Find the area of the shaded region, the graph to the right, depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

The area of the shaded region is ——?

Round to four decimal places as needed

Answer:

Vhc = 401.92 cm3

Step-by-step explanation:

Vcylender = Pi*r2*h

Vhalfcyldr = (Pi*r2*h)/2

then

h= 16cm

r = 8cm/2 = 4cm

then

Vhalfcylinder = ((3.14)*(4)2*16) / 2

Vhc = 401.92 cm3

The solutions for the given equation are x=-3 and x=1.

The given equation is (x + 1)² - 4(x + 1) + 2 = 0.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

(x + 1)² - 4(x + 1) + 2 = 0

⇒ (x + 1)² - 4(x + 1)=-2

⇒ (x+1)[(x+1)-4]=-2

⇒ x+1=-2, (x+1)-4=-2

⇒ x=-2-1, x+1=-2+4

⇒ x=-3, x+1=2

⇒ x=-3, x=1

Therefore, the solutions for the given equation are x=-3 and x=1.

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The parabola's vertex is (-3/2, -22). Because this is the lowest point on the parabola, the function's minimum value is -22.

To determine the maximum or minimum value of the quadratic function y = 2x² + 12x + 5, you need to find the vertex of the parabola formed by this function.

To find the vertex of the parabola, you can use the formula x = -b / (2a), where x is the x-coordinate of the vertex, a is the coefficient of the x² term, and b is the coefficient of the x term.

In this case, the coefficient of the x² term is 2, and the coefficient of the x term is 12. Therefore, the x-coordinate of the vertex is x = -12 / (2×2) = -6 / 4 = -3/2.

To find the y-coordinate of the vertex, you can substitute the x-coordinate back into the original equation:

y = 2(-3/2)² + 12(-3/2) + 5 = 2(-9/4) + (-18) + 5 = -9 + (-18) + 5 = -22.

Therefore, the vertex of the parabola is (-3/2, -22). This is the lowest point on the parabola, so the minimum value of the function is -22.

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Answer:

Below

Step-by-step explanation:

These are both equations of lines.....one has slope =6 and the other has slope = 4   so they will cross at ONE point

Answer:

Step-by-step explanation:

The area of each triangle is one-half the area of the rectangle. So, the area A of a triangle is given by the formula A=12bh where b is the base and h is the height of the triangle.

Answer:

30=t i think

Step-by-step explanation:

So basically what you do is since it is division you would multiply 5 by its self and you multiply on the other side because if you do something on one side you have to do it on another so that would leave you with 30=t

The true statement about n is (a) The value of n is 1/5 because (⁵√2)⁵ = 2¹ and (2¹/⁵)⁵ = 1, so ⁵√2 = 2¹/⁵

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

Expression =  ⁵√2

Also from the question, we understand that the expression is to be expressed as

2ⁿ

This means that

⁵√2 = 2ⁿ

Re-express ⁵√2 using the law of indices

2ⁿ = 2¹/⁵

By comparison, we have

n = 1/5

This means that the value of n is 1/5

Hence, the true statement is (a)

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Answer:

1236

Step-by-step explanation:

The value of slope for line equation 1 is -5/2. The value of slope for line equation 2 is 5/3.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the slope and y-intercept of the equation y = 3x - 7 are 3 and 0, respectively.

Here,

y=mx+c

where m is slope.

line equation 1,

y=-5/2x-5

m=-5/2

line equation 2,

y=5/3x

m=5/3

For line equation 1, the slope is equal to -5/2. For line equation 2, the slope is equal to 5/3.

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The probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

What is Conditional Probability?

From the question, we know that the probability that the Yankees will win a game is 0.53.

[tex]\implies P(W)=0.53[/tex]

Also, then the probability that the Yankees will lose a game is given as,

[tex]P(L)=1-P(W)\\\implies P(L)=1-0.53\\\implies P(L)=0.47[/tex]

It is also given that, the probability that the Yankees will score 5 or more runs is 0.48.

[tex]\implies P(A)=0.48[/tex]  -----(1)

So, the probability that the Yankees will score less than 5 runs is,

[tex]P(S)=1-P(A)\\\implies P(S)=1-0.5\\\implies P(S)=0.5[/tex]------(2)

We also know the probability that the Yankees will win and score 5 or more runs is 0.42.

[tex]\implies P(B)=0.42[/tex]

Also, then the probability that the Yankees will lose or score less than 5 runs is given as,

[tex]P(C)=1-P(B)\\\implies P(C)=1-0.42\\\implies P(C)=0.58[/tex]

Next, the probability that the Yankees will lose and score less than 5 runs is,

[tex]P(D)=0.42+0.5-0.58\\\implies P(D)=0.34[/tex]

Now, the required probability is the probability that the Yankees will lose and score 5 or more runs.

It can be calculated using the conditional probability formula, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]

So, the required probability  that the Yankees will lose and score 5 or more runs is given as,

P(they score 5 or more runs / probability that they lose game) = P(they lose and score 5 or more runs) / P(they lose the game)

[tex]\implies P(E)=\frac{0.47-0.38}{0.47} \\\implies P(E)=0.2766[/tex]

Therefore, the probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.

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Answer:

No

Step-by-step explanation:

1 = 2(-5) - 9

1 = -10 - 9

1 ≠ -19, therefore that point does not lie on the line

Answer:

unexplainable

Step-by-step explanation:

does not make since

Answer:

66 [tex]cm^{2}[/tex]

Step-by-step explanation:

Front: 6 x 5 = 30

Back:  6 x 4 = 24

Left side: 1/2 (3 x 4) =6

Right side: 1/2 ( 3 x 4) 6

Add

30 + 24 + 6 + 6 = 66

There are 8 bags of basmati rice are there if a crate contains bags of basmati rice Which weigh 5 lb each and bags of jasmine rice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

a crate contains bags of basmati rice Which weigh 5 lb each and bags of jasmine rice which weigh 3 pounds each.

The equation can be framed:

x + y = 20

5x + 3y = 76

After solving

By substitution method:

we get:

y = 12

x = 20 - 12 = 8

Thus, there are 8 bags of basmati rice are there if a crate contains bags of basmati rice Which weigh 5 lb each, and bags of jasmine rice.

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By using the formula for area of rectangle, it can be calculated that-

a) Expression for total area = [tex]6^2 + 2 \times 6 + 24[/tex]

Total area = 72 square inches

b) Length of the figure =  9 inches

Breadth of the figure =  8 inches

What is area of a rectangle?

Area of a rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is calculated by

Area = l [tex]\times[/tex] b

Side of the square = 6 inches

Area of the square = [tex]6^2[/tex] square inches

Length of white rectangle = 2 inches

Breadth of white rectangle = 6 inches

Area of white rectangle = [tex]2 \times 6 =[/tex] 12 square inches

Area of blue rectangle  = 24 square inches

Total area = [tex]6^2 + 2 \times 6 + 24[/tex] =

                     36 + 12 + 24 =

                     72 sq. inches

b) Let the breadth of the blue rectangle be b inches

Length of the blue rectangle = 2 + 6 = 8 inches

Total area = 8b square inches

By the problem,

[tex]8b = 24 \\b = \frac{24}{8}\\[/tex]

b = 3 inches

Length of the figure = 6 + 3 = 9 inches

Breadth of the figure = 2 + 6 = 8 inches

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The polygon ABCD is transformed 4 units to the left after being reflected across the x-axis.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

Reflect the polygon ABCD across the x-axis as;

A(x, y) → A'(x, -y) (x, -y) (x, -y)

According to this rule, A's coordinates are

A(1, -5) →  A'(1, 5) (1, 5) (1, 5)

ABCD is shifted 4 units further to the left.

Now apply to the translation:

A"(x - 4, y) = A'(x, y) (x - 4, y)

A'(1, 5) → A"(1 - 4, 5) (1 - 4, 5) (1 - 4, 5)

→ A"(-3, 5) (-3, 5) (-3, 5)

Thus Polygon ABCD will eventually overlap Polygon A'B'C'D' through a series of transformations.

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Answer:

hope it help

the last answer is 6

I showed you step by step. for any explanation write it in the comment

A resemblance While retaining shape, metamorphosis can alter both location and size.

When the sides of two figures are proportionate and the accompanying angles are congruent, the figures are said to be comparable.

Get the two triangles to face in the same direction, or in the same orientation, to check if they resemble one another. You accomplish this by turning one shape so that it is in alignment with the other. A rotation is the name given to such a change.

Similarity refers to two figures that share the same shape but differ in size. A rigid motion and a rescaling make up a similarity transformation. To put it another way, a similarity transformation may change both location and size while maintaining shape.

Let the given points be G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

A resemblance While retaining shape, metamorphosis can alter both location and size.

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Answer:

  not similar

Step-by-step explanation:

You want to know if ∆GHI ~ ∆JKL when they are defined by coordinates G(-2, 3), H(4, 3), I(4, 0) and J(1, 0), K(6.-2), L(1, -2).

Corresponding angles of similar triangles are congruent, and corresponding sides are proportional.

Here, angle G is an acute angle less than 45°, while corresponding angle J is an acute angle greater than 45°. These corresponding angles in the similarity statement are not congruent, so the similarity statement is false.

__

Additional comment

Side ratios in ∆GHI are 3 : 6 : 3√5 = 1 : 2 : √5.

Side ratios in ∆JKL are 2 : 5 : √29.

For comparison purposes, we like to list them shortest to longest.

These ratios are different, so even if the order of the vertices were straightened out, the triangles still would not be similar. If the triangles had the same side length ratios, the vertex order for a proper similarity statement would be ∆GHI ~ ∆KLJ.

The total commission that's earned will be $360.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, an employee who earns $12/hour, worked 37 hours this week, is paid a commission of $40 for each sale, and makes 9 sales during the same week. Employees receive commission, also referred to as a sales commission, based on the sales they generate. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services. Sales commissions are a common incentive used by employers to boost employee productivity. A commission can be paid instead of or in addition to a salary.

The total commissions will be:

= Amount of commission × Number of sales

= $40 × 9

= $360

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what are we supposed to be solving

Answer:

Step-by-step explanation:

duh

The graph of the odd-degree polynomial reaches positive and negative infinity.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

The given polynomial is shifted towards the left it reaches negative infinity quicker than positive infinity.

Also, the graph of the polynomial is of odd degree as it is symmetric about the origin shifted towards left.

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Answer:

the functions domain is;  x < -19 or x > -19

x= -19

Sorry otherwise im not sure what you need here :P

The 15th term of the given geometric sequence will be (C) 5/4096.

Mathematicians refer to a succession of non-zero numbers as a geometric progression or geometric sequence.

Each term after the first is derived by multiplying the previous term by a fixed, non-zero value called the common ratio.

So, the geometric sequence will be:

nth term formula: aₙ = a₁rⁿ⁻¹

Now, insert the values and calculate as follows:

aₙ = a₁rⁿ⁻¹

a₁₅ = 20(1/2)¹⁵⁻¹

a₁₅ = 20(1/2)¹⁴

a₁₅ = 20(1/16384)

a₁₅ = 20/16384

a₁₅ = 5/4096

Therefore, the 15th term of the given geometric sequence will be (C) 5/4096.

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Complete question:
Find the 15th term in the geometric sequence below. 20, 10, 5, 2.5, . . .

A.-25/4,096

B.-5/4,096

C.5/4,096

D.25/4,096

Answer:

Step-by-step explanation:

Part A:

For number 1, the bus drives non-linear. It is not a constant rate but it is increasing.

For number 2, the bus is at a stopping point.

For number 3, the bus drives in a non-linear rate but it still increasing.

For number 4, the bus is at its last stop, the middle of the bus ride, the peak of the time.

For number 5, the bus comes to a non-linear decrease in the route. and eventually the end.  

Part B:  

The bus is increasing in numbers 1 and 3, and decreasing for number 5, and at a constant at numbers 2 and 4.  

Part C:  

The graph is non-linear, as the slope is not at a constant.

Answer:

Sorry i don't know. But i think this is a good priblem

The value of x from the parallelogram ABCD is 10.

A parallelogram is a special kind of quadrilateral that is formed by parallel lines. The angle between the adjacent sides of a parallelogram may vary but the opposite sides need to be parallel for it to be a parallelogram. A quadrilateral will be a parallelogram if its opposite sides are parallel and congruent.

Given that, ∠A=120-2x, ∠B=70+x, ∠C=105-x² and ∠D=40+4x.

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary.

Here, ∠A and ∠D are consecutive angles

Now, 120-2x+40+4x=180

⇒ 160+2x=180

⇒ 2x=20

⇒ x=10

So, ∠A=120-2x=100, ∠B=70+x=80, ∠C=160-6x=100 and ∠D=40+4x=80

Therefore, the value of x is 10.

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"Your question is incomplete, probably the complete question/missing part is:"

The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A=120-2x, ∠B=70+x, ∠C=160-6x and ∠D=40+4x.

An equation of a line with slope(m) = 4/5 and y-intercept(b) = 1 can be formed as y = (4/5)x + 1.

The slope is the rate of change of the y-axis with respect to the x-axis.

The equation of a line in slope-intercept form is y = mx + b, where

slope = m and y-intercept = b.

We know the greater the absolute value of a slope is the more steeper is it's graph or rate of change is large.

An equation of a line in slope-intercept form with slope(m) = 4/5 and

y-intercept(b) = 1 can be formed as y = (4/5)x + 1.

The graph of this line is attached below.

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A graph of the two (2) points (-0.5, 0) and (9, 0) that represent the distance which this object would travel in different amounts of time at that rate is shown in the image attached below.

Mathematically, a linear function is sometimes referred to as the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

d = mt + b

Where:

Therefore, the required linear function that relates the distance (d) and speed (s) at time (t) seconds is given by this mathematical expression;

d(t) = 18t + 9

For instance when time (t) = -0.5 seconds, the distance traveled by this object placed on a conveyor belt is given by;

d(t) = 18t + 9

d(-0.5) = 18(-0.5) + 9

d(-0.5) = -9 + 9

d(-0.5) = 0 feet.

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Answer:

Step-by-step explanation:

Answer 2

You would divide 7 by 3.5 and you get 2 If the equation was what times 3.5 =7  

[tex]3x^2+x-10=\boxed{(x+2)(3x-5)}[/tex]