A number, .f, rounded to 1 d.p. is 49.2
Another number, g,
rounded to 1 d.p. is 7.8
What are the lower and upper bounds of
f - g?

Using differentials both answers, rounded to four decimal places, are 214.9203.

To use differentials to approximate the value of \((5.99)^3\), we will follow these steps:

1. Choose a point close to 5.99, where the function is easy to evaluate. We'll use 6 as our point.
2. Find the differential of the function y = \(x^3\), which is dy = \(3x^2\)dx.
3. Evaluate the differential at the chosen point, x = 6.
4. Determine the change in x, which is dx = 5.99 - 6 = -0.01.
5. Use the differential to approximate the change in y, which is dy ≈ \(3(6)^2\)(-0.01).
6. Add the change in y to the value of the function at the chosen point to approximate the value of the expression.

Following these steps:

1. Chosen point: x = 6.
2. Differential: dy = 3\(x^2\) dx.
3. Evaluating the differential at x = 6: dy = \(3(6)^2\) dx = 108 dx.
4. Change in x: dx = -0.01.
5. Change in y: dy ≈ 108(-0.01) = -1.08.
6. Approximate value of the expression: \((6^3)\)+ (-1.08) = 216 - 1.08 = 214.92.

Thus, using differentials, we approximate the value of \((5.99)^3\) to be 214.92.

For comparison, using a calculator: \((5.99)^3\) ≈ 214.9203.

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Answer:

cot x

Step-by-step explanation:

using the identities

csc x = \(\frac{1}{sinx}\)

sin(\(\frac{\pi }{2}\) - x) = cos x

then

csc x × sin (\(\frac{\pi }{2}\) - x)

= \(\frac{1}{sinx}\) × cosx

= \(\frac{cosx}{sinx}\)

= cot x

Answer:  " Yes; Kim is  correct."

Explanation:  [refer to the end of this "answer"].

Note: Any "triangle" has 3 sides and 3 angles.

An isosceles triangle has 2 (angles) with the exact same measurements.

We are given the following information:

We have an isosceles angle:
 with one of the angles = 48°
 _______
Does this mean that one of the angles must be:  66 ° ?

If so; then:  either:
       48 + 66 + 48 = 180 ?
or:   48 + 66 + 66 = 180 ?

1)  First: Start with 48 + 66 + 48 ≟ 180 ?

   (48 + 66 + 48) ≟ 180 ?   ;  162 ≟ 180?  No; " 162 < 180 " .

2) Second: Try:  "48 + 66 + 66 = 180 " .

   (48 + 66 + 66) ≟ 180 ? ;  180 ≟ 180 ? ; Yes! "180 = 180".
_______
So:  Kim is correct; because isosceles triangles must have angles with 2 (two) equal measurements.  Note that all triangles have angles that add up to 180° .  
So:  As shown above:
    If one angle of the triangle is 48°; then: **each** of the other angle measurements must be 66°.
  So:  Yes; Kim is correct when he says that one of the other angles must be 66°.
   (48 + 66 + 48) ≟ 180 ?   ;  162 ≟. 180?  No; " 162 < 180 " .
_______
Hope this is helpful to you!  Wishing you well!
_______

Answer:

4.25c + 3.5p = 36.50

c + 6 = p

c = candies and p = pretzels

Step-by-step explanation:

So for the first equation, the prices will be the coefficients of each variable, since for each candy/pretzel it will be that price. We also know that both of these prices together equal 36.50, so that will be on the other side of the equal sign. So the equation representing this info is 4.25c + 3.5p = 36.50

And for the second equation I saw that Mason bought 6 more pretzels than candies. So no matter what number the candies is, the pretzels should always be 6 more than the candies. So the equation representing this information is c + 6 = p

Lastly I just defined the variables that I used to right the system. That is all! Hope this helps you this should be correct :)

0.02 can be written in fraction form as 1/50.

Step 1: We need to multiply the numerator and denominator by 100 since there are 2 digits after the decimal.

0.02 = (0.02 × 100) / 100

= 2 / 100 [ since 0.02 × 100 = 2 ]

Step 2: Reduce the obtained fraction to the lowest term

Since 2 is the common factor of 2 and 100 so we divide both the numerator and denominator by 2.

2/100 = (2 ÷ 2) / (100 ÷ 2) = 1/50

Hence, 0.02 can be written in fraction form as 1/50.

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Answer:

x=1/2

Step-by-step explanation:

98+29x=96+33x

Step 1: Simplify both sides of the equation.

29x+98=33x+96

Step 2: Subtract 33x from both sides.

29x+98−33x=33x+96−33x

−4x+98=96

Step 3: Subtract 98 from both sides.

−4x+98−98=96−98

−4x=−2

Step 4: Divide both sides by -4.

−4x

−4

=

−2/−4

x=1/2

Answer:

a: x= 65

b: k= 23

c: x= 31

d: m: .60

I'm not sure which ones to circle sorry

Step-by-step explanation:

hope this helps otherwise!!:)

Answer:

V≈523.6in³

d Diameter

Step-by-step explanation:

so its b

We can conclude that -

Given is the spreadsheet data.

Mean is defined as the average of the given number of terms.

Mathematically, mean can be written as -

Mean = ∑x{i}/n

We can write -

Therefore, we can conclude that -

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Answer:

The mean refund calculated by the tax preparers under the old set of requirements is $343.89. The mean refund calculated by tax preparers under the new set of requirements is $369.45.

Step-by-step explanation:

This was the answer straight from Plato

The answer would be 73.86

Answer:

siesta  bien

Step-by-step explanation:

Answer:

1) x < 2

2) x > -4

3) x < 6

The function y = √(6 + 7x) can be expressed in the form f(g(x)) as f(6 + 7x), where the inner function is g(x) = 6 + 7x and the outer function is f(u) = √u.

To write the given function y = √(6 + 7x) in the form f(g(x)), we need to identify the inner function g(x) and the outer function f(u).

Let's start by identifying the inner function.

In this case, the inner function is g(x) = 6 + 7x. It is the expression inside the square root.

Now, let's identify the outer function.

The outer function is f(u) = √u. It takes the square root of the input value u.

By substituting the inner function g(x) into the outer function f(u), we can rewrite the given function in the form f(g(x)):

y = f(g(x)) = f(6 + 7x) = √(6 + 7x)

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Using CPCT the length of the segment AB = ED for the given triangle.

The term "CPCT" stands for "Corresponding parts of Congruent Triangle," meaning that if two triangles are congruent, they are precisely mirror copies of one another and their corresponding parts, such as side lengths and angles, can be assumed to be equal. According to the concept of corresponding parts of congruent triangles, or cpct, corresponding sides and corresponding angles of two congruent triangles are identical.

In the given figure it is given that C is the midpoint of BE thus,

BC = CE

In triangle ABC and triangle DCE we have:

angle C = angle C vertically opposite angles.

BC = CE (C is the midpoint)

Angle A = angle E (given)

Thus, using CPCT the length of the segment AB = ED for the given triangle.

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Let v be a vector space and f ⊆ v be a finite set. To show that f ∪{u} is a linearly independent set, we need to prove that the only linear combination of its elements that equals the zero vector is the trivial one (i.e., all coefficients are zero).

Suppose that there exist scalars a1, a2, ..., an, b such that:

b*u + a1*v1 + a2*v2 + ... + an*vn = 0
where v1, v2, ..., vn are elements of f.

We want to show that all coefficients are zero.

Since u /∈span f, we know that u cannot be written as a linear combination of elements of f. Therefore, b ≠ 0.

We can rearrange the equation to get:
b*u = -(a1*v1 + a2*v2 + ... + an*vn)

Since f is linearly independent, we know that the only linear combination of its elements that equals the zero vector is the trivial one. Therefore, a1 = a2 = ... = an = 0.

Substituting this into the equation, we get
b*u = 0

Since b ≠ 0, we know that u = 0, which contradicts the fact that u is not in the span of f.

Therefore, our assumption that there exist nontrivial coefficients that satisfy the equation is false, and f ∪{u} is indeed a linearly independent set.

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The probability is 0.421 that the mean time spent commuting from home to work by a sample of 12 employees.

Empirical states that if most of the values or observations of a data set fall within the 3-population standard deviation, then the distribution of the data said to be a normal otherwise non-normal. It is also known by the name of the three-sigma rule.

We have the following information from the question is:

Sample size (N) = 12,

standard deviation (σ) = 8.1

and  mean (μ) = 42.7

The probability mean time spent commuting from home to work by a sample of 12 employees will be between 43.26 and 49.35 minutes is:

\(p[43.26 < x(bar) < 49.35]\)

\(p[\frac{43.26-43.7}{\frac{8.1}{\sqrt{12} } } < z < \frac{49.35-43.7}{\frac{8.1}{\sqrt{12} } }]\)

=> -0.18 < z < 2.41

=> p[z ≤ 2.41] - p[z ≤ 0.18] = 0.992 - 0.571

                                         = 0.421

Therefore, the probability 0.421 (rounded to three decimal places)  

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Answer:

NO

Step-by-step explanation:

We can know the answer by using the Pythagorean Theorem.

In a triangle with uneven sides, the longest side is called the hypotenuse. In this case, it is 50.

   Using the theorem: a² + b² = c²  

(Let's say c is the hypotenuse and a and b are the other sides)

    10² + 35² = 50²

    100 + 1225 = 2500

    1325 ≠ 2500

So the answer is NO

Answer:

False

Step-by-step explanation:

The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36 = 0.028

The likelihood that a specific occurrence will occur.

The proportion of the total number of possible outcomes to the number of outcomes in an exhaustive set of equally probable outcomes that result in a particular event.

Two six-sided dice are rolled there are 36 possibilities for outcomes which means 6 possibilities for the first dice and 6 for the second dice.

Therefore 36 is the total possibility outcome.

Count the number of outcomes for the one dice show 5 and the second dice show 6.

There is only one possibility two show the (5, 6) from the total s3 outcomes.

so the probability of rolling a 5 and a 6 i = 1/36 or about 0.028.

Therefore, the total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 1/36.

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Answer:

50.24

Step-by-step explanation:

8/2 = 4

3.14 x 4^2 = 50.24

Tthe Fourier series may converge to a value that is different from the left and right limits of f at the point of discontinuity, or it may not converge at all (known as Gibbs phenomenon).

To determine the specific value to which the Fourier series converges at a point of discontinuity, we would need to analyze the specific function f and its Fourier series.

This typically involves calculating the Fourier coefficients, examining the convergence properties of the series, and potentially using techniques such as Cesàro summation to obtain a more accurate estimate of the limit.

Without further information about the specific function and point of discontinuity, we cannot provide a more specific answer.

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Answer:

the answer is 27

Step-by-step explanation:

3x+9+90=180

3x+99=180

3x=180-99

x=81/3

x=27

Answer:

Step-by-step explanation:

3x + 9 + 90 = 180

3x + 99 = 180

3x = 81

x = 81/3

x = 27

3(27) + 9 = 81 + 9 = 90

The correct equation for the quartic function with zeros at -4, -1, 2, and 3 is a. y = (x + 4)(x + 1)(x - 2)(x - 3).

The maximum number of turning points that a polynomial function can have is determined by its degree. In this case, the given polynomial function f(x) = 4x^7 + 9x^5 - 3x^4 + 2x^2 - 5 has a degree of 7.

The general rule is that a polynomial of degree n can have at most n-1 turning points. Therefore, in this case, the maximum number of turning points for the polynomial function is 7 - 1 = 6.

So, the correct answer is d. 6.

To find the quartic function with zeros at -4, -1, 2, and 3, we can use the zero-product property and write the equation as a product of linear factors:

y = (x - (-4))(x - (-1))(x - 2)(x - 3)

Simplifying this expression gives us:

y = (x + 4)(x + 1)(x - 2)(x - 3)

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Answer:

d.) 21

Explanation:

Rules:

Solve:

\(\rightarrow \sf \dfrac{4|a|}{2} + |a-3|\)

[insert a = -6]

\(\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|\)

[simplify the following]

\(\sf\rightarrow \dfrac{4(6)}{2} + 9\)

\(\sf\rightarrow 12 + 9\)

\(\sf\rightarrow 21\)

When he made $1000 for the week, his 15% commission is;

It is known that he too $450 home for the week, then;

His new flat rate salary is $450 - $150 = $300

By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

We can start by determining the common factor between the two terms in order to factor the phrase 0.15c - 0.072. The common factor in this situation is 0.006, which we may factor out to obtain:

0.15c - 0.072 = 0.006(25c - 12) (25c - 12)

As a result, factoring the expression 0.15c - 0.072 gives 0.006 (25c - 12).

It is possible to utilise this factored form to further simplify calculations or to resolve equations that contain this statement. If we needed to find c in the equation 0.15c - 0.072 = 0, for instance, we could use the factored form to obtain:

0.006(25c - 12) = 0

25c - 12 = 0

c = 12/25

In conclusion, factoring the expression 0.15c - 0.072 involves finding the common factor between the two terms, which is 0.006. By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).

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the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.To find the values of m and b for the straight line that provides the best least-squares fit to the data, we need to complete the table and use the formulas for calculating the slope (m) and y-intercept (b).

First, let's complete the table by calculating the xy column:

X    y    xy

1    8    8

2    10   20

3    12   36

4    3    12

  Σχ=10   Σy=20   Σxy=76

Now, we can use the formulas:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

b = (Σy - m(Σx))/n

Plugging in the values from the table:

m = (76 - (10)(20)/4) / (30 - (10)²/4)

  = (76 - 200/4) / (30 - 100/4)

  = (76 - 50) / (30 - 25)

  = 26 / 5

  = 5.2

b = (20 - 5.2(10))/4

  = (20 - 52)/4

  = -32/4

  = -8

Therefore, the values of m and b for the best least-squares fit line are m = 5.2 and b = -8.

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=4\pi \sqrt{3} \end{cases}\implies 4\pi \sqrt{3}=2\pi r\implies \cfrac{4\pi \sqrt{3}}{2\pi }=r\implies 2\sqrt{3}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2\sqrt{3} \end{cases}\implies A=\pi (2\sqrt{3})^2 \\\\\\ A=\pi ( ~~ 2^2\sqrt{3^2} ~~ )\implies A=\pi ( ~~ 2^2(3) ~~ )\implies A=\implies A=12\pi\)

Fot the two random samples of customers from Internet provider, a) The null and alternative hypothesis are \(H_0 : \mu_1 = \mu_2 \\ H_a : \mu_1< \mu_2\).

b) The appropriate test that we will use is Two sample t-test.

We have an independent random sample with sample size from provider A, n₁ = 8

Sample size for provider B, n₂ = 10

Sample mean for sample A, \(\bar X_1\) = 35.2 years

Standard deviations, s₁ = 8.2

Sample mean for sample B, \(\bar X_2 \) = 38.4 years

standard deviations, s₂ = 5.8

Level of significance, a = 10% = 0.10

a) Now, we have check the claim that the average age for customers is less for those using Internet provider A than for Internet provider B, is true or not. Consider the null and alternative hypothesis are defined as \(H_0 : \mu_1 = \mu_2 \\ H_a : \mu_1< \mu_2\).

b) As we have two samples with all details like mean, standard deviations, etc. So, to check the validity of null hypothesis we will use two sample t test. The test statistic value is written as

\(t = \frac{ \bar X_1 - \bar X_2 }{\sqrt{s_p²(\frac{1}{n_1}+\frac{1}{n_2}})}\), where Pooled standard deviations,\(s_p =\frac{( n_1 - 1)s_1² + (n_2 - 1)s_2²}{n_1 + n_2 - 2} \).

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Given:

The probability for success of an event is P(A)

The probability of success of a second, independent event is P(B).

To find:

The probability of both events occurring, in that order.

Solution:

If A and B are two independent events, then

\(P(A\cap B)=P(A)\cdot P(B)\)

It is given that,

The probability for success of an event is P(A)

The probability of success of a second, independent event is P(B).

Since A and B both are independent event and we need to find the probability of both events occurring, in that order, i.e., \(P(A\cap B)\), therefore \(P(A\cap B)=P(A)\cdot P(B)\).

Hence, the correct option is A.