Question 10 ) What is the solution to the equation ? A x=11 B x=13 C x=16 D x=20

Answer:

4

Step-by-step explanation:

The value for $\frac{0.\overline{72}}{0.\overline{27}}$ as a common fraction in lowest terms is 2.666

To convert repeating decimals to fractions, we can use the following method:

Let's call the repeating decimal 0.72... = x, and the repeating decimal 0.27... = y.

Then 10x = 7.2... and 10y = 2.7...

Subtracting the original expressions from the above:

10x - x = 7.2... - 0.72...

=> 9x = 7

=> x = 7/9

And similarly,

10y - y = 2.7... - 0.27...

=> 9y = 2

=> y = 2/9

Therefore,

0.72... / 0.27... = x / y = (7/9) / (2/9) = 7/2 = 3.5

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. To convert a repeating decimal to a fraction, we need to identify the repeating pattern and convert it to a fraction. This is done by multiplying both the numerator and denominator by a power of 10 that makes the repeating part an integer.

Then, the resulting fraction can be simplified to its lowest terms. In this case, the repeating decimals 0.72... and 0.27... can be converted to the fractions 7/9 and 2/9 respectively, and dividing the two results in a fraction of 7/2 can be simplified to 3.5.

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The length of the curve over the given interval is 2πa, where a is the constant in the polar equation r = 8a cos θ.

To find the length of the curve defined by a polar equation, we use the formula:

L = ∫\(a^b\) √[r² + (dr/dθ)²] dθ

where a and b are the angles of the interval and r is the polar equation.

In this case, r = 8a cos θ, so we need to find dr/dθ:

dr/dθ = -8a sin θ

Now we can substitute into the formula for L:

L = ∫\((-\pi /16)^(^\pi^ /^1^6^)\) √[(8a cos θ)²+ (-8a sin θ)²] dθ

Simplifying under the square root:

L = ∫\((-\pi /16)^(^\pi ^/^1^6^)\) √[64a²(cos²θ + sin²θ)] dθ

L = ∫\((-\pi /16)^(^\pi^ /^1^6^)\) 8a dθ

L = 16a(π/16 - (-π/16))

L = 2πa

Therefore, the length of the curve over the given interval is 2πa, where a is the constant in the polar equation r = 8a cos θ.

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Make all the y values negative for a 90 degree turn.

A -  4,-5

B -  4,-4

C -  5,-4

D -  2,-1

E -  1,-2

In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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Ken bought a total of 91 bags of apples and oranges combined.

What is Statistics?

The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Ken bought 7 bags of apples. To find out how many bags of oranges he bought, we need to use the information that he bought 12 times as many bags of oranges as apples.

So, we can start by multiplying the number of bags of apples by 12:

7 x 12 = 84

This means that Ken bought 84 bags of oranges.

To find the total number of bags he bought, we just need to add the bags of apples and oranges together:

7 + 84 = 91

Therefore, Ken bought a total of 91 bags of apples and oranges combined.

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Answer:

4

Step-by-step explanation:

y = kx

Use point (3, 12).

12 = k * 3

k = 12/3 = 4

y = 4x

Answer: 4

Divide y by x:

12/3 = 4

36 / 9 = 4

The constant of variation is 4

Answer:

B

Step-by-step explanation:

The required inequality expression is y > 2x + 1

The standard formula of the equation of a line is y = mx + b

where

From the graph, using the coordinate (1, 3) and (0,1)

Slope = 1-3/0-1
Slope = -2/-1

Slope = 2

Since the line pass through the y-axis at y = 1, hence b =1

The required equation will be y > 2x + 1

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Answer:

B for me

Step-by-step explanation:

Yun lang po correct me if iam wrong

The Required equation for the ellipse is given by   \(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\) Option B. is correct

Ellipse is cross-section part of a cone structure when cutting it out a horizontal cross-section of a cone.

(x-h)^2/a^2 + (x-k)^2/b^2 = 1
(h,k) = centre of the ellipse.
a, b = semi minor or major axis,

\(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\)

thus, the required equation of ellipse is given by \(\frac{(x-4)^2}{49}+\frac{y+1}{100} = 1\).

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Answer:

14

Step-by-step explanation:

Let us suppose, the number of guests that can be invited as x.

No. of people Amount of money

5 $35

x(let) $98

Here, the relationship is directly proportional,

So,

5/x =35/98

or, x × 35 = 5 × 98

or, x = 5 × 98/35

Therefore, x = 14

So, 14 members can be invited to her party if she spends $98 on her retirement party.

Answer:

960$

Step-by-step explanation:

First you want to find out how much money she makes per hour by doing 840/35. That equals 24, so now you multiply it by the amount of hours for this week. 24*40= 960$.

Hope this helps :D

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Answer:

(a)SSS congruence of two triangles

Step-by-step explanation:

Congruence is a relationship that expresses the similarity between two triangles. The relationship between two triangles with their three sides being congruent is termed as the side-side-side (SSS) congruence property of the triangles. This implies that the two triangles are similar with respect to their three sides.

In corollary, since the three sides of the two triangles are congruent, then the three angles respectively would be congruent.

Friedman's Rank Test is appropriate in the case where a researcher wanted to compare the ratings of three different video games. Each game was given eight ratings by eight reviewers.

The Friedman test is a non-parametric statistical test developed by Milton Friedman. Similar to Parametric Repeated Measures ANOVA, it is used to detect differences in treatment across multiple test trials.

Friedman test assumptions

Wilcoxon sign rank test is used to compare the location of two populations using a set of matched pairs.Since no set of matched pairs is here, so we will not use this. Since the number treatments (types of video games) is 3 and ratings is ordinal in nature, so Friedman's Rank test is appropriate.

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The probability that x equals 7 is 1/9. The 63 possible outcomes is equally likely, the probability of getting a sum of 7 is given by the ratio of favorable outcomes to total outcomes, which is 7/63.

To find the probability that the sum of three dice equals 7, we need to determine the number of outcomes that satisfy this condition.

There are several ways to achieve a sum of 7:

(1, 2, 4), (1, 3, 3), (2, 2, 3), (2, 3, 2), (3, 1, 3), (3, 2, 2), and (4, 1, 2).

Therefore, there are 7 possible outcomes that result in a sum of 7.

Since each of the 63 possible outcomes is equally likely, the probability of getting a sum of 7 is given by the ratio of favorable outcomes to total outcomes, which is 7/63.

This simplifies to 1/9.

Thus, the probability that x equals 7 is 1/9.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

280

Step-by-step explanation:

first, find the area of the triangle

formula: 1/2 (base × height)

so the area of the triangle is

= 1/2 (16×5)

= 1/2 (80)

= 40

then, find the area of the rectangle

formula: length × breadth

the area of the rectangle is

= 15 × 16

= 240

the area of the composite figure is the sum of the areas of the triangle and rectangle

= 40 + 240

= 280

Answer:

Second choice, 11/30

Step-by-step explanation:

38 + 22 = 60

He flipped tails 22 times out of 60 tries, so it's 22/60

Simplify with 2 and it's 11/30

Answer:

275 * 0.03 = accrued interest

accrued interest + initial deposit = total after one year

Step-by-step explanation:

An x-bar and R-chart were constructed using the given data. The x-bar chart displays the sample averages, while the R-chart shows the sample ranges. By analyzing these charts, we can determine if the process is in control.

To construct the x-bar and R-charts, we use the sample averages and sample ranges provided in the table. The x-bar chart helps us monitor the central tendency of the process, while the R-chart monitors the variability or dispersion within the samples.

Plotting the x-bar chart:

   Calculate the overall mean (x-double bar) by averaging all the sample averages.

   Calculate the average range (R-bar) by averaging all the sample ranges.

   Calculate the control limits for the x-bar chart using the formulas: Upper control limit (UCL) = x-double bar + A2 * R-bar, Lower control limit (LCL) = x-double bar - A2 * R-bar, where A2 is a constant factor depending on the sample size.

   Plot the sample averages on the x-bar chart along with the control limits.

Plotting the R-chart:

   Calculate the control limits for the R-chart using the formulas: UCL = D4 * R-bar, LCL = D3 * R-bar, where D3 and D4 are constant factors depending on the sample size.

   Plot the sample ranges on the R-chart along with the control limits.

By examining the x-bar and R-charts, we can assess whether the process is in control. If the data points fall within the control limits, with no specific patterns or trends, the process is considered in control. If any data points fall outside the control limits or show non-random patterns, it suggests the process is out of control and further investigation is required.

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THIS QUESTION IS INCOMPLETE HERE IS THE GENERAL SOLUTION.

Answer:

217.70 cubic units

Step-by-step explanation:

           h= 5 units & r = 4 units

          \(\sf \boxed{Volume \ of \ cone = \dfrac{1}{3} \pi r^2h}\)

                                       \(\sf = \dfrac{1}{3}*3.14*4*4*5\\\\ = 83.73 \ cubic units\)

            r = 4 units

                   \(\sf \boxed{Volume \ of \ hemisphere = \dfrac{2}{3} \pi r^3}\)

                                                          \(\sf = \dfrac{2}{3}*3.14*4*4*4\\\\= 133.97 \ cubicunits\)

Volume of composite solid = 83.73 + 133.97

                                               = 217.70 cubic units

In this question we are provided with the height and radius. We are asked to calculate the volume of a composite solid

First we will find the volume of a cone

We know,

\( \orange{\star \: \small\boxed{ \sf{ Volume_{(cone)} = \dfrac{1}{3}πr²h}}}\)

Where,

Substituting the values we get

\( \small\bf Volume_{(cone)} = \dfrac{1}{3} \times 3.14×4 × 4×5\)

\( \rightarrow \small\rm{ Volume_{(cone)} = \dfrac{1}{3}×251.2}\)

\( \small\sf{ Volume_{(cone)} = 83.73 \:cubic \: units }\)

Now we will calculate the volume of a hemisphere

We know,

\( \red{\star \: \small \boxed{\sf{ Volume_{(hemisphere)} = \dfrac{2}{3}πr³}}}\)

Substituting the values we get

\( \small\bf{ Volume_{(hemisphere)} = \dfrac{2}{3} \times 3.14 × 4 × 4 × 4}\)

\( \rightarrow\small\rm{ Volume_{(hemisphere)} = \dfrac{2}{3} \times 200.96}\)

\( \rightarrow\small\rm{Volume_{(hemisphere)} = 2 \times 66.98} \)

\( \small\sf{ Volume_{(hemisphere)} =133.97}\)

Now we will calculate the volume

Volume = 83.73 + 133.97 = 217.70 cubic units

A $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.  A $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

The formula to calculate the value of a CD after a specific duration at a specific interest rate compounded annually is given by:

A = P(1 + r/n)^(nt)

where P is the principal,

r is the annual interest rate,

n is the number of times compounded per year,

t is the number of years, and

A is the value of the CD at maturity.

Here, we need to calculate the value of a $1,000 initial investment in each bank's CD at maturity.

Let's calculate the value of a $1,000 investment in Bank ABC's CD.

P = $1,000

r = 5.0% compounded annually

t = 10 years

n = 1

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.05/1)^(1x10)A = $1,628.89

Therefore, a $1,000 initial investment in Bank ABC's CD would be worth $1,628.89 at maturity.

Let's calculate the value of a $1,000 investment in Bank XYZ's CD.

P = $1,000

r = 4.95% compounded daily

t = 10 years

n = 365

We have all the values; let's put them in the formula and solve:

A = $1,000(1 + 0.0495/365)^(365x10)A = $1,622.82

Therefore, a $1,000 initial investment in Bank XYZ's CD would be worth $1,622.82 at maturity.

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Answer:

x=5 :)

Step-by-step explanation:

1) You have to move all the terms which do not include x to the opposite side of the equation so you can solve x for a simple variable.

To do this subtract 8 from both sides!

\(\sqrt{3x+1}+8=4\) will become \(\sqrt{3x+1}=-4\)

2) Get rid of the square root

To do this square both sides of the equation

\(\sqrt{3x+1} = 3x+1\)

\((-4)^2=16\)

You will now be left with 3x+1 = 16

3) Get rid of 1 from both sides (subtract)

\(3x+1-1=3x\)

\(16-1=15\)

You will now be left with 3=15

4) Divide both sides by 3 to get the result for x

\(3x\) ÷ \(3\) \(=x\)

\(15\) ÷ \(3=5\)

You are left with x=5!!!

Hope this helps, have a great day!!!!

Part 1: Solve for the variable

x = 5

Part 2: Is the answer extraneous or not?

Step-By-Step

Part 1:

Isolate x

Subtract 8 to both sides

\(\sqrt{3x+1}\) + 8 = 4

\(\sqrt{3x+1}\) = -4

Square both sides of the equation (this will remove the radical sign)

3x + 1 = 16

Subtract 1 to both sides

3x = 15

Divide 3 on both sides

x = 5

What is an extraneous solution?

An extraneous solution is an answer you find when solving for a variable in an equation (x), but when you plug the x  back into the equation, the equation results in a false conclusion. This sometimes occurs when you have an equation with a square root.

Plug x (5) into the original equation

\(\sqrt{3(5)+1}\) + 8 = 4

Solve using PEMDAS

\(\sqrt{15+1}\) + 8 = 4

\(\sqrt{16}\) + 8 = 4

4 + 8 = 4

12 \(\neq\) 4

This is false, thus 5 is an extraneous solution

extraneous solution

Based on the diagram presented, it can be concluded that for every 1 cup of fruit juice, 1.2 cups of iced tea and 0.6 cup of sugar are used.

The diagram shows the three ingredients required to prepare a pitcher of fruit tea and the amount of the ingredients required.

Ingredients required:

Fruit juce: 2.5 cups

Sugar: 1.5 cups

Iced tea: 3 cups

Let's use the rule of three to find the answer:

Sugar required:

2.5 cups = 1.5 cups

1 cup  = x

x= 1.5 / 2.5 = 0.6 cups

Iced tea required:

2.5 cups = 3 cups

1 cup  = x

x = 3 / 2.5 = 1.2

Note: Here you can find the missing diagram:

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Answer:

4480

Step-by-step explanation:

I did it

Answer:

12<6+n

this is the answer

A small p-value provides strong evidence against the null hypothesis. The null hypothesis is the hypothesis that there is no significant difference or relationship between two variables.

The p-value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis is true.
If the p-value is small, typically less than 0.05, it means that the observed result is unlikely to have occurred by chance alone if the null hypothesis is true. This suggests that there is strong evidence against the null hypothesis and that we should reject it in favor of the alternative hypothesis. .
For example, if we conduct a hypothesis test to determine whether a new drug is more effective than a placebo, a small p-value would indicate that the drug is indeed more effective. This is because the observed results are highly unlikely to occur if the drug is not effective.
In summary, a small p-value provides strong evidence against the null hypothesis and supports the alternative hypothesis. It suggests that the observed results are not due to chance and that there is a significant difference or relationship between the variables being studied.

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Respuesta:

616,250

Explicación paso a paso:

Dado que:

Precio inicial = 725.000

Porcentaje de descuento por pagar en efectivo = 15% = 0,15

El precio con descuento será:

Importe inicial - descuento

Descuento = 0,15 * 725000 = 108,750

Precio con descuento = (725000 - 108750) = 616,250

Answer:

Height of trapezoid = 12 m

Step-by-step explanation:

Area of trapezoid = [(base1+base2)/2] * height

150= [(9+16)/2]* H

H= (150*2)/25

H= 12 m

Answer:

h=10m

Step-by-step explanation: