7) suppose that a machine shop orders 200 bolts from a supplier. to determine whether or not to accept the shipment of bolts, the manager of the shop randomly selects 12 bolts. if none of the 12 randomly selected bolts is found to be defective, she concludes that the shipment is acceptable. otherwise, she sends back the order to the supplier. a. if 20 bolts out of the 200 that had been sent are defective, what is the probability that none of the selected bolts are defective? b. if 10 bolts out of the 200 that had been sent are defective, what is the probability that at least one of the selected bolts is defective and hence the order is sent back?

Answer:

5.09

Step-by-step explanation:

2x2=4-3=1+1=2  +   3+2=5-2=3

            2+3//=5.09

Therefore, the insect population will remain stable, neither increasing nor decreasing and the estimated  stable population is 2.

Given the equation:3-12+16 PO) 15-2+1

In order to determine the stability of a population of insects, we must first calculate the equilibrium value of PO.

A population's equilibrium is defined as the point at which the population remains stable over time, indicating that the population is neither declining nor growing indefinitely.

Stable population equilibrium is defined as follows:

Let P* be the equilibrium value of the population.

This implies that:P* = 15 - 2 + 1 / 3 - 12 + 16

This simplifies to:P* = 14/7 or 2

Therefore, the equilibrium value of the insect population is 2. If the population is greater than 2, it will decrease. If it is less than 2, it will increase.

In this case, the population of insects will settle into an equilibrium state.

The value of the stable population is 2.

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Answer:

a. 5,12,13

Step-by-step explanation:

we know in right angle triangle

AC^2 = AB^2 + BC^2

here let

AC = 13

AB = 5

BC = 12

So,

13 ^2 = 5^2+ 12^2

169 = 25 + 144

169 = 169

so,

sides of right angle triangle are 5,12,13

and only the largest value in given data can be AC as AC is hypotenuse

Answer:

−2.333

Step-by-step explanation:

-7 - 3y  =   -1 • (3y + 7)

y = -7/3 = -2.333

Answer:

A

Step-by-step explanation:

Change in population (in thousands) in 10 year period:

1970-1980: 175-158 = 17

1980-1990: 195-175 = 20

1990-2000: 227 - 195 = 32

32,000 is the largest growth in a 10 year period, so the answer is 1990-2000.

Answer: A

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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(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we differentiate y(t) with respect to t and substitute the given differential equation and initial condition.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we divide the interval [0, 2] into subintervals of width h and approximate the integral using the formula: ∑[f(u(i))*h], where f(u(i)) represents the function evaluated at each subinterval.

(a) To show that y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem dy/dt = e⁻ᵗ², y(0) = 0, we first differentiate y(t) with respect to t. Using the Fundamental Theorem of Calculus, we have:

dy/dt = d/dt [ᵗ∫₀ e⁻ᵘ² du]

Applying the Leibniz rule for differentiating under the integral sign, we obtain:

dy/dt = ∫₀ e⁻ᵘ² du

Now we substitute the given differential equation dy/dt = e⁻ᵗ² and the initial condition y(0) = 0:

e⁻ᵘ² = e⁻ᵗ²

Since e⁻ᵘ² and e⁻ᵗ² are equal, the given function y(t) = ᵗ∫₀ e⁻ᵘ² du satisfies the initial value problem.

(b) To approximate the integral ²∫₀ e⁻ᵘ² du using the Euler Method with h = 1/2, we first divide the interval [0, 2] into subintervals of width h = 1/2. In this case, we will have four subintervals: [0, 1/2], [1/2, 1], [1, 3/2], and [3/2, 2].

Using the Euler Method, we approximate the integral within each subinterval by evaluating the function e⁻ᵘ² at the left endpoint of the subinterval and multiplying it by the width of the subinterval. Then, we sum up these approximations for all subintervals.

For example, in the first subinterval [0, 1/2], the approximation would be:

Approximation for

[0, 1/2] = e⁻⁰² * (1/2) = (1/2)

Similarly, we can calculate the approximations for the other subintervals:

Approximation for

[1/2, 1] = e⁻¹/₂² * (1/2) ≈ (0.60653/2)

Approximation for

[1, 3/2] = e⁻¹² * (1/2) ≈ (0.13534/2)

Approximation for

[3/2, 2] = e⁻³/₂² * (1/2) ≈ (0.18394/2)

Finally, we sum up these approximations:

Approximation for

²∫₀ e⁻ᵘ² du ≈ (1/2) + (0.60653/2) + (0.13534/2) + (0.18394/2)

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Answer:

h = -1, j = 3

Step-by-step explanation:

Let's subtract the first equation from the second one:

(2h + j) - (2h - 3j) = 1 - (-11)

2h + j - 2h + 3j = 1 + 11

4j = 12

j = 12 : 4

j = 3

Then let's solve the second equation as we know j:

2h + 3 = 1

2h = -2

h = -2 : 2

h = -1

Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

Answer:

h) (3 - 2b)/4b²

k) (2b - 3a)/ab³

Step-by-step explanation:

h) 3/4b² - 1/2b

multiply 1/2b, both top and bottom, by 2b, so 1/2b = 2b/4b²:

3/4b² - 2b/4b² = (3 - 2b)/4b²

k) 2/ab² - 3/b³

multiply 2/ab², both top and bottom, by b, so 2/ab² = 2b/ab³:

multiply 3/b³, both top and bottom, by a, so 3/b³ = 3a/ab³:

2b/ab³ - 3a/ab³ = (2b - 3a)/ab³

Answer:

  3(x +2)

Step-by-step explanation:

If the number is represented by x, then "the sum of a number and 2" is ...

  x + 2

Three times that sum is ...

  3(x +2)

Answer:

f^-1(x) = _x__

               5

Step-by-step explanation:

Answer:

\( {f}^{ - 1} (x) = \frac{x}{5} \)

Step-by-step explanation:

f(x) = 5x

To find f^-1(x) equate f(x) to y

That's f(x) = y

y = 5x

Interchange the variables

x = 5y

Make y the subject by dividing both sides by 5

y = x/5

The final answer is

f^-1(x) = x/5

Hope this helps you.

Solution

The answer is

Absolute Value Function

The total surface area of the triangular prism is 680 cm².

To find the total surface area of the triangular prism with dimensions 30

cm, 18 cm, 7 cm, and 24 cm, follow these steps:

Identify the dimensions: The base of the triangular prism is a triangle with

sides 30 cm, 18 cm, and 24 cm. The height of the prism is 7 cm.

Calculate the area of the triangular base: Use Heron's formula to find the

area of the triangle. First, find the semi-perimeter (s) of the triangle:

s = (30 + 18 + 24) / 2 = 72 / 2 = 36 cm.

Apply Heron's formula: Area = √(s(s - a)(s - b)(s - c)), where a, b, and c are

the side lengths of the triangle.

Area = √(36(36 - 30)(36 - 18)(36 - 24)) = √(36 × 6 × 18 × 12) = √31104 = 176 cm².

Calculate the area of the three rectangular faces: The three rectangular

faces have dimensions 30 cm x 7 cm, 18 cm x 7 cm, and 24 cm x 7 cm.

Find their areas by multiplying the dimensions:

30 × 7 = 210 cm², 18 × 7 = 126 cm², and 24 × 7 = 168 cm².

Add the areas of all the faces together: Add the triangular base area and

the areas of the three rectangular faces to find the total surface area:

176 cm² (base) + 210 cm² + 126 cm² + 168 cm² = 680 cm².

The total surface area of the triangular prism is 680 cm².

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Answer:

The answers are:

Step-by-step explanation:

1)Adjacent

2)Vertical

3)Corresponding

4)None of these

5)1,7  3,5  4,6  2,8 (<--angle numbers)

6)4,5  2,7 (<--angle numbers)

7)1=85, 2=95, 3=85, 4=85

8)1=60, 2=120, 3=60, 4=120

9)1=90, 2=90, 3=90, 4=90

10) No, they are not parallel. A protractor would show that the intersection angles are different, meaning the lines aren't parallel.

SORRY it took so long hope this helps!!

Answer:

1.

adjacent

2.

vertical

3.

corresponding

4.

none (just regular interior and thats not an option)

5.

(<5,<7) (<6,<8) (<1,<3) (<2,<4)

6.

(<2,<7) (<6,<3)

7.

<1= 85

<2= 95

<3= 85

<4= 85

8.

<1= 60

<2= 120

<3= 60

<4= 120

9.

<1= 90

<2= 90

<3= 90

<4= 90

10. No, its not parallel because the corresponding angles 1 and 7 aren't equal. You can use a protractor to figure this out by finding the measurement of angles 1 and 7. Because they aren't equal degrees, the lines will cross at some point

Answer:

\(\displaystyle [-2, -1]\)

Step-by-step explanation:

To use the Elimination method, you must get rid of one pair of variables, so that one side is set to zero. So, in this case, we must get rid of \(\displaystyle x,\)therefore we will split the second equation in negative half :

\(\displaystyle \left \{ {{y = 2x + 3} \atop {-\frac{1}{2}[y = 4x + 7]}} \right. \\ \\ \\ \left \{ {{y = 2x + 3} \atop {-\frac{1}{2}y = -2x - 3\frac{1}{2}}} \right. \\ \\ \frac{1}{2}y = -\frac{1}{2}; -1 = y, -2 = x \\ \\ \\ \boxed{[-2, -1]}\)

I am joyous to assist you at any time.

Answer:

(a) 2.0%

(b) Between 62.0% and 66.0%

Step-by-step explanation:

The explanation is attached below.

Therefore , the solution of the given problem of angles comes out to be

r1 (1) = r2.

An angle is a form in Euclidean geometry composed of two rays, called the hook's flanks, that converge at a point in the middle known as the vertex of the angle. In the plane that they are located, two ray may combine to make an angle. The collision of two planes also produces an angle. Dihedral angles are what we call them.

Here,

Make the pair of elements

r1 (t) = r2 (s) t = 7 - s

or

t + s = 7 equal to one another.

35 + t2 = s2, or 35 - t2 = 4, or s2 - t2 = 35

Step 2: Using the t value from equation 1, simplify equation 3.

35 + ( 7 - s ) ( 7 - s )

2 = s2 14s = 84 s = 6 and t = 1 are equivalent to.

Step 3: In formulas (1), (2), and, substitute these values of "t" and "s"

(3).

r1 (1) = r2

(6) = (1, 3, 36) (1, 3, 36)

Therefore , the solution of the given problem of angle comes out to be

r1 (1) = r2.

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Answer: 60%

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

The equation of the line is y = 4x. Option B

First, we need to know that the general equation of a line is expressed as;

y = mx + c

Such that the parameters of the formula are expressed as;

From the information given, we have that the points in the line are;

(1,-4)

(2,-8)

Now, let us determine the slope of the line, we have to take the change in the value of the points

Slope, m = -8 -(-4)/2-1

expand the bracket

Slope, m = 4

Then, the intercept is;

-8 = 4(2) + c

c = 0

Equation of the line would be;

y = 4x

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Answer:

4

Step-by-step explanation:

you would do 20÷5=x

to check it it would be 5x=20

5×4=20

Answer: X=4

Step-by-step explanation:

If your school has 20 clubs, 20 divided by 5 is 4

Answer:

3 hours 38 minutes is what calculators online say

Step-by-step explanation:

Let b be the base of the traingle

Let h be the height of the triangle

The height of a triangle is 3 feet less than the base:

The area of the triangle is 230 square feet.

The area of a triangle is:

For the given triangle:

Solve b in the equation above:

Use the quadratic formula:

As the length of the base cannot be a negative quantity you use the solution 1.

The base of the triangle is 23ft

Use the value of b to find the heigth:

Answer:

Answer:

safe speed for the larger radius track u= √2 v

Explanation:

The sum of the forces on either side is the same, the only difference is the radius of curvature and speed.

Also given that r_1= smaller radius

r_2= larger radius curve

r_2= 2r_1..............i

let u be the speed of larger radius curve

now, \sum F = \frac{mv^2}{r_1} =\frac{mu^2}{r_2}∑F=

r

1

mv

2

=

r

2

mu

2

................ii

form i and ii we can write

v^2= \frac{1}{2} u^2v

2

=

2

1

u

2

⇒u= √2 v

therefore, safe speed for the larger radius track u= √2 v

Step-by-step explanation:

\( {12}^{2} + {9}^{2} = {a}^{2} \\ 144 + 81 = {a}^{2} \\ {a}^{2} = 225 \\ a = 15\)

Answer:

a = 15

a = - 15

Step-by-step explanation:

Exponentiation

12² + 9² = a²

144 + 9² = a²

so a equal to 15, -15

The function g defined based on the function f, g(x) = f(x) + k, indicates that if the value of k = 7, the graph of g is shifted 7 units upwards compared to the graph of f

The transformation of a function is another function that changes the original function into another function based on specified or defined operations on the original function.

The function type represented by the function f = A linear function

The definition of the function g is g(x) = f(x) + k

The formula for the transformation of a  function, y = -a·f(-(x ± h)) ± k, indicates that we get;

+k = The vertical shift of the function upwards

-k = The vertical shift of the function downwards

Therefore, if the value of k in the function, g(x) = f(x) + k, is 7, it represents a vertical shift of the graph of the function, f(x), upwards, by 7 units

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