3y = -4)  use the distributive property.

-6x - 9y = 12

-6x - 9y = 12

x + 9y = 13

Add the equation.

-5x = 25

Divide both sides by -5.

x = -5

Plug in -5 for x.

2(-5) + 3y = -4

-10 + 3y = -4

+10     = +10   Add 10 to both sides.

3y = 6

Divide both sides by 3:

y = 2

We get the same answer in both strategies, you could use either one.

The sum of the measures of the exterior angles of the 14 sides polygon shown is 360 degrees.

The sum of the measures of the exterior angles of any polygon is always equal to 360 degrees.

This means that the exterior angles for the sides of this 14 sided polygon would be:

= 360 / 14

= 25. 71 degrees

Regardless of the polygon, so long as it is a regular polygon, the exterior angles will always add up to 360 degrees so the sum of exterior angles here is the same measure of 360 degrees.

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Answer:

x + y = 22

3x + 5 = 35

3x = 30, so x = 10 and y = 12.

We can conclude  that there is a segment of the questioned population that values outdoor recreation and has children. The percentage of persons who belong to this subset is shown by the overlap percentage 15%.

29% of individuals say they have children and 52% say they like outdoor activities. 15% of respondents also mention having children and enjoying outdoor activities.

This evidence leads us to the conclusion that there is a correlation between those who prefer outdoor activities and those who are parents. There are people in the poll who fit into both categories as seen by the 15% of respondents who say they like outdoor activities and have children.

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Answer: What is the least number of gumballs jack has to buy to be certain he gets 6 gumballs of the same color?

Step-by-step explanation:

To be certain he gets 6 gumballs of the same color, Jack must buy at least 16 gumballs.

This is because he could buy 5 gumballs of each color (for a total of 15 gumballs) and still not have 6 gumballs of the same color. However, if he buys one more gumball, he will have at least 6 gumballs of one color.

Therefore, the least number of gumballs Jack has to buy to be certain he gets 6 gumballs of the same color is 16.

{Hope This Helps! :)}

Domain:  the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. It is the set X in the notation f: X → Y, and is alternatively denoted as . Since a (total) function is defined on its entire domain, its domain coincides with its domain of definition.

Vertical Line test:  the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function. If all vertical lines intersect a curve at most once, then the curve represents a function.

Relation: Relations are used to describe a connection between the elements of two sets. They help to map the elements of one set (known as the domain) to elements of another set (called the range) such that the resulting ordered pairs are of the form (input, output).

Practical Range: range is a statistical measurement of dispersion, or how much a given data set is stretched out from smallest to largest. In a set of data, the range is the difference between the greatest and smallest value.

Function: Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Practical Domain: The domain is the set of all possible x-values which will make the function "work" and will output real y-values.

function Notation: Function notation is a way of expressing a relationship between two variables. A function is most often denoted by letters such as f, g, and h, and the value of a function f at an element x of its domain is denoted by f(x). In function notation, f(x) represents the output of the function f for a given input x. The letter 'f' is commonly used to represent a function, but other lower case letters such as 'g' or 'h' can also be used. The function notation formula is f(x) = y, where y is the output of the function for a given input x. The set of all pairs (x, f(x)) is called the graph of the function.

the only critical number of g(y) is -1/4.

To find the critical numbers of the function g(y) = y - 2y^2 - 2y + 4, we need to find its derivative and set it equal to zero.

g'(y) = 1 - 4y - 2

Setting g'(y) = 0, we get:

1 - 4y - 2 = 0

-4y - 1 = 0

y = -1/4

what is number?

A number is a mathematical object used to represent a quantity or value. Numbers can be classified into different types based on their properties and the set of numbers they belong to. Some common types of numbers include:

Natural numbers: These are the counting numbers, such as 1, 2, 3, and so on.

Whole numbers: These are the natural numbers plus zero, such as 0, 1, 2, 3, and so on.

Integers: These are the whole numbers plus their negative counterparts, such as -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: These are numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3/4.

Irrational numbers: These are numbers that cannot be expressed as a ratio of two integers, such as pi (3.14159...) or the square root of 2 (1.41421...).

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Answer:

the answer is B D and E

Step-by-step explanation:

as you can see the enlargement is by 3

Answer:

D and E :)

Step-by-step explanation:

The new position of the submarine in relation to sea level is -1200 feet (below sea level).

The initial position of the submarine is -1260 feet below sea level, and it descends at a rate of 5 feet per minute for 12 minutes. To calculate the new position of the submarine in relation to sea level, we can use the formula: New position = Initial position - (rate of change x time).

By substituting the given values into the formula, we can calculate the new position:

New position = -1260 - (-5 x 12)

New position = -1260 + 60

New position = -1200 feet

Therefore, the new position of the submarine in relation to sea level is -1200 feet below sea level.

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The total area of the crown is 26cm²

We can divide the crown in some simpler figures, these are:

A rectangle of 8cm by (2 + 1/4) cm, the area is the product of the two dimensions, so we can write this as:

A = 8cm*(2 + 1/4)cm

A = 18cm²

And in 4 triangles whose base is of 2cm, and its height is also of 2cm, then the area of each triangle is:

T = 2cm*2cm/2 = 2cm²

Then the total area of the crown is:

area = 18cm² + 4*2cm²

area = 18cm² + 8cm²

area = 26cm²

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After the given sequence of operations, the parent node of element 1 is the node representing the set {1,5,6,7}.

The sequence of operations given involves the Union-Find algorithm, which is used for disjoint set data structure. In this algorithm, each element is represented by a node, and each node is initially considered as a parent node. Union operation is used to combine two sets, and Find operation is used to determine which set an element belongs to.
In the given sequence of operations, the sets {1,5,6,7} and {2,3,4,8} are formed by performing union operations. Now, to determine the parent node of element 1, we need to perform a Find operation on it. Since element 1 is part of the set {1,5,6,7}, we need to find the parent node of any element from this set.
By following the sequence of operations, we can see that union(1,5) combines the sets {1} and {5} into one set {1,5}. Similarly, union(5,6) combines sets {1,5} and {6} into one set {1,5,6}. Finally, union(1,7) combines sets {1,5,6} and {7} into one set {1,5,6,7}. Therefore, the parent node of element 1 is the node representing the set {1,5,6,7}.
In conclusion, after the given sequence of operations, the parent node of element 1 is the node representing the set {1,5,6,7}.

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A. The x-intercepts of the graph represent a zero profit and $8 profit respectively, while the maximum value of the graph represents the maximum profit.

The interval over which the function is increasing is [0, 4] and the interval over which the function is decreasing is [4, 8]

With respect to the sale and profit, it means that the profit increases until it reaches the maximum profit of $270 and decreases after the vertex (4, 270).

B. An approximate average rate of change of the graph from x = 1 to x = 4 is $50 per unit sale.

C. The constraints of the domain is x > 0.

By critically observing the graph shown above, the x-intercepts are (0, 0) and (8, 0) while the maximum value of the graph is located at the vertex and it represent the maximum profit of $270.

Furthermore, the interval over which this quadratic function is increasing is [0, 4] and the interval over which the quadratic function is decreasing is [4, 8].

Part B.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this mathematical expression:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function g(t) over the interval [1, 4]:

a = 1; f(a) = 120

b = 4; f(b) = 270

By substituting the given parameters into the average rate of change formula, we have the following;

Average rate of change = (270 - 120)/(4 - 1)

Average rate of change = 150/3

Average rate of change = 50

Therefore, the average rate of change from x = 1 to x = 4 represent a profit of $50 per unit sale.

Part C.

In conclusion, the constraints of the domain is x > 0 or [1, 8] because the company cannot sell zero erasers and make profit.

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Complete Question;

The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?

Part C: Describe the constraints of the domain.

The factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

The factors are the polynomials which are multiplied to produce the original polynomial.

Use the identity (a²-b²)=(a+b)(a-b)

1) 2a²-2b²

= 2(a²-b²)

= 2(a+b)(a-b)

2) 6x²-6y²

= 6(x²-y²)

= 6(x+y)(x-y)

3) 4x² - 4

= 4(x²-1)

= 4(x+1)(x-1)

4) ax²-ay²

= a(x²-y²)

= a(x+y)(x-y)

5) cm²-cn²

= c(m²-n²)

= c(m+n)(m-n)

6) st²-s

= s(t²-1)

= s(t+1)(t-1)

7) 2x²-18

= 2(x²-9)

= 2(x²-3²)

= 2(x+3)(x-3)

8) 2x²-32

= 2(x²-16)

= 2(x²-4²)

= 2(x-4)(x+4)

9) 3x²-27y²

= 3(x²-9y²)

= 3(x²-(3y)²)

= 3(x+3y)(x-3y)

10) 18m²-8

= 2(9m²-4)

= 2((3m)²-(2)²)

= 2(3m+2)(3m-2)

Therefore, the factors of the given polynomial 18m²-8 are 2, (3m+2) and (3m-2).

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Answer:

The length of the hypotenuse is 13 cm, so the area of the missing square is 13^2 = 169 cm.

Answer:

Step-by-step explanation:

0.9411764706 since you would just divide 16/17.

Answer:0.94

Step-by-step explanation:

You can put 16/17 into the calculator and you will get 0.941176471, so you just round to the nearest hundredths, like it asks ,and there you go.

The volume of the hemisphere is 261.8 cubic feet

We can easily find the volume of the hemisphere since the base of the sphere is circular. The volume of the hemisphere is derived by Archimedes. The volume of a hemisphere = (2/3)πr³ cubic units.

In this problem, we simply substitute the values into the formula and then solve for the volume.

v = 2/3πr³

radius(r) = diameter(d) / 2

r = 10 /2

r = 5ft

Substituting the values;

v = 2/3π(5)³

v = 261.8ft³

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A distance-time graph below shows a car travelling then the Speed of the car is 8.88 miles per hour

Speed is the time rate at which an object is moving along a path,

A distance-time graph below shows a car travelling

We know that speed is distance by time

From the graph the distance is 80 and time is 9

Speed= 80/9

=8.88 miles per hour

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The length of side x in the right triangle is approximately 38.2 units.

It looks like you have a right triangle problem where you need to solve for side x. The given information is the hypotenuse (Z) with a length of 56 units, an angle (M) of 43°, and side x which is opposite to angle M.
To solve for x, we can use the sine function in the context of the right triangle. The sine function is defined as:
sin(M) = opposite side (x) / hypotenuse (Z)
We are given the values for angle M (43°) and the hypotenuse (Z = 56 units). Plugging these values into the equation, we get:
sin(43°) = x / 56
Now, to solve for x, we will multiply both sides of the equation by 56:
x = 56 * sin(43°)
Next, use a calculator or trigonometric table to find the sine of 43°:
sin(43°) ≈ 0.682
Now, multiply this value by 56:
x ≈ 56 * 0.682
x ≈ 38.192
Finally, round your answer to the nearest tenth:
x ≈ 38.2
So, the length of side x in the right triangle is approximately 38.2 units.

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A) Yes, we can conclude that △ABD≅△ACD .

B) Rob says AB = AC and BD = CD. I agree.

C) The expression for the distance around the kite (perimeter) in centimeters is 4x + 30.

A) According to the principles of geometry, when two angles are marked alike, it means that they are equal.

Thus, ∠BAD ≅ ∠CAD; and

∠BDA ≅∠ADC

Since ∠BDA ≅∠ADC and

AD = DA (Based on the Reflexive postulate,

Then on the basis of the Angle  - Side - Angle theorem, △ABD≅△ACD.

B) AB = AC and BD = CD

This is because we have already proven that △ABD≅△ACD on the basis of A-S-A theorem.

C) Since both triangles are equal, the expression for their perimeter =

x + 15 + x + x + 15 + x

= 4x + 30

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