A real number is positive, negative, or zero. True or false​

Answer:

Step-by-step explanation:

If two variables, x and y have a direct variation, it means that an increase in x would lead to a corresponding increase in y. A decrease on x would lead to a corresponding decrease in y.

Therefore, we would compare the scenarios to determine which is not a direct variation. The correct option is

d) Time taken will be less if number of workers are increased to complete the same work.​

The rest are direct variation scenarios

The possible number of pizza special is (7 x 11 x 6 x 3 x 2 = 2772 variations.

The integral test to determine the following  series converges.

Part 1: Convergence condition for the series

n=2 (-1)-¹√√n (n-3)², converge, diverge absolutely.

We will apply the Cauchy Condensation

Test to determine the convergence condition of the given series.

n=2 (-1)-¹√√n (n-3)²

Let's rewrite the general term an in terms of 2^n.

2^n an = 2^n (-1)-¹√√2ⁿ (2ⁿ-3)²

= -2^(n-½)√√(2-³)²= -2^(n-½)2-³/2

= -2^(n-1/2-3/2)=-2^(n-2)

Thus, by Cauchy's condensation test, the convergence of the given series is equivalent to the convergence of the following series: n=0 2ⁿ (-2)ⁿ,

This is a convergent Geometric Series with a = 2 and r = -2.

Since the absolute value of r is less than 1, the series converges.

Therefore, the given series converges.

Part 2: Use the integral test to determine the following series converges or diverges.

4n³ / x=2(1+2n²)³

Here, a_n=4n³/ (1+2n²)³

Integrate this from 1 to infinity, ∫[4n³/(1+2n²)³]dn=a=-2/[(1+2n²)²] which is less than infinity.

Therefore, the given series converges.

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Answer:

x = 45 degrees

Step-by-step explanation:

A circle has 360 degrees

65 + 85 + 50 + 115 = 315 degrees

Then we take

360 - 315 = 45 degrees

So, x = 45 degrees.

Therefore, the ladder reaches a height of 12 feet up the wall.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the other two sides (the distance from the base of the wall and the height of the ladder on the wall). In this case, we have a right triangle with a base of 9 feet, a hypotenuse of 15 feet, and an unknown height.
So, using the Pythagorean theorem, we can solve for the height:
15^2 = 9^2 + height^2
225 = 81 + height^2
144 = height^2
12 = height
Therefore, the ladder reaches a height of 12 feet up the wall.

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Answer:

Is this what you are looking for?

Answer:

c=30 -9over 4 f f= 40 over 3 negative 4 over 9 c

Step-by-step explanation:

hopefully that helps you

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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Using proportions, it is found that the total distance covered by him in 6 days is of 28.5 km.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The daily distance is of 2 x 2.375 km, as 1000 m = 1 km and he walks both ways. Hence, the total distance covered by him in 6 days is given by:

D = 6 x 2 x 2.375 = 28.5 km.

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The formula for a circle's area is \(A=\pi r^2\). We are given an area of 38.465 square inches for a quarter of it.

Multiply this value by 4 to compensate for the quarter circle.

\(4 \times 38.465=\pi r^2\)

\(153.86=\pi r^2\)

Divide both sides by pi (Note: I'm using the conventional value of 3.14)

\(49=r^2\)

Take the positive square root of both sides

\(7=r\)

The radius is 7 inches. Let me know if you have any questions, thanks!

The  implicit differentiation of \(\dfrac {dz}{dx}\) is \(\dfrac {yz}{7e^{7z}-xy}\) and for \(\dfrac {dz}{dy}\)  it is \(\dfrac {xz}{7e^{7z}-xy}\).

In implicit differentiation, we differentiate every aspect of an equation with variables (commonly x and y) through treating one of the variables as a feature of the other.

It is given that,

\(e^{7z}=xyz\)

Differentiate both sides with respect to x,

Only treat y as constant and z and x as variables.

\(\frac{{e^{7z}}{dx} }{\frac{dz}{dx}} =\frac{yd(xz)}{dx}\)

use chain rule in left hand side

\(\frac {e^{7z}}{dx} \times \frac{dz}{dx} =\frac{yd(xz)}{dx}\)

use product rule in RHS

\(7e^{7z} \times\frac{dz}{dx}=yx \times\frac{dz}{dx+z} \\\\7e^{7z} \times\frac{dz}{dx}=xy \times\frac{dz}{dx} +yz\\\\\frac{dz}{dx}=\frac{yz}{7e^{7z-xy}}\)

It is given that,

\(e^{7z}=xyz\)

Differentiate both sides with respect to y,

Only treat x as constant and z and y as variables.

\(\dfrac {d (e^7z)}{dy}= \dfrac {d(xyz)}{dy}\)

use chain rule in left hand side

\(\dfrac {d (e^7z)}{dy} \times \dfrac{dy}{dx}=\dfrac {yd(xz)}{dy}\)

use product rule in RHS

\(7 (e^{7z}) \times \dfrac{dz}{dy}=xy \dfrac{dz}{dy+z}\\\\(7e^{7z})\times \dfrac{dz}{dy}=xz\\\\\dfrac{dz}{dy}=\dfrac {xz}{7e^{7z}-xy}\)

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Answer:

Pythagorean Theorem: a^2 + b^2 = c^2

6^2 + 15^2 = c^2

36 + 225 = 261

So, the answer is 261

Let me know if this helps!

Answer:

21

Step-by-step explanation:

2 dozen=24

24-3=21

The measures of the numbered angles are:

m∠1 = 65°

m∠2 = 55°

m∠3 = 60°

m∠4 =  65°

m∠5 = 55°

m∠6 = 60°

m∠7 = 120°

m∠8 =  60°

m∠9 =  120°

m∠10 = 115°

m∠11 = 85°

m∠12 = 115°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties. Angles are formed when two lines or rays intersect or when a line intersects a plane.

m∠1 = 65° (corresponding angles)

m∠2 = 180 - 60 - m∠1  (angles on a straight line)

m∠2 = 180 - 60 - 65 = 55°

m∠3 = 60° (vertically opposite angles)

m∠4 = m∠1 (vertically opposite angles)

m∠4 =  65°

m∠5 = m∠2 (vertically opposite angles)

m∠5 = 55°

m∠6 = m∠3 (alternate angles)

m∠6 = 60°

m∠7 = 180 - m∠6 (angles on a straight line)

m∠7 = 180 - 60 = 120°

m∠8 = m∠6 (vertically opposite angles)

m∠8 =  60°

m∠9 = m∠7 (vertically opposite angles)

m∠9 =  120°

m∠10 = 180 - 65 (angles on a straight line)

m∠10 = 180 - 65 = 115°

m∠11 = 85° (vertically opposite angles)

m∠12 =  m∠10 (vertically opposite angles)

m∠12 = 115°

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the answer i got was 18.12

Answer:

6+7√3  or  18.12

Step-by-step explanation:

7√3+2√9= 7√3+2*3= 6+7√3

6+7√3= 18.12

Option D   represents the inequality.

Given,

√5x • √x+3

Now for solving the inequality,

5x≥0

x≥0

x + 3≥ 0

x ≥ -3

Now to conclude the final inequality combine both the regions of x and find out the common region of variable x.

Thus,

x ≥ 0 will satisfy the inequality.

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Answer:

625%

Step-by-step explanation:

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

11

Step-by-step explanation:

find HCF using factor tree

99={3×3×11}

33={3×11}

121={11×11}

HCF =11

Answer:

The answer is C.

Step-by-step explanation:

Firstly, you have to find the new commission sales after first 5 computera are sold. In order to do so, you have to multiply it by 1.5 :

$100 × 1.5 = $150

Next, you have to find the total amount :

($100×5) + ($150×3)

= $500 + $450

= $950

The recursive rule for the number of acres at the beginning of the nth day in a forest fire that grows by 20% each day and is battled by firefighters who can put out 15 acres per day is given by: A(n) = 1.2 * A(n-1) - 15, where A(n) represents the number of acres at the beginning of the nth day. Using this rule, we can calculate that there are 89.6 acres burning at the beginning of the 8th day.

Explanation: To determine the recursive rule for the number of acres at the beginning of the nth day, we need to consider the given information. The forest fire initially covers 60 acres and grows by 20% each day. This means that the number of acres at the beginning of the next day (n+1) is 1.2 times the number of acres at the beginning of the current day (n). However, the firefighters are able to put out 15 acres of fire per day.

Therefore, to calculate A(n), we start with the initial number of acres, which is 60, and apply the recursive rule. A(n) = 1.2 * A(n-1) - 15. This formula takes into account the growth of the fire by 20% and the reduction of 15 acres due to the firefighters' efforts. By substituting the values, we can calculate the number of acres at the beginning of each day.

To find the number of acres burning at the 8th day, we substitute n = 8 into the recursive rule. A(8) = 1.2 * A(7) - 15. We need to determine A(7) first by substituting n = 7, and so on, until we reach the initial value A(1) = 60. Once we have calculated A(8), we can determine that there are 89.6 acres burning at the beginning of the 8th day

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Answer:

the first one i think

Step-by-step explanation:

-3 is the y-intercept and that i all i got, sorry :(

Answer:

Its the first one! <3

Answer:

-113

Step-by-step explanation:

sub the values

x^3-2y^2-3x^3+z^4

(3)^3-2(5)^2-3(3)+(-3)^4

27-50-9-81

-113

Answer:

wut

Step-by-step explanation:

Given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

The two base angles of any isosceles triangle are always congruent to each other.

Therefore:

m∠CBD = m∠CDB

m∠CBD = 180° - 125° (supplementary angles)

m∠CBD = 55°

Therefore:

m∠CBD = m∠CDB = 55°

In summary, given that ACE is an isosceles triangle, the measure of ∠CDB is: 55°

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Answer:

Step 1: Take the absolute value of each number. Step 2: Subtract the number with a smaller absolute value from the number with bigger or larger absolute value. Step 3: Copy the sign of the number with the bigger or larger absolute value.

Step-by-step explanation:

Based on the mentioned informations and provided values, 21 red beads were removed.

Let the number of red beads removed be x. Then we have:

Total points = (7x + 5y + 3z + 2w) = 147000, where y, z, w are the number of yellow, green, and blue beads removed, respectively.

We can also write the above Linear equation as:

7x = 147000 - 5y - 3z - 2w

Since 147000 is divisible by 1000, we can divide both sides by 1000 to get:

7x = 147

x = 21

Therefore, 21 red beads were removed.

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A fraction is a part of a number or any number of equal parts, it is found that 531.25 as a mixed number would be 53100 25/100.

A fraction represents a part of a number or any number of equal parts.

There is a fraction, containing numerator(upper value) and denominator(lower value). When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. The proper fraction is also called fraction which is less than 1. And an improper fraction is ≥ 1; A mixed fraction contains a sum of whole number and a proper fraction.

WE need to find the fraction form first;

531.25  = 531.25 /1

= 53125 /100

Then as a mixed fraction;

53125 /100

53100 25/100

A fraction is a part of a number or any number of equal parts, it is found that 531.25 as a mixed number would be 53100 25/100.

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Answer:

Yes

Step-by-step explanation:

We can test this claim using the one proportion z test :

x = 25 ; n = 100

Phat = x / n = 25 / 100 = 0.25

H0 : P = 0.15

H0 : P > 0.15

The test statistic :

Z = (phat - p) ÷ √p(1-p)/n

Z = (0.25-0.15) ÷ √(0.15*0.85)/100

Z = 2.8

Using the Pvalue from Zscore calculator :

α = 0.05

Pvalue (Z < 2.8) =0.0026

Pvalue < α ; We reject the Null

Answer:

Step-by-step explanation:

if there are 500 tixets and 7 prizes (1 top prize+1 second prize+5 third prize) your chances of wining are 7/500=0.014 or 1.4% chance

with a 1.4% chance of win and a 98.6% chance to loose in average you can expect to loose.