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Answer:

-8-6

-8+6

6-(-8)

Step-by-step explanation:

The distance of the student from the foot of the tower is 25.63m the nearest 1/2 is 25.5m.

Given that From the top of a tower 14m high

The angle of depression of a student is 32°

we can use trigonometry to find the distance from the foot of the tower to the student:

tan(32°) = opposite/adjacent = 14/distance

Rearranging this equation gives:

distance = 14/tan(32°)

= 25.63m

Therefore, the distance of the student from the foot of the tower is approximately 25.63m nearest 1/2, this is 25.5m.

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So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

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Answer:

√800

=28.28

rounded into nearest tenth is ...

=30

We can see here that the relationship that exists between the triangular numbers and the rectangular numbers​ is that a doubling of the triangular number will give the rectangular number.

When dots or other items are placed in the form of a triangle, a triangular number is one that may create an equilateral triangle. It is a run of numbers that adheres to a particular pattern.

Beginning with 1, the series of triangular numbers continues by adding subsequent positive integers. The total of all positive integers up to a specific number makes up each triangular number.

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Answer:

(2^2)(20−√9) =68

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

Use x for the equation: (x - 1/2)*1/2 = 1/8

Just go backwards

1/8 is the result, and to get it, you multiply by 1/2, so instead of that, you divide 1/8 by 1/2 instead (Dividing a number by a fraction is the same as multiplying it by its reciprocal. The reciprocal of 1/2 is 2): (1/8)/(1/2) = 1/8 * 2 = 2/8 = 1/4, now since we subtracted 1/2, we add instead: 1/4 + 1/2 = 1/4 + 2/4 = 3/4

Answer:

£1248

Step-by-step explanation:

1200x4%

=£48

1200+48=£1248

Gagu will be paid £1248 after the increase.

The amount Gagu paid per month after the 4% increment is £1248

If there is x% increment in y then the increment will be (x/100)*y and the  new amount after x% increment will be now  y + (x*y)/100

Given that Gagu is paid £1200 per month. He is going to get a 4% increase in the amount of money he is paid.

Initial payment  = £1200

4% increment  = 4% of initial pay  = 4(1200)/ 100 = £ 48

After increment new payment = Initial payment + 4% increment = 1200+48

                                                                                                          =  £1248

Therefore, The amount Gagu paid per month after the increase is £1248

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Answer:

Area = 15a^3b^6

Perimeter: 10a^2b^4+6ab^2

Step-by-step explanation:

Formula For Area: L*W

Input The Numbers: 5a^2b^4 * 3ab^2

5a^2b^4 * 3ab^2 = 15a^3b^6

Area = 15a^3b^6

Formula for perimeter: P=2(l+w)

Input the Numbers: P = 2(5a^2b^4 + 3ab^2)

2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2

Perimeter: 10a^2b^4+6ab^2

Hope this helped!

Answer:

The answer is -285

Step-by-step explanation:

Answer: 8n

Step-by-step explanation:

Suppose the number is 'n'

Its product with number eight is given by

\(\Rightarrow n\times 8=8n\)

Answer:

8n

Step-by-step explanation:

edguenity 2020-2021

Answer: Luis’s, because he flipped the inequality sign when he subtracted

Step-by-step explanation:

Here is the complete question:

Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality

7.2b + 6.5 > 4.8b – 8.1.

Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.

Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.

Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.

Which student’s first step was incorrect, and why?

a. Amelia’s, because the variable term must be isolated on the left side

b. Luis’s, because he flipped the inequality sign when he subtracted

c. Shauna’s, because she did not apply the subtraction property of equality properly.

d. Clarence’s, because the terms he added together were not like terms.

The inequality given is:

7.2b + 6.5 > 4.8b – 8.1.

We are informed that Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.

If Luis started by subtracting 4.8b from both sides, he should get:

7.2b + 6.5 > 4.8b – 8.1.

7.2b + 6.5 - 4.8b > 4.8b – 8.1 - 4.8b

2.4b + 6.5 > - 8.1

But looking critically, we would realise that what Luis got us different as the inequality sign has been changed from greater than to less than and this is incorrect.

The inequality sign can only be flipped in case whereby there's a division or multiplication of a negative number from both sides.

Therefore, Luis’s first step was incorrect because he flipped the inequality sign when he subtracted.

Answer:

The slope is 5.

Explanation:

In the slope-intercept form of an equation

m is the slope, and b is the y-intercept of the equation.

Now in our case,

therefore, the slope is 5 and the y-intercept is -3.

The number of shirts ordered(m) is a variable cost while the cost of order which is the flat fee is fixed.

The equation that represents the relationship between the number of T-shirts ordered(m), the number of colors on the shirts(n), and the total cost of order is:

Total cost = 3m  +  50mn

Variable expenses vary according on the amount of output produced. Labor, commissions, and raw materials are examples of variable expenses. Regardless of industrial output, fixed expenses remain constant. Lease and rental payments, insurance, and interest payments are examples of fixed costs.

Variable costs include the costs of raw materials and packaging for a manufacturing company, as well as credit card transaction fees and shipping expenditures for a retail company, which climb and fall with sales. A variable cost is distinguished from a fixed cost.

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To test the claim that the mean weight of tortilla chip bags from Factory A is the same as the mean weight from Factory B, we can conduct a two-sample t-test.

The null hypothesis, denoted as H0, assumes that the means are equal: μA = μB. The alternative hypothesis, denoted as Ha, assumes that the means are not equal: μA ≠ μB.

We calculate the test statistic, which follows a t-distribution under the null hypothesis, using the formula:

t = (xA - xB) / sqrt((sA^2 / nA) + (sB^2 / nB))

where xA and xB are the sample means, sA and sB are the sample standard deviations, and nA and nB are the sample sizes.

Plugging in the values:

t = (11.09 - 11.03) / sqrt((0.04^2 / 120) + (0.09^2 / 90))

Calculating this expression, we find the value of t. We then compare this value to the critical value of the t-distribution at a significance level of 0.05, with degrees of freedom equal to (nA - 1) + (nB - 1).

If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that there is evidence to support the claim that the mean weight of tortilla chip bags from Factory A is different from the mean weight of bags from Factory B. Otherwise, if the calculated t-value falls within the critical region, we fail to reject the null hypothesis, indicating that there is not enough evidence to support the claim of a difference in means.

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Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

Answer:

moon = 7

star = 4

Step-by-step explanation:

First equation:

moon + 1 = star + star

   7   + 1 = 4 + 4

Second Equation:

moon = 3 + star

    7 = 3 + 4

Hope this helps

Answer:

star =2

Step-by-step explanation:

m=moon s= star

m+1=s+s     you took the one form here

m=3+s         and added it here

now subtract the one which would be 2 so the star = 2

your moon is correct

Answer:

None

Step-by-step explanation:

0y+3y=3y.

10+3y=13y, 13y is not equal to 3y

y+12=12y, 12y is not equal to 12y

12 is not equal to 3y

y is not equal to 3y

13y-y=12y which is not equal to 3y.

If you made a typo, put it in comment.

Answer:

My friend's mower will take approximately 0.75 h to mow the lawn alone.

Step-by-step explanation:

To solve this problem we can use the idea of average speed and apply to this problem, using the appropriate formula shown below:

\(speed = \frac{distance}{time}\)

Where each lawn mower has a speed at which they can mown, the distance is the lawn they're mowing and the time is how long they will take to do it. In the case where my equipment is working alone, its speed "x" can be modeled as below:

\(x = \frac{lawn}{1.5}\)

When my friend's mower does the job, its speed "y" can be seen as:

\(y = \frac{lawn}{time}\)

When both work together the speed can be seen as:

\(x + y = \frac{lawn}{0.5}\)

Applying the first two equations on the second, gives us:

\(\frac{lawn}{1.5} + \frac{lawn}{time} = \frac{lawn}{0.5}\\\frac{1}{time} = \frac{1}{0.5} - \frac{1}{1.5}\\\frac{1}{time} = 2 - 0.667\\\frac{1}{time} = 1.333\\1.333*time = 1\\time = \frac{1}{1.333} = 0.75\)

My friend's mower will take approximately 0.75 h to mow the lawn alone.

The given statement is to be proved using mathematical induction. We can prove the statement using mathematical induction as follows:

Step 1: For n = 1, p(1) is true because 1³ - 1 = 0, which is divisible by 3.

Therefore, p(1) is true.

Step 2: Assume that p(k) is true for k = n, where n is some positive integer.

Then, we need to prove that p(k + 1) is also true.

Now, we have to show that (k + 1)³ - (k + 1) is divisible by 3.

The difference between two consecutive cubes can be expressed as:

\($(k + 1)^3 - k^3 = 3k^2 + 3k + 1$\)

Therefore, we can write (k + 1)³ - (k + 1) as:

\($(k + 1)^3 - (k + 1) = k^3 + 3k^2 + 2k$\)

Now, let's consider the following expression:

\($$k^3 - k + 3(k^2 + k)$$\)

Using the induction hypothesis, we can say that k³ - k is divisible by 3.

Thus, we can write: \($$k^3 - k = 3m \text { (say) }$$\) where m is an integer.

Now, consider the expression 3(k² + k). We can factor out a 3 from this expression to get:

\($$3(k^2 + k) = 3k(k + 1)$$\) Since either k or (k + 1) is divisible by 2, we can say that k(k + 1) is always even.

Therefore, we can say that 3(k² + k) is divisible by 3. Combining these two results, we get:

\($$k^3 - k + 3(k^2 + k) = 3m + 3n = 3(m + n)$$\) where n is an integer such that 3(k² + k) = 3n.

Therefore, we can say that \($(k + 1)^3 - (k + 1)$\) is divisible by 3.

Hence, p(k + 1) is true.

Therefore, by the principle of mathematical induction, we can say that p(n) is true for every positive integer n.

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Answer:

7

Step-by-step explanation:

1+3=4

2+3=5

3+3=6

4+3=7

Answer:

you don't give enough information to help answer this question

The length of one side of the box is 10 inches.

Suppose that: The side length of the considered cube is L units.

Then, we get the Volume of that cube = L³ cubic units.

The volume of a cube is of the form V =  L³, where L is the side length.

Given that the shipping box has a volume of 1,000 cubic inches.

Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:

1000 =  L³

Cube root both sides:

L = \(\sqrt[3]{1000}\)

Therefore, each side is 10 inches.

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There are $42.95 more will be in the account if Cho waits 10 years instead of 5 years.

What is compounded continuously?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

Given:

Cho started a savings account with $2800.

The account pays 0.3% compounded continuously.

Cho wanted to withdraw the money after 5 years, but her friend says she should wait until 10 years.

First to find the amount after 5 years.

 \(P_0 = 2800\), r = 0.3% = 0.003,  t = 5

Consider the compounded continuously formula

\(P = P_0e^r^t\)

Plug the values in the formula,

\(P=2800e^0^.^0^0^3^*^5\)

P = $2842.32

The amount in the account after 5 years is $2842.32.

Now to find the amount in the account after 10 years.

\(P_0 = 2800\),  r = 0.003, t = 10

Plug the values in the formula,

\(P=2800e^0^.^0^0^3^*^1^0\)

P = $2885.27

The amount in the account after 10 years is $2885.27.

Now,

$2885.27 - $2842.32 = $42.95

Hence, there are $42.95 more will be in the account if Cho waits 10 years instead of 5 years.

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Answer:

Step-by-step explanation:

a.v = 10 * 5 * 7 = 350cm^3

b.because 1m^3=1000dm^3=1000000cm^3

so 1cm^3=0.000001m3

350cm^3=0.00035m^3

According to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

Descarte's Rule of Signs determines the number of real zeros in polynomial functions.

This indicates that -

The number of positive real zeros in the polynomial function f(x) is less than or equal to an even number depending on the sign change of the coefficients.

The number of negative real zeros in f(x) is an even number equal to or less than the number of sign changes of the coefficients of f(-x) terms.

Here, the polynomial function is given as -

\(P(x)=x^{3}-x^{2} -x-5\) ----- (1)

We have to find out the number of positive and negative real zeros that  the given polynomial can have.

The given polynomial already has its variables in the descending powers. So, we can easily determine the number of sign changes in the coefficients of P(x).

So, the coefficients of the variables in P(x) are -

1, -1, -1, -5

From above, we see that -

There is a sign change in the first and second variable coefficients

There is no sign change in the second and third variable coefficients

There is no sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, there can be exactly three positive real zeros or less than three but an odd number of zeros.

So, we can determine that the number of positive real zeroes of the given polynomial can be 1.

To find out the negative real zeroes of the given polynomial, we have to find out P(-x) and determine the sign changes in the variable coefficients of P(-x).

From equation (1), we can write P(-x) as -

\(P(x)=x^{3}-x^{2} -x-5\\= > P(-x)=(-x)^{3}-(-x)^{2} -(-x)-5\\= > P(-x)=-x^{3}-x^{2} +x-5\)----- (2)

So, the coefficients of the variables in P(-x) are -

-1, -1, +1, -5

From above, we see that -

There is no sign change in the first and second variable coefficients

There is a sign change in the second and third variable coefficients

There is a sign change in the third and fourth variable coefficients

According to Descartes' Rule of Signs, since there are two sign changes of the coefficient variables, there can be two negative real zeros or less than two but an even number of zeros.

So, we can determine that the number of negative real zeroes of the given polynomial can be 2 or 0.

Thus, according to Descartes' Rule of Signs, there is 1 positive real zero and 2 or 0 negative real zeroes of the polynomial.

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Answer:

A = 1/8 or -1/8

Step-by-step explanation:

Answer:

1.1-5.4=4.3

Step-by-step explanation:

because the total is 5.4 and the turtle was 1.1 up so subtract to see how much the turtle sank to the Bottom

The required length of the shorter side of the triangle pendant is 13 inches.

A triangle pendant addresses indication, edification, disclosure, and a higher viewpoint. It is much of the time used to stamp the patterns of development that lead to a higher condition. Shop the Workmanship Decor Blossom Pendant Pink.

We have,

Let the longer sides which are equal be x,

Then shorter side is x - 9.

Perimeter Triangle pendant = 57 inches

So, x + x + x - 9 = 57

3x = 66

x = 22 inches

So, the Shortest side = x - 9 = 22 - 9 = 13 inches.

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