Find the greatest number which divides 350 and 860 leaving remainder 10 in each case. ​

Since f(-1) is positive and f(3) is negative, by the IVT, we can conclude that there is at least one zero of the function on the interval [-1, 3]. Therefore, we can say with certainty that there is definitely a zero of f(x) = x² - 2x - 2 on the interval [-1, 3].

To use the IVT to determine an interval where there definitely is a zero of the function f(x) = x² - 2x - 2, we need to evaluate the function at the endpoints of an interval and determine whether the function changes sign over that interval.

Let's consider the interval [-2, 3] as an example. Evaluating f(-2) and f(3), we get:

f(-2) = (-2)² - 2(-2) - 2

= 4 + 4 - 2

= 6

f(3) = 3² - 2(3) - 2

= 9 - 6 - 2

= 1

Since f(-2) is positive and f(3) is positive as well, we cannot use the IVT to conclude that there is a zero of the function on the interval [-2, 3].

However, we can try another interval. Let's try the interval [-1, 3]. Evaluating f(-1) and f(3), we get:

f(-1) = (-1)² - 2(-1) - 2

= 1 + 2 - 2

= 1

f(3) = 3² - 2(3) - 2

= 9 - 6 - 2

= 1

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Answer:

The value of variable x = 12

Step-by-step explanation:

Given:

Given triangle is an equilateral triangle

Side of given triangle = 10 unit

Angle S = 5x°

Find:

The value of variable x

Computation:

We know that each angle of an equilateral triangle is 60°

So,

Angle S = 60

By putting value of angle S

5x = 60

The value of variable x = 60 / 5

The value of variable x = 12

Answer:

Marko bikes approximately 16.13 miles.
A very slow rate.

Step-by-step explanation:

average speed = 534 minutes per mile

time taken = 8614

d = t/s

distance = 8614 / 534

= 16.13 miles

Answer:

  -3 < x < 1

Step-by-step explanation:

In general, an absolute value function is a piecewise-defined function, with each piece having its own applicable domain. However, the absolute value inequality |a| < b is fully equivalent to the compound inequality -b < a < b. This can be used to solve the given inequality.

We can isolate the absolute value expression by undoing the operations done to it.

  3|x +1| -2 < 4 . . . . . given

  3|x +1| < 6 . . . . . . . add 2

  |x +1| < 2 . . . . . . . . divide by 3

The absolute value inequality is now in the form described above, so can be "unfolded" to a compound inequality:

  -2 < x +1 < 2

Subtracting 1 finds the solution for x:

  -3 < x < 1

Answer:

6625

Step-by-step explanation:

We know that:  P = 5000

                          R = 6.5%

                          T = 5

Formulate and substitute: I = 5000rt

Calculate the product or quotient: 5000 x (1 + 0.325)

Calculate the sum or difference: 5000 x 1.325

Calculate the product or quotient: 6625

The equation of the tangent plane to the given parametric surface at the specific point is -2x + 4z = 0  .

In the question ,

it is given that ,

the function is r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .

Now,

According to the give function,

r(u,v) = (u² , 2usin(v) , ucos(v))

Then, solving it , We get ,

r(u,v) = (u² , 2usin(v) , ucos(v))

\(r_{u}\) = (u , 2sin(v) , cos(v))

\(r_{u}\) (1,0) = (2 , 0 , 1)

\(r_{v}\) = (0 , 2ucos(u) , -sin(v))

\(r_{v}\) (1,0) = (0 , 2 , 0)

So , the matrix become

\(\left[\begin{array}{ccc}i&j&k\\2&0&1\\0&2&0\end{array}\right]\)

On simplifying , we get

i(−2) −j(0) \(+\) k(4) = (−2 , 0 , 4)

r(2,0) = (2 , 0 , 1)

The  plane is

r = −2x \(+\) 4z

r(2,0,1) = −2(2) \(+\) 4(1) = d

−4 \(+\) 4 \(=\) d

d = 0

Therefore , the equation of tangent is -2x + 4z = 0 .

The given question is incomplete , the complete question is

Find an equation of the tangent plane to the given parametric surface at the specified point.  r(u,v) = u²i + 2usin(v)j + ucos(v)k ; u = 1, v = 0 .

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\(\huge\textsf{Hey there!}\)

\(\large\text{2(3x + 4y + x)}\)

\(\large\textsf{DISTRIBUTE 2 WITHIN the PARENTHESES}\)

\(\large\text{2(3x) + 2(4y) + 2(x)}\)

\(\large\text{2(3x) = \boxed{\bf 6x }}\)

\(\large\text{6x + 2(4y) + 2(x)}\)

\(\large\text{2(4y) = \boxed{\bf 8y}}\)

\(\large\text{6x + 8y + 2(x)}\)

\(\large\text{2(x) = \boxed{\bf 2x}}\)

\(\large\text{6x + 8y + 2x}\)

\(\large\textsf{COMBINE the LIKE TERMS}\)

\(\large\text{(6x + 2x) + (8y)}\)

\(\large\text{6x + 2x = \boxed{\bf 8x}}\)

\(\large\text{8x + 8y}\)

\(\boxed{\boxed{\large\text{Answer: \huge \bf 8x + 8y}}}\huge\checkmark\)

\(\large\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

The total number of faces in a pyramid= 1+n

The third value to the table: final balance is $612.50 and the fourth value to the table: principal amount is $675 and final balance = $783.

Simple interest is the borrowing amount added only to the principal amount.

The formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100,

Where S.I. is simple interest, P is principal amount, T is time period and R is interest rate in a year.

For the third value of the table:

We have P = $500, R = 4.5%, T = 5 years and S.I. = $112.50

The final balance = principal amount + interest rate

The final balance = $500 + $112.50

The final balance = $612.50.

For the third value of the table:

We have let P = $x, R = 8%, T = 2 years and S.I. = $108.0

Substituting all the values in the formula,

x × 2 × 8 / 100 = 108

x = 10800 / 16

x = $675

Hence, principal amount = $675

The final balance = principal amount + interest rate

The final balance = $675 + $108

The final balance = $783.

Therefore, the third value to the table: final balance is $612.50 and the fourth value to the table: principal amount is $675 and final balance is $783.

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The length of the reflected line segment is approximately 11.66 units.

The endpoints of the line segment mentioned in the question are (0,5) and (6,5). After the line segment is reflected across the x-axis, the endpoints of the reflected line segment are (0, -5) and (6, -5).To find the length of the reflected line segment, we will use the distance formula.

Using the distance formula:d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (5 - 5)²]d = √[36 + 0]d = √36d = 6 units. So the length of the original line segment is 6 units.Now, let's find the length of the reflected line segment.Using the distance formula :d = √[(x₂ - x₁)² + (y₂ - y₁)²]d = √[(6 - 0)² + (-5 - 5)²]d = √[36 + 100]d = √136d = 11.66 (approx) units. So the length of the reflected line segment is approximately 11.66 units.

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Answer:

15t+9 ft

Step-by-step explanation:

Given data

Width=  6t-1.5 ft

Length= 1.5t+6 ft

Required

The perimeter

The expression for perimeter is

P= 2L+2W

P= 2(1.5t+6)+ 2(6t-1.5)

open bracket

P= 3t+12+ 12t-3

collect like terms

P= 3t+12t+12-3

P= 15t+9 ft

Hence the perimeter is  15t+9 ft

The side of the square is x^5 .

Area of a square = (side)² = a²,

Given;

area of a square = \(x^{10}\)

Equating it with the general formula of square

Area of a square = a²,

          a² =  \(x^{10}\)

Taking square root on both sides,

\(a = \sqrt{x^{10}} \\\\a = x^5\)

Hence, the side of the square is x^5.

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Answer:

£16.25

Step-by-step explanation:

Jon. £9 to nearest pound so £9.50

Ellie. £6.50 to the nearest 50p so £6.75. £

9.5+6.75 = £16.25

From what we know about rounding, we will see that the possible total amount of money is given by the inequality:

£14.75 ≤ M ≤ £16.23

When we round a given number to a given place, what we need to do is look at the number at the right of that place.

So we know that Jon, to the nearest pound has £9.

We know that to the nearest £0.50, so we look at the half of 0.5, which is 0.25, for example:

1.23 would be rounded to 1.

1.25 would be rounded to 1.50

1.27 would be rounded to 1.50

Ellie has £6.50, then she has:

So, adding the minimums and maximums together we get:

minimum = £8.50 + £6.25 = £14.75

maximum  = £9.49 +  £6.54 =  £16.23

So the possible total amount of money, defined by M, is in the interval:

£14.75 ≤ M ≤ £16.23

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The value of x in the triangle is 46.40° .

The angle of a triangle can be found using sine rule.

Therefore, applying sine rule,

a / sin A = b / sin B = c / sin C

Hence,

5 / sin x = 6.9  / sin 88°

cross multiply

5 sin 88° = 6.9 sin x

5 × 0.99939082701 = 6.9 sin x

4.9969541351 = 6.9 sin x

divide both sides by 6.9

sin x = 4.9969541351  / 6.9

sin x = 0.72419625146

x = sin⁻¹ 0.72419625146

x = 46.4020264383

Therefore,

x = 46.40°

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Answer:

Step-by-step explanation:

Hope it helped

Answer:

√65 (units)

Step-by-step explanation:

A(3, -2) and B(7, 5)

AB=√ [(xB-xA)²+(yB-yA)²]

AB=√ [(7-3)²+(5+2)²]=√(16+49)

AB=√65 (units)

The vectors u and v such that w = span{u, v} are u = [1, 0, 0] and v = [0, 1, 0], respectively.

To find vectors u and v such that w = span{u, v}, we need to express the vectors in w in terms of linear combinations of u and v.

Let's consider the vectors in w. We can write a generic vector in w as follows:

w = b × u + c × v

where b and c are arbitrary scalars.

Now, let's choose u = [1, 0, 0] and v = [0, 1, 0].

Substituting these values into the equation for w, we have:

w = b × [1, 0, 0] + c × [0, 1, 0]

= [b, 0, 0] + [0, c, 0]

= [b, c, 0]

So, any vector in w can be expressed as a linear combination of u and v. Therefore, w = span{u, v}.

This shows that w is a subspace of \(R^3\) because it can be spanned by a set of two linearly independent vectors (u and v).

A subspace is a vector space that contains the zero vector, is closed under addition and scalar multiplication, and is closed under linear combinations.

In this case, since w can be expressed as a linear combination of u and v, it satisfies the conditions for being a subspace.

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Answer:

6.8=6 8/5

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hope it help

The answer of the given question based of a suggestive survey the answer is  "What do you like and don’t like about the CEO?"

The CEO or Chief Executive Officer is  highest-ranking executive in  company who is responsible for making major corporate decisions, managing  overall operations, and leading  organization towards achieving its goals and the objectives. The CEO reports to board of directors and is responsible for success or failure of company.

The suggestive survey question is: "What do you like and don’t like about the CEO?"

This question is suggestive because it implies that the respondent should have opinions about the CEO, and it encourages the respondent to share both positive and negative opinions. This can bias the responses towards certain answers, rather than allowing the respondent to express their own thoughts freely.

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Answer:

Length of the segment of a secant 'x' is 4 cm.

Step-by-step explanation:

If a secant and a tangent are drawn from a point outside the circle, then the product of the segments of the secant is equal to the square of the length of the tangent.

By this property,

\(4\times x = 8^2\)

\(4x = 64\)

\(x=\sqrt{16}\)

\(x=4\) cm

Therefore, length of the segment of a secant 'x' is 4 cm.

The theoretical probability of rolling a one or two on a number cube is 2/5 or 0.4.

To find the theoretical probability of rolling a one or two on a number cube, we need to determine the number of outcomes that correspond to rolling a one or two, and divide that by the total number of possible outcomes.

From the table, we can see that Alexandria rolled a one or two a total of 24 times out of 60 rolls. This means that the probability of rolling a one or two is: P(1 or 2) = 24/60

Simplifying the fraction by dividing both the numerator and denominator by the greatest common factor, we get: P(1 or 2) = 4/10

This can be further reduced to: P(1 or 2) = 2/5

Therefore, the theoretical probability of rolling a one or two on a number cube is 2/5 or 0.4.

In summary, the theoretical probability is the expected probability of an event occurring, based on mathematical reasoning. Here, we used the number of favorable outcomes to calculate the probability of rolling a one or two, and expressed the answer as a fraction in simplest form.

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It seems that the formula for the distance (d) in miles that can be seen on the surface of the ocean from a certain height (h) in feet is missing. However, based on the given information, we can assume that the formula is:

d = sqrt(1.5h)

To find the height (h) in feet required to see a distance of 19.5 miles, we can rearrange the formula to solve for h:

h = (d^2 / 1.5)

Substituting d = 19.5 miles, we get:

h = (19.5^2 / 1.5) = 253.5 feet

Therefore, the platform would have to be at a height of approximately 253.5 feet to see a distance of 19.5 miles on the surface of the ocean.

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Isaak should use the value 1.75 as the common ratio in the formula to represent the given sequence.

To find the common ratio in a geometric sequence, we divide any term in the sequence by its preceding term. Let's calculate the ratios for the given sequence:

112/64 = 1.75

196/112 ≈ 1.75

343/196 ≈ 1.75

We observe that each term in the sequence is approximately 1.75 times the preceding term. This suggests that the common ratio is 1.75.

An explicit formula for a geometric sequence is given by the formula:

an = a1 * \(r^{n-1}\)

Where:

an represents the nth term in the sequence,

a1 is the first term in the sequence,

r is the common ratio,

n is the position of the term.

By substituting the given values into the formula, we have:

64 * \((1.75)^{n-1}\)

Using this formula, Isaak can find any term in the sequence by substituting its position (n) into the formula.

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X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.

X.509 certificates are widely used in public key infrastructure (PKI) systems to verify the authenticity and integrity of digital identities. They contain various information related to the certificate itself and the entity it represents. Let's examine the options to determine which one does not apply to an X.509 certificate:

A) Certificate version: X.509 certificates include a version number to indicate the format and features of the certificate.

B) The issuer of the certificate: X.509 certificates specify the entity or authority that issued the certificate, which is crucial for validating the certificate's trustworthiness.

C) Public Key Information: X.509 certificates contain public key information, such as the public key itself and related parameters, to facilitate secure communication and cryptographic operations.

D) Owner's symmetric key: X.509 certificates do not typically include the owner's symmetric key. They primarily focus on the public key infrastructure and asymmetric key cryptography.

Therefore, among the given options, D) Owner's symmetric key is the item that does not apply to an X.509 certificate.

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Step-by-step explanation:

1. Six families are represented.

2. Four families have at least three children.

3. Range = 15 - 1 = 14

4. Only one family has at most one child

Answer:

The investment firm's total profit is $4,000

Step-by-step explanation:

The Profit from Company A = 11% * $8,000

= 11 * $8,000/100

= $880

The Profit from Company B = 13% * $24,000

= 13 * $24,000/100

= $3,120

The total profit = $880 + $3120

= $4,000

Thus, the investment firm's total profit is $4,000

The correct option is D, Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population Mean.

The Central Limit Theorem (CLT) is a fundamental concept in probability theory and statistics. It states that if you take repeated random samples of a population, the sample means will follow a normal distribution, regardless of the shape of the population distribution, provided the sample size is large enough. This means that as the sample size increases, the sample mean becomes more and more normally distributed.

The CLT is important because it helps us to understand the properties of large samples, even when the population is not normally distributed. It is used in many areas of research, including social sciences, finance, engineering, and more. The theorem provides a powerful tool for estimating population parameters, such as the mean or variance, and for testing hypotheses about them. It also helps to explain why the normal distribution is so commonly observed in real-world data, and why it is often used as a model for statistical analysis.

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Complete Question:-

Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population:

a. Standard deviation divided by n

b. Mean divided by n

c. Standard Deviation divided by the square root of n

d. Mean

The amount of alcohol remaining after 4 hours would be approximately 64 mg/dL.

We can use the formula for exponential decay to model the amount of alcohol remaining in the blood after t hours:

\(Q(t) = Q_o* e^{(-kt)\)

where Q₀ is the initial amount of alcohol in the blood, k is the decay constant, and t is the time elapsed.

We know that Q₀ = 200 mg/dL, and Q(2) = 128 mg/dL. We can use this information to solve for k:

\(128 = 200 * e^{(-k*2)\)

\(e^{(2k)} = 200/128\)

2k ≈ ln(1.5625)

k ≈ -0.345

Now we can use this value of k to find Q(4):

\(Q(4) = 200 * e^{(-0.345*4)\)

Q(4) ≈ 64

Therefore, the amount of alcohol is 64 mg/dL.

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Answer:

about 5.99 or D. 6 cm

Step-by-step explanation:

you can use this formula

\(V=4/3 * \pi *r^{3}\)