Find the distance between the points (10,9) and (-2, -7).

The two positive numbers are 6 and 11

From the question, we understand that:

There are two positive numbers

Represent these numbers with x and y

So, we have the following equations

x = y - 5

6x - 3y = 3

Substitute x = y - 5 in 6x - 3y = 3

6(y - 5) - 3y = 3

Open the brackets

6y - 30 - 3y = 3

Evaluate the like terms

3y = 33

Divide by 3

y = 11

Substitute y = 11 in x = y - 5

x = 11 - 5

So, we have

x = 6

hence, the numbers are 6 and 11

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Given:

Total number of marbles = 26

Number of blue marbles = 13

Number of red marbles = 10

Number of yellow marbles = 3

To find:

The probability of getting a blue marble then a red marble (without replacement).

Solution:

Total number of marbles = 26

Number of blue marbles = 13

Probability of getting a blue marble is first draw is:

\(P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}\)

\(P(Blue)=\dfrac{13}{26}\)

\(P(Blue)=\dfrac{1}{2}\)

After drawing 1 marble, the remaining number of marbles in the bag is 25.

Probability of getting a red marble is second draw is:

\(P(Red)=\dfrac{\text{Number of red marbles}}{\text{Remaining number of marbles}}\)

\(P(Red)=\dfrac{10}{25}\)

\(P(Red)=\dfrac{2}{5}\)

Now the probability of getting a blue marble then a red marble (without replacement) is:

\(P(\text{Blue then red})=P(Blue)\times P(Red)\)

\(P(\text{Blue then red})=\dfrac{1}{2}\times \dfrac{2}{5}\)

\(P(\text{Blue then red})=\dfrac{1}{5}\)

Therefore, the probability of getting a blue marble then a red marble (without replacement) is \(\dfrac{1}{5}\).

The first proposition is true: If \(2x^2 + 2x + 2\) is even, then x must be even. The second proposition is false: If \(2x^2 + 3x + 4\) is even, x does not have to be even.

(i) To prove that if \(2x^2 + 2x + 2\) is even, then x must be even, we can use contraposition. The contrapositive statement is: If x is odd, then \(2x^2 + 2x + 2\) is odd. Let's assume x is odd and express it as x = 2k + 1, where k is an integer. Substituting this into the equation, we get \(2(2k + 1)^2 + 2(2k + 1) + 2 = 8k^2 + 12k + 6 = 2(4k^2 + 6k + 3)\)

Since \(4k^2 + 6k + 3\) is an integer, the whole expression is even. Therefore, the proposition holds true.

(ii) To prove that if \(2x^2 + 3x + 4\) is even, then x must be even, we can use a counterexample. Let's consider x = 1. Substituting it into the equation, we get \(2(1)^2 + 3(1) + 4 = 2 + 3 + 4 = 9\). Since 9 is odd, the proposition is false. Thus, there exists a counterexample where x is odd and the expression is even.

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Answer: 45

Step-by-step explanation:

After solving the equation the value of ∠A is 0.64.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: AB = 6

BC = 4

We have to find angle A.

Adjacent is adjacent to the angle,

The opposite is opposite the angle,

and the longest side is the Hypotenuse.

Sinx = Opposite / Hypotenuse

Sinx = 4/6

Sinx = 0.6

Now solve that equation!

sinx = 0.6

x = sin⁻¹(0.6)

x = 0.64

Hence, the value of ∠A is 0.64.

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Answer:

A) f(x) = 895(1.07)^x

Answer:

0 i think

Step-by-step explanation:

Answer:

The answer is -69,420 ! 69,420 - 69,420 = 0. next you multiply it and its 0 again then you add it 69,420 then subtract it equals 0 then subtract again it equals -69,420 then multiply it equals -69,420 then you have to add 69,420 it equals 0 again then you subtracted 69,420 and that means its -69,420!

Step-by-step explanation:

Angle 1 and angle 3 are vertical angles, which mean they are exactly the same angle.

Angle 1 = angle 3 = 37 degrees.

The answer is Angle OKL.

Answer:

The answer is 19s +23

Step-by-step explanation:

You add together all the sides and simplfy down.

4s+10+s+4+4s+10+10s-1

Add all the like terms

until it gets to 19s+23

Answer:

19s + 23

Step-by-step explanation:

P = 2(4s + 10) + s+4+19s-1

P = 8s + 20 + s + 4 + 10s - 1

P = 19s + 23

Answer:

I dont get it. :(

there is no picture?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of X is 45 because all the angles of a triangle add up to 180 degrees. The triangle is a right triangle as shown in the picture, the square in the corner of the triangle indicates this, any right angle is 90 degrees and when you minus 90 from 180 you get 90. Now, there are two more angles in the triangle so the value of X is 45, (90/2=45).

Answer:

1270

Step-by-step explanation:

420+300+550

$420+300=720+550=1270

Answer:

2.2 pounds

Step-by-step explanation:

Your welcome

To interpret scores on it, he is presently administering the test to a representative sample of all golfers. Dr. zimmer is clearly in the process of validating their test.

Validation refers to the process of evaluating the accuracy and reliability of a test or measurement instrument. When Dr. Zimmer is administering the test to a representative sample of golfers, he is collecting data that will allow him to determine the validity of the test and its ability to accurately measure golfers' knowledge of the sport's history.

This process is important for ensuring that the test results are meaningful and can be used to make accurate inferences about the population being studied.

By comparing the scores on the test to other measures of golfers' knowledge, such as interviews or other tests, Dr. Zimmer can determine the test's ability to accurately measure the construct it is intended to measure. Therefore, Dr. Zimmer is in the process of validating his test by collecting data and evaluating its accuracy and reliability.

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Answer:

x = 35 , y = 72.5

Step-by-step explanation:

(a)

x and 35° are vertical angles and are congruent, then

x = 35

(b)

y. y and 35 lie on a straight line and sum to 180°, that is

y + y + 35 = 180

2y + 35 = 180 ( subtract 35 from both sides )

2y = 145 ( divide both sides by 2 )

y = 72.5

Answer:

y = 72.5 degrees

X = 35 degrees

Step-by-step explanation: A straight line is 180 degrees. The line with the two y degrees and the 35 degrees is a straight line, which is = 180 degrees. Because the y degrees are the same variable (y) they are equal degrees. All you need to do to find y is 180-35 =145. Divide that by 2 to find both y’s. 145 / 2 = 72.5. You can do the same for x, or realize that x and 35 are alternate interior angles, meaning they are the same measure: 35 degrees.

The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.

Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.

Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.

Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.

The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.

Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.

This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.

Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.

Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.

Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).

Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).

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Answer:

3. alternative interior angle

4. consecutive exterior angle

5. corresponding angle

6. consecutive interior angle

7. corresponding angle

8. alternative exterior angle

Step-by-step explanation:

since the braindead jacka** above was no help

The equation 3(v+2) + v = 4(v - 1) + 9 have no solution.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, let's solve the equation for the variable v.

A variable is a number represented by a letter in an equation.

Therefore,

3(v+2) + v = 4(v-1) + 9

open the bracket on both sides

3(v+2) + v = 4(v - 1) + 9

3v + 6 + v = 4v - 4 + 9

combine like terms

3v + 6 + v = 4v - 4 + 9

3v + v + 6 = 4v + 5

4v + 6 = 4v + 5

Hence,

4v - 4v = 5 - 6

0 = -1

Therefore, the equation has no solution

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The subspace has a basis consisting of two vectors, its dimension is 2.

The subspace is given by the set of all vectors in \(R^4\) of the form (a, b, c, d) such that a - 3b = c = 0. We can rewrite this as:

(a, b, c, d) = (3b, b, 0, d) = b(3, 1, 0, 0) + (0, 0, 0, d)

This means that any vector in the subspace can be written as a linear combination of the two vectors (3, 1, 0, 0) and (0, 0, 0, 1). Therefore, these two vectors form a basis for the subspace.

To see that they are linearly independent, suppose that:

c1(3, 1, 0, 0) + c2(0, 0, 0, 1) = (0, 0, 0, 0)

This implies that c1(3, 1, 0, 0) = (0, 0, 0, 0), which in turn implies that c1 = 0. Substituting this into the original equation, we get:

c2(0, 0, 0, 1) = (0, 0, 0, 0)

This implies that c2 = 0 as well. Therefore, the only linear combination of (3, 1, 0, 0) and (0, 0, 0, 1) that equals the zero vector is the trivial one, which means that these two vectors are linearly independent.

Since the subspace has a basis consisting of two vectors, its dimension is 2.

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To test the claim that the amounts dispensed by the new machine have a smaller standard deviation, we can perform a hypothesis test using the F-distribution. The null and alternative hypotheses for this test are:

Null Hypothesis (H₀): The standard deviation of the amounts dispensed by the new machine is greater than or equal to the standard deviation of the original machine. Symbolically, σ₁ ≥ σ₀.

Alternative Hypothesis (H₁): The standard deviation of the amounts dispensed by the new machine is smaller than the standard deviation of the original machine. Symbolically, σ₁ < σ₀.

In this case, σ₁ represents the standard deviation of the new machine, and σ₀ represents the standard deviation of the original machine.

To perform the hypothesis test, we can use the F-test statistic:

F = (s₁² / σ₁²) / (s₀² / σ₀²),

where s₁ is the sample standard deviation of the new machine (26 milliliters), σ₁ is the population standard deviation of the new machine (unknown), s₀ is the sample standard deviation of the original machine (81 milliliters), and σ₀ is the population standard deviation of the original machine (known).

We will compare the computed F-test statistic with the critical F-value obtained from the F-distribution table or calculated using statistical software. The critical F-value will depend on the desired level of significance (0.05) and the degrees of freedom associated with the numerator and denominator of the F-test statistic.

If the computed F-test statistic is less than the critical F-value, we will reject the null hypothesis and conclude that there is evidence to support the claim that the amounts dispensed by the new machine have a smaller standard deviation.

Please note that the specific degrees of freedom for the F-distribution depend on the sample sizes used and can be calculated as (n₁ - 1) for the numerator and (n₀ - 1) for the denominator, where n₁ and n₀ are the sample sizes for the new machine and original machine, respectively.

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The absolute minimum value of the function on the interval [0,4] is -2, which occurs at x=0, and the absolute maximum value is 78, which occurs at x=4.

To find the absolute maximum and minimum values of the function f(x) = 5x^2 + 3x - 2 on the interval [0,4], we need to find the critical points and the endpoints of the interval.

First, we find the derivative of the function:

f'(x) = 10x + 3

Next, we set the derivative equal to zero to find the critical points:

10x + 3 = 0

x = -3/10

However, since -3/10 is not in the interval [0,4], we do not have any critical points in this interval.

Next, we check the endpoints of the interval:

f(0) = -2

f(4) = 78

Therefore, the absolute minimum value of the function on the interval [0,4] is -2, which occurs at x=0, and the absolute maximum value is 78, which occurs at x=4.

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Answer:

D. Jake and Liu

Step-by-step explanation:

41 is prime so Teresa is wrong. The other two are not prime.

The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.

Equation of plane passing through (x1,y1,z1) is given by

A(x-x1)+B(y-y1)+C(z-z1)=0

where, A, B, and C are direction ratios

In the question, it is given that the plane passes through (1,2,1)

So, the equation of the plane will be in the form,

A(x-1)+B(y-2)+C(z-1)=0

It is also given that the plane is perpendicular to give 2 planes.

So, their normal to the plane would be perpendicular to the normal of both planes.

So, the required normal is a cross-product of the normals of planes

x-y-z-10=0 and x-2y+z-2=0

i.e,

-3i-2j-k=0

so, the direction ratios,

A=-3, B=-2, C=-1

putting the direction ratios in the previous equation of the plane,

-3(x-1)-2(y-2)-1(z-1)=0

-3x+3-2y+4-z+1=0

-3x-2y-z+8=0

is the required equation of the plane

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Thus, the interval estimate of the number of drivers under the age of 19 in 2008, together with its margin of error of 0.0245.

An unknown population parameter's value is likely to be within the bounds of a confidence interval (CI), which is a range of values. Given the qualities of your sample data, these intervals reflect a likely domain for the parameter.

Confidence intervals are computed using a predetermined degree of confidence and are obtained from sample statistics.

Margin of error ME = z(α/2)√[p(1-p)/n]

confidence interval = 95%

z(α/2) value for the 95% confidence interval = 1.96 (taken from attached table)

P = 75% = 0.75

1-p = 1 - 0.75 = 0.25

n = 1200

Put the values in formula:

ME = (1.96)*√[0.75*0.25 / 1200]

ME = (1.96)*√0.00015625

ME = 0.0245

Thus, the interval estimate of the number of drivers under the age of 19 in 2008, together with its margin of error of 0.0245.

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Complete question:

Fewer young people are driving. In 1983, 87% of 19-year-olds had a driver’s license. Twenty-five years later (in 2008) that percentage had dropped to 75%. Suppose these results are based on a random sample of 1200 19-year-olds in 1983 and again in 2008.  At a 95% confidence, what is the margin of error and the interval estimate of the number of 19-year-old drivers in 2008?

Answer:

C mate

Step-by-step explanation:

Answer:

i believe the answer is B

Step-by-step explanation:

Given

What number comes next in the sequence?

16, 8, 4, 2, 1, ?

Solution

This is a Geometric sequence, we need to find the common ratio

The formula for the common ratio is

Now

The final answer

The firm will produce 4 units of output to maximize profits when the price is $47 per unit.

To maximize profits, a firm in a perfectly competitive market should produce the quantity of output where marginal cost (MC) equals marginal revenue (MR):

MC = dC/dq = 3q^2 - 6q + 23

MR = P = 47

Setting MC equal to MR:

3q^2 - 6q + 23 = 47

Simplifying and rearranging:

3q^2 - 6q - 24 = 0

q^2 - 2q - 8 = 0

Using the quadratic formula:

q = [2 ± sqrt(2^2 - 4(1)(-8))] / 2(1)

q = [2 ± sqrt(36)] / 2

q = [2 ± 6] / 2

So, q = 4 or q = -2. Since we cannot have a negative quantity of output, we choose q = 4.

Therefore, the firm will produce 4 units of output to maximize profits when the price is $47 per unit.

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