on her first six test, Sandra's scores were 75 70 80 80 85 and 90 find the mean of the six scores

Name all angles when there are two parallel lines cut by a transversal?

Alternate interior angles

Corresponding angles

Vertically opposite

From figure 1,

Since the angles marked with colour fulfil the vertically opposite angles properties ,so

(2x+35)° = (8x-49)°

⇒(2x-8x)=(-49-35)°

⇒-6x=-84

⇒x = 14°

Hence , x = 14°

From figure 2,

Since the angles marked are corresponding angles,therefore on equating both angles we get

(10x-18)°=(15x-48)°

⇒(10x-15x)=(-48+18)°

⇒-5x = -30°

⇒ x = 6°

From figure 3,

Since the given two angles are alternate interior angles ,so

(7x+5)°=(12x-75)°

⇒(7x-12x)=(-75-5)°

⇒-5x=-80°

⇒x = 16°

From figure 4 ,

Since the two angles lies in a straight line ,so sum is 180°

(27x-21)°+(10x-16)°=180°

⇒37x -37° = 0

⇒ x = 1°

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Given that 'y' is directly proportional to 'x',

Let 'k' be the constant of proportionality.

Then the equation becomes,

Given that 'y' is 14 when 'x' is 12,

Substitute the values in the equation,

Substitute the value of 'k' in the equation,

Thus, the required equation that relates 'x' and 'y' is,

To use the comparison test or limit comparison test, we need to find a known series that either diverges or converges and is similar to the given series.

Using the comparison test, we can compare the given series to the series 1/n^2, which is a p-series with p=2 and converges.

To see if our series is smaller or larger than 1/n^2, we can simplify the given series by canceling out k^4 from the numerator and denominator:

k^4 / (16k^6 5) = 1 / (16k^2 5)

Now, we can compare 1 / (16k^2 5) to 1/n^2:

1 / (16k^2 5) < 1/n^2 for all k > 1

Therefore, since our series is smaller than a convergent series, it must also converge.

Alternatively, we can use the limit comparison test by finding the limit of the ratio of the given series to 1/n^2 as n approaches infinity:

lim (n→∞) [k^4/(16k^6 5) / (1/n^2)] = lim (n→∞) (n^2 / (16k^6 5))

This limit is zero for all k > 1, which means the given series and the series 1/n^2 have the same behavior and both converge.

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Answer:

x=7+√15

x=7-√15

Step-by-step explanation:

Answer:

for 1st depositsx

p=$36000

r=2.6%

t=9years

compound amount =p(1+r/100)^t

=$36000(1+2.6/100)^9=$45355.37

for another deposit.

p=$36000

r=2.6%

t=9years

simple amount

=ptr/100=36000×2.6×9/100=$8424

total amount =$8424+$36000=$44424

the sum of the balances of these accounts at the end of 9 years=$44424+$45355.37=$89,779.37

Answer:

[C] 29 Miles

Step-by-step explanation:

Given that the vessel sails 41 miles S 45° E.

We need to determine the how far south the vessel has sailed.

Let us use the Pythagorean theorem to find the distance of the vessel has sailed.

Thus, we have,

\(Cos 0= \frac{adj}{hyp}\)

Substituting \(0 = 45\)° , \(adj = x\), and \(hyp = 41\)

Hence, we get,

\(cos\) \(45 = \frac{x}{41}\)

Simplifying, we have,

\(0.71 = \frac{x}{41}\)

Multiplying both sides by 41, we have,

\(29.11 = x\)

Rounding off to the nearest integer, we have,

\(29 = x\)

Thus, the vessel has sailed 29 miles South.

Therefore, Option C is the correct answer.

[RevyBreeze]

Answer:

12.9

Step-by-step explanation:

7 1/6. / 5/9.

=43/6. / 5/9

=reciprocate to multiplication

=43/6. * 9/5 6 cancel 9

=43/2. *. 3/5

=12.9

Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

We have that the Decrease of £16870 by 3%  is mathematically given as

P=168193.9=>168193.90 2dp

Arithmetic

Question Parameters:

Decrease £16870 by 3% Give your answer rounded to 2 DP.

Generally the equation for the 3%  of 16870  is mathematically given as

X=0.03*16870

X=506.1

Therefore Decrease £16870 by 3% we have

16870  - 506.1

P=168193.9

Answer:

= £16363.9

Step-by-step explanation:

- Decrease is a reduction and can be done only by subtraction in two ways;

\( = (100 - 3)\% \\ = 97\%\)

- Then multiply the result to the value being decreased;

\( = \frac{97}{100} \times 16870 \\ \\ = 16363.9 \: \: euros\)

\( = \frac{3}{100} \times 16870 \\ \\ = 506.1 \)

- Then reduce the original by the result:

\( = 16870 - 506.1 \\ = 16363.9 \: euros\)

If a case-control study were conducted to investigate the relationship between an exposure and a rare disease like neck cancer, the most likely relative measure that would be estimated is the odds ratio.

This is because the prevalence of neck cancer in the general population is low, which means that the incidence rate is also low. As a result, it is difficult to calculate the relative risk directly in a case-control study. Instead, the odds ratio is used as a measure of association between the exposure and the disease outcome.

The odds ratio is calculated by comparing the odds of exposure in cases to the odds of exposure in controls. The odds ratio can provide an estimate of the strength and direction of the association between the exposure and the disease outcome in the population being studied.

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Calculate each of the probabilities using the formulas above, and subtract the cumulative probability of 5 or fewer adults saying yes from 1 to find the probability of more than 6 adults saying yes.

To solve this problem, we can use the binomial probability formula. Let's break down the information given:

Probability of an adult knowing what they will have for dinner: 28% or 0.28

Number of adults asked: 22

We want to find the probability that more than 6 adults will say yes.

First, let's find the probability of exactly 6 adults saying yes:

P(X = 6) = (22 C 6) * (0.28^6) * (0.72^16)

Here, (22 C 6) represents the number of combinations of choosing 6 adults out of 22. The term (0.28^6) represents the probability of 6 adults saying yes, and (0.72^16) represents the probability of the remaining 16 adults saying no.

Next, let's find the probability of 5 or fewer adults saying yes:

P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

To calculate P(X = 0), P(X = 1), ..., P(X = 5), P(X = 6), you can use the same formula as above, plugging in the respective values of X.

Finally, to find the probability of more than 6 adults saying yes, we can subtract the probability of 5 or fewer adults saying yes from 1:

P(X > 6) = 1 - P(X ≤ 6)

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The coordinates of the 3 respective points from the given parameters are; (6, -2); (-1, 1); (2, 6)

1) The coordinates of the point located 5/6 of the way from A to B is;

x = ⁵/₆(7 - 1) + 1

x = 6

y = ⁵/₆(-4 - 8) + 8

y = -2

x, y = (6, -2)

2) The coordinates of the point located ¹/₄ of the way from A to B is;

x = -3 + ¹/₄(5 - (-3))

x = -1

y = 0 + ¹/₄(4 - 0)

y = 1

x, y = (-1, 1)

3) The coordinates of the point located ¹/₆ of the way from A to B is;

x = ¹/₆(7 - 1) + 1

x = 2

y = ¹/₆(-4 - 8) + 8

y = 6

x, y = (2, 6)

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Answer:

Lower right

Step-by-step explanation:

In a linear function, you always add the same number to the y to get the next y. See in that table the first y is 7. Add 2 to get to 9. So to be linear, you need to add 2 to get each other y. So, 7, 9, 11, 13, that's how you know it's a linear function because you add 2 to get the next y term (the fancy term is a common difference, but the idea is simple!)

Answer:

it the last chart the that saids

Step-by-step explanation:

x=2,4,6,8

y=7,9,11,13

you just have to subtract the y and then the x and divide them by each other

like this this the y = 9-7=2 and then the x = 4-2 =2 you divide what you got for x and y 2/2 =1 and do the same for the other and it be the same number for it to be linear function

The probability that a randomly selected can in the box is dented or contains vegetables is 19/20.

To solve the problem, we need to use the formula for the probability of the union of two events:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected can is dented or contains vegetables. Let's call these events D and V, respectively.

We are given that there are 20 cans in total, 12 of which contain vegetables, and 5 of which are dented, with 2 of the dented cans containing vegetables. This information allows us to calculate the probabilities of the individual events

P(D) = 5/20 = 1/4

P(V) = 12/20 = 3/5

P(D and V) = 2/20 = 1/10

To find the probability of the union of these events, we plug these values into the formula

P(D or V) = P(D) + P(V) - P(D and V)

= 1/4 + 3/5 - 1/10

= 19/20

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Answer:

$612

Step-by-step explanation:

to solve, you want to multiply these two values.

You can make this easier by taking the tens place of both numbers out and the ones place out and multiplying them:

32 x 26

30 x 20 = 600

2 x 6 = 12

Then add these values together:

600 + 12 = 612

A graph of the line that passes through the points (3, -7) and (-3, 5) is shown in the image attached below. Also, the equation of this line is y = -2x - 1.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, the points on the line include the following:

Substituting the given points into the formula, we have;

Slope, m = (5 - (-7))/(-3 - 3)

Slope, m = (5 + 7)/(-6)

Slope, m = 12/-6

Slope, m = -2

At point (3, -7), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y + 7 = -2(x - 3)

y + 7 = -2x + 6

y = -2x + 6 - 7

y = -2x - 1

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Answer:

41.4 kgs

Step-by-step explanation:

Take the number of bags times the weight of each bag

6 * 6.9

41.4 kgs

Answer:

41.4 kilograms of sugar

Step-by-step explanation:

its 41.4 kilograms of sugar because you take the 6 bags and multiply that by the 6.9

Answer: On the vertical number line, 64 is located above 50.

Step-by-step explanation: This is the answer on Plato

Answer:

"On the vertical number line, 64 is located above 50"

Step-by-step explanation: this was edmentums answer not mine!

Answer:

Supplementary

Step-by-step explanation:

If you add the angles from A and B, they make a straight line, or 180 degrees. This angle relationship is called supplementary.

The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

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The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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So the probability of getting either a multiple of 2 on the first roll or a total of 6 for both rolls is: 1/2 + 5/36 - (1/2 x 5/36) = 19/36 Therefore, the probability of getting either a multiple of 2 on the first roll or a total of 6 for both rolls is 19/36.

Answer:

The probability is 2

Step-by-step explanation:

6-3= 2

Multiple times equals 3 times.

Answers:    middle box:   1.32

                   middle right box:   -3.3

                   bottom left:   -0.5

                   bottom middle:   0.6

Step-by-step explanation:

[Find out the middle box]

\(-1.2\) x \(-1.1\)\(=1.32\)

[Find out the box in the middle right]

\(3\) x \(-1.1 = -3.3\)

[To Find out the bottom left box - divide each side by three]

\(x\) x \(3 = -1.5\)

\(x = -0.5\)

[Bottom middle box]

\(-0.5\) x \(-1.2 = 0.6\)

General Rule:

\(negative\) x \(negative = positive\)

\(negative\) x \(positive = negative\)

Hope this helps   :)

Answer:

Step-by-step explanation:

I think you mean

x² - 49.

If so it factors to (x +7)(x - 7)

Answer:

This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.

Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

Answer:

its -9

Step-by-step explanation:

got it right on edge

Answer:

4a +6

Step-by-step explanation:

Simplify the expression

Hope it helps! :)

Please mark me brainliest

Answer:

4a+6

Step-by-step explanation:

To simplify you need to:

2/3(6a+9)=

4a+6

(a) False. If the null hypothesis is rejected using ANOVA, it means that there is significant evidence to suggest that at least one of the means is different from the others.

However, it does not necessarily mean that all the means are different from one another. Additional tests such as pairwise comparisons are needed to determine which specific means are significantly different from one another.

(b) True. When ANOVA is used, the F-statistic is calculated by dividing the variability between groups by the variability within groups. Therefore, if the null hypothesis is rejected, it means that the variability between groups is higher than the variability within groups.

(c) True. Pairwise comparisons are used to determine which specific means are significantly different from one another. If the null hypothesis is rejected using ANOVA, then pairwise comparisons will identify at least one pair of means that are significantly different.

(d) True. When conducting pairwise comparisons, it is important to adjust the significance level to account for the multiple comparisons being made. In this case, there are four groups, so the appropriate level of significance is 0.05/4 = 0.0125. This helps to control the overall type I error rate.

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To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

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