Do these ratios form a proportion?

3 large staplers : 17 small staplers

6 large staplers : 34 small staplers HELP

Answer:

70° and 20°

let the other 2 angles be 7x and 2x

90+7x+2x=180

9x=180-90

x=90/9

x=10

7x=7x10

70

2x=2×10

2p

The equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

What are parallel lines?

Parallel lines are coplanar infinite straight lines that do not intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.

To find an equation for the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5),

We use the equation of a line: v = v₀ + tv₁

where v₀ and v₁ are points on the line and t is a real number.

Substitute the given points in for v₀ and v₁: v = (0, 1, −8) + t(6, 7, −5)

This equation of the plane is Ax + By + Cz = D, where A, B, C, and D are constants to be determined.

Equate the components:

0x + 1y - 8z = D....(1)

6x + 7y - 5z = D...(2)

Now, we subtract equation (1) from (2) and we get

6x - 0x + 7y - 1y - 5z + 8z = 0

6x + 6y + 3z = 0

Hence, the equation of the plane containing the two parallel lines v₁ = (0, 1, −8) t(6, 7, −5) and v₂ = (8, −1, 0) t(6, 7, −5) is 6x + 6y + 3z = 0.

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Answer:

11 hours

Step-by-step explanation:

270/18=15 per hour

so 165/15 = 11

Answer:

11 hours

Step-by-step explanation:

270:18 simplified is 15:1

165/15 = 11

Hope this helps!

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

The area function Ap(x) represents the area of the region under the curve y = t³ between the vertical lines y = p and t = x. To find the formula for Ap(x), we need to integrate the function y = t³ with respect to t between the limits p and x.

∫[p,x] t³ dt = [t⁴/4]pᵡ

Now, substitute x for t in the above expression and subtract the result obtained by substituting p for t.

Ap(x) = [(x⁴/4) - (p⁴/4)]

Therefore, the formula for the area function Ap(x) is Ap(x) = (x⁴/4) - (p⁴/4). This formula depends on x and the parameter p, which represents the vertical line y = p.

In simpler terms, Ap(x) is the area of the shaded region between the curve y = t³ and the vertical lines y = p and t = x. The formula for Ap(x) is obtained by integrating the function y = t³ with respect to t and subtracting the result obtained by substituting p for t from the result obtained by substituting x for t.

In summary, the area function Ap(x) represents the area of the region under the curve y = t³ between the vertical lines y = p and t = x. The formula for Ap(x) is (x⁴/4) - (p⁴/4), which depends on x and the parameter p.

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The error made in subtracting the two rational expressions 1/(x - 2) - 1/x is that the common denominator is not correctly identified and applied.

To subtract rational expressions, we need to find a common denominator and then subtract the numerators. In this case, the common denominator should be (x - 2) * x. However, the error lies in neglecting the parentheses in the first expression, leading to a miscalculation of the common denominator.

The correct subtraction of the given expressions should be: (x - 2)/(x - 2) - 1/(x * (x - 2)). Simplifying this expression further would result in (x - 2 - 1)/(x * (x - 2)), which can be simplified as (x - 3)/(x * (x - 2)).

Therefore, the error made in the subtraction lies in incorrectly identifying and applying the common denominator, which resulted in an inaccurate calculation of the expression.

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Answer:

84

Step-by-step explanation:

substitute n = 5 into the expression

16n + 4

= 16(5) + 4

= 80 + 4

= 84

Answer:

The expression will have the value of 84

Step-by-step explanation:

\(16n + 4\)

given expression

Thus, plug n=5

\(16(5) + 4 \\ 80 + 4 = 84\)

Finally, we get the value 84

According to the question The length of the radius of each circle is 12/π cm or approximately 3.82 cm.

We are given two circles that intersect and share a common chord, which is 12 cm long. The angles formed by the chord and a radius at the points of intersection are both 45°. To solve the problem, we draw the radii from the centers of the circles to the points of intersection.

We find that the angles formed by these radii and the chord are 135° each. By analyzing the angles in the isosceles triangles formed, we determine that the lines connecting the centers of the circles to the points of intersection are parallel.

Since the chord lengths and the intercepted arcs in the circles are congruent, we conclude that the lengths of the intercepted arcs in the first circle are also 12 cm. Using the formula for arc length, we express this as r₁ * θ = 12 cm, where θ is the central angle in radians.

Converting the given 45° central angle to radians (π/4), we solve for r₁ to find the length of the radius of each circle.

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The vector w can be expressed as:
w = 5v1 - 5v2 - v3

Given the orthogonal set of vectors v1, v2, and v3 in R5, and the vector w in the span of these vectors, you have provided the following information:

- (v1,v1) = 35
- (v2,v2) = 334
- (v3,v3) = 1
- (w,v1) = 175
- (w,v2) = -1670
- (w,v3) = -1

To find w in terms of v1, v2, and v3, use the following formula for orthogonal projections:

w = (w,v1)/||(v1)||^2 * v1 + (w,v2)/||(v2)||^2 * v2 + (w,v3)/||(v3)||^2 * v3

Since (v1,v1) = 35, ||(v1)||^2 = 35.
Since (v2,v2) = 334, ||(v2)||^2 = 334.
Since (v3,v3) = 1, ||(v3)||^2 = 1.

Substitute the given values:

w = (175/35) * v1 + (-1670/334) * v2 + (-1/1) * v3

Simplify the coefficients:

w = 5 * v1 - 5 * v2 - v3

So, the vector w can be expressed as:

w = 5v1 - 5v2 - v3

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Answer:

\(\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}\)

( i )

now ,

since diameter = 10 cm

\(\implies \: radius = \frac{10}{2} = 5 \: cm \\ \)

now ,

\(slant \: height \: ( \: l \: ) = \sqrt{h {}^{2} + r { }^{2} } \\ \\ \implies \: \sqrt{(12) {}^{2} + (5) {}^{2} } \\ \\ \implies \: \sqrt{144 + 25} \\ \\ \implies \: \sqrt{169} \\ \\ \implies \: 13 \: cm\)

now ,

\(CSA \: of \: cone = \pi \: \times r \times l \\ \\ \implies \: \pi \: \times 5 \times 13 \\ \\ \implies \: 65\pi \: cm {}^{2} \)

_____________________________

_____________________________

( ii )

now when we flatten the cone ,

the slant height becomes the radius of the sector , while the arc becomes the circumference of cone !

\(\therefore \: radius = l = 13 \: cm \\ \\ arc \: length = circumference = 2\pi \: r\)

now ,

\(s = d \: \theta \: ( \: for \: a \: sector \: ) \\ \\ \therefore \: l\theta \: = 2\pi \: r \\ \\ \implies \: \theta = \frac{2\pi \: r}{l} \\ \\ \implies \: \theta = \frac{2 \times \pi \times 5}{13} \\ \\ \implies \: \theta \: = \frac{10\pi}{13} \\ \\ \implies \theta \: = \: 0.77 \pi \)

hope helpful :D

Step-by-step explanation:

i)

remember, the radius is half the diameter !

the overall surface area of a cone (base circle + "mantle", the lateral, curved surface) is

A = pi×r × (r + sqrt(h² + r²))

so, only the "mantle" or lateral curved stave area is

pi×r × sqrt(h² + r²) = pi×5 × sqrt(12² + 5²) = pi×5×sqrt(169) =

= pi×5×13 = 65×pi cm²

ii)

the length of the arc of the sector is the circumference of the circle, that was the base of the original cone.

that is

2×pi×r = 2×pi×5 = 10×pi cm

the total circumference of the large circle containing that sector is

2×pi×r' = 2×pi×sqrt(h² + r²)

as the radius r' of the circle containing the sector (representing the "mantle" of the cone) is the lateral height of the cone (the distance along its side from the base to the top). and that is per Pythagoras simply the square root of the sum of the square of the inner height and the square of the base radius.

in our case that is

2×pi×sqrt(12² + 5²) = 2×pi×13 = 26×pi cm

the angle of the sector is then 10/26 of the total of 360° for the whole circle :

360 × 10/26 = 138.4615385...°

or, if you need this in terms of pi too, remember that 360° are represented by 2×pi (the arc length of the standard circle).

2×pi × 10/26 = pi × 20/26 = pi × 10/13 =

= 0.769230769... × pi

Answer:

1/18

Step-by-step explanation:

Since x=2/3, we can plug in 2/3 for x, and we have 2/3 divided by 12.

Based on what we know about fractions, we can say that dividing by 12 is the same as multiplying by 1/12.

Therefore, we have the expression 2/3*1/12.

Next, we get 2/36, which can be simplified into 1/18.

Answer:

Number 1: -8.7. Number 2: -2

Step-by-step explanation:

To find the first one, subtract 11 from 2.3.

2.3-11= -8.7 , so that's the answer for the first one.

To find the answer to the second one, just do -4+-2=-2, so that's the answer for the second one.

Answer:

\(\boxed{\sf{x=\dfrac{21}{4}=5.25 }}\)

Step-by-step explanation:

Isolate the term of x from one side of the equation.

Use the distributive property.

Distributive property:

\(\Longrightarrow: \sf{A(B+C)=AB+AC}\)

Expand the form multiply.

4*x=4x

4*3=12

Rewrite the problem down.

4x-12=9

Add by 12 from both sides.

4x-12+12=9+12

Solve.

Add the numbers from left to right.

9+12=21

4x=21

Divide by 4 from both sides.

4x/4=21/4

Solve.

Divide the numbers from left to right.

x=21/4

21/4=5.25

x=21/4=5.25

I hope this helps you! Let me know if my answer is wrong or not.

The answer is B. Apply the distributive property to get 4x−12=9. You would do 4 times x to get 4x and then 4x3 to get 12. Then apply that information to the equation to get 4x−12=9.

Answer:

Kroger has the best unit price for turkey.

Step-by-step explanation:

12.62/10.7 = about $1.18 per pound

8.45/8.5 = about $1 per pound

To use Green's Theorem to evaluate f · dr, we first need to calculate the curl of f:

curl(f) = (∂Q/∂x) - (∂P/∂y)
where P = x sin(y) and Q = y - cos(y)

∂Q/∂x = 0
∂P/∂y = x cos(y)

So curl(f) = x cos(y)

Now we can apply Green's Theorem:

∫∫(curl(f)) · dA = ∫C f · dr
where C is the curve we are evaluating and dA is the differential area element.

The curve C is given by the equation (x - 7)^2 + (y - 5)^2 = 4. This is a circle centered at (7, 5) with radius 2. The orientation of the curve is clockwise, which means we need to reverse the sign of our answer.

We can parameterize the curve C as follows:

x = 7 + 2cos(t)
y = 5 + 2sin(t)
where 0 ≤ t ≤ 2π

Now we can evaluate the line integral using the parameterization and the formula f(x, y):

f(x, y) = y - cos(y), x sin(y)
= (5 + 2sin(t)) - cos(5 + 2sin(t)), (7 + 2cos(t))sin(5 + 2sin(t))

So we have:

∫C f · dr = -∫0^2π [(5 + 2sin(t)) - cos(5 + 2sin(t))](-2sin(t) dt + [(7 + 2cos(t))sin(5 + 2sin(t))]2cos(t) dt

Evaluating this integral gives the answer: -32π

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As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one.  Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.

given

1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.

2. The smallest common multiple shared by two numbers is referred to as the least common number.

LCM of 4 and 6 is 12, for instance.

3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.

HCF of 6 and 8 is 2, for instance.

4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.

5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.

As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

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Answer:

1/6

Step-by-step explanation:

Answer: 1/6

Step-by-step explanation: 60 minutes in a hour and one sixth of it is 10 minutes

The factors of the denominator in the rational function are (x - a) and (x - b)^2, where a and b are the values we need to determine.

To find the values of a and b, we need to factor the denominator of the rational function. The given expression, 23 + 422 - 162 - 64, can be simplified as follows:

23 + 422 - 162 - 64 = 423 - 162 - 64

= 423 - 226

= 197

So, the expression is equal to 197. However, this does not directly give us the values of a and b.

To factor the denominator in the rational function (x - a)(x - b)^2, we need more information. It seems that the given expression does not provide enough clues to determine the specific values of a and b. It is possible that there is missing information or some other method is required to find the values of a and b. Without additional context or equations, we cannot determine the values of a and b in this case.

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The number of degrees of freedom for the standardized test statistic in the comparison of population means using two small, independent samples is 33.

To calculate the number of degrees of freedom for the standardized test statistic in the comparison of population means using two small, independent samples, we can use the following formula:

df = (s1²/n1 + s2²/n2)² / [ (s1²/n1)² / (n1 - 1) + (s2²/n2)²/ (n2 - 1) ]

where s₁and s₂ are the sample standard deviations, n₁and n₂are the sample sizes for the two groups, and df is the number of degrees of freedom.

In this problem, we have:

s₁= 3.2

s₂ = 2.5

n₁= 16

n₂ = 22

Plugging these values into the formula, we get:

df = ((3.2²/16) + (2.5²/22))²/ [((3.2²/16)²/(16-1)) + ((2.5²/22)²/(22-1))]

Simplifying this expression, we get:

df = 33.33

Rounding to the nearest whole number, we get:

df = 33

Therefore, the number of degrees of freedom for the standardized test statistic in the comparison of population means using two small, independent samples is 33.

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Answer:

Square

Rectangle

Step-by-step explanation:

not a pro at shapes.

Answer:

3

Step-by-step explan4ation:

Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.

The missing component in this study is a control group. A control group is essential in experimental studies to provide a comparison and determine the effectiveness of the energy drink on memory levels.

In order to truly test the effectiveness of the energy drink on memory levels, the company would need to have a group of people who did not consume the energy drink but were otherwise similar to the group that did consume it. By comparing the memory levels of these two groups, the company could determine if the energy drink truly had an impact on memory or if the reported improvements were simply due to chance or other factors. Without a control group, the results of the study are not as reliable or valid.
So the missing component in this study is a control group.  Without a control group, it is difficult to establish a causal relationship between the energy drink and improved memory.

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Proved that the middle term in the expansion of (1+x)^2n is [ 1×3×5...(2n-1) / n! ] 2^n × x^n

The given expansion is (1 + x)^2n

Number of terms in the expansion = 2n + 1

The middle term of the expansion = (2n + 1) + 1 /2

= (2n + 2) / 2

= n + 1

The n + 1 term of the expansion will be the middle term

The equation of the expansion is

a = 2nCn(1)^n (x)^(2n - n)

Expand the terms

= [ (2n)! / n!(2n - n)!] x^n

Expand the term

=[ (2^n(n!) 1×3×5...(2n - 1) / n! × n! ]x^n

=[ 1×3×5...(2n-1) / n! ] 2^n × x^n

Therefore, proved that the [ 1×3×5...(2n-1) / n! ] 2^n × x^n is the middle term

The complete question is:

Sow the middle term in the expansion of (1 + x)^2n is [ 1×3×5...(2n-1) / n! ] 2^n × x^n

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The volume of the cuboid is 1152 ft³

A cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid.

A rectangular prism is called a cuboid and the volume of a cuboid is expressed as;

V = base area × height

The base is rectangle, the area of a rectangle is expressed as;

A = l× w

A = 18 × 8

A = 144 ft²

V = base area × height

V = 144 × 8

V = 1152 ft³

Therefore, the volume of the cuboid is 1152 ft³

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Answer:

• A rectangle is a geometrical shape with 4 sides, where each two opposite sides are identical.

• Each side of a rectangle is perpendicular to each other.

• When a rectangle is stretched or made slant in either clockwise or anticlockwise, it forms a geometric shape known as a parallelogram.

→ Perimeter of a rectangle:

\({ \rm{perimeter = 2(length + width) }} \\ \)

→ Area of a rectangle

\({ \rm{area = length \times width}} \\ \)

The subset of the data set with x2, x3, and x4 would include 6 missing values.

The subset of the data set with x2, x3, and x4 would include 6 missing values.

1. Subset the data set to include only x2, x3, and x4.

2. Count the number of missing values in each variable.

3. Add the number of missing values for each variable together.

4. The total number of missing values in these three variables is 6.

The subset of the data set with x2, x3, and x4 would include 6 missing values.

Subset the data set to include only x2, x3, and x4.

The complete question is :

Subset the data set to include only x2, x3, and x4. How many missing values are there in these three variables?

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Answer:

Step-by-step explanation:

305ml × 10 = 3,050ml

3,050ml = 3.05L