Thuy wrote the system of equations. 24 x + 36 y = 72. Negative 16 x + 8 y = 80. If the second equation is multiplied by 3, what should the first equation be multiplied by to eliminate the x variable by addition?

Given data:

The given radius of sphere is r=9.

The volume of the sphere is,

Substitute the given values in the above expression.

Thus, the volume of sphere is 972π.

Answer: $18.19

Step-by-step explanation:

Given

The original Price of the meal is \(\$20\)

After a 15% discount, the price reduced to

\(\Rightarrow \text{Reduced Price}=20\times -20\times 0.15\\\Rightarrow \text{Reduced Price}=20[1-0.15]=20\times 0.85\\\Rightarrow \text{Reduced Price}=\$17\)

After this, a sales tax is applied

So, there would be an increase in price

\(\Rightarrow \text{New Price}=17+17\times 0.07\\\Rightarrow \text{New Price}=17[1+0.07]=17\times 1.07\\\Rightarrow \text{New Price}=\$18.19\)

So, the father pays an amount of \(\$18.19\)

Answer:

9

Step-by-step explanation:

The smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

The nullity of a matrix is the dimension of its null space, which represents the set of vectors that satisfy the equation A * x = 0, where A is the matrix and x is a vector.

The nullity of a matrix can range from 0 to the number of columns in the matrix. In this case, since A is a 3 x 8 matrix, the minimum possible value of nullity(A) is 0, indicating that the null space is trivial and contains only the zero vector. This occurs when the matrix is full rank, meaning that its columns are linearly independent.

On the other hand, the maximum possible value of nullity(A) is 8, which would occur if the matrix has rank 0. In this case, all the columns of the matrix are linearly dependent, and the null space spans the entire vector space of size 8.

Therefore, the smallest possible value of nullity(A) is 0, and the largest possible value of nullity(A) is 8.

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When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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Answer:

can you change this picture?

Isaiah's thinking is correct. Compound interest does earn $341.95 more than simple interest in 60 months.

Let P be the principal amount of $7,000

Let r be the annual interest rate of 6%

Let n be the number of compounding periods per year.

Using formula for simple interest: I = Prt, the interest earned after 60 months is:

I = 7,000 × 0.06 × 5

I = $2,100.

Using formula for compound interest \(A = P(1 + r/n)^{nt}\). The amount after 60 months with monthly compounding is:

\(A = 7,000*(1 + 0.06/12)^{12*5}\\A = 7,000*1.34885015255\\A = 9441.95106785\\A = $9441.95\)

The interest earned is:

I = A - P

I = $9441.95 - $7,000

I = $2,441.95.

The difference in interest earned between compound and simple interest is:

= $2,441.95 - $2,100

= $341.95.

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In the given frequency table, the relative frequency of 24 represents the proportion of family members who chose to go on a hike out of the total number of family members.

To calculate the relative frequency, we divide the frequency of the specific category (in this case, hike) by the total frequency. In this case, the frequency of the hike is 24, and the total frequency is 38.

Relative Frequency = Frequency of Hike / Total Frequency

Relative Frequency = 24 / 38

Simplifying the fraction, we get:

Relative Frequency ≈ 0.632

So, the relative frequency of 24 represents approximately 0.632 or 63.2%. This means that around 63.2% of the family members chose to go on a hike at the family reunion.

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Answer:

MY GUY THAT ANSWER IS C

Step-by-step explanation:

EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Square tile with measure of each side is 16inches have area equals to 1652 centimeters( round off to nearest square centimeters).

As given in the question,

Measure of each side length of a square tile = 16 inches

Conversion

1 inch = 2.54 centimeters

16 inches = ( 16 × 2.54 )centimeters

                = 40.64centimeters

Area of a square tile is :

= ( Side length ) × ( Side length)

= (40.64) × (40.64)

= 1651.6096 centimeters

= 1652 centimeters ( round off to nearest square centimeters)

Therefore, the area of a square tile with given measure of each side is equal to 1652 centimeters ( round off to nearest square centimeters).

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Answer:

16\(\frac{2}{3}\)%

Step-by-step explanation:

To convert from a fraction to a percentage, you can multiply the fraction by 100%.

\(\frac{1}{6}\) × 100% = 16\(\frac{2}{3}\)%

The volume of a hemisphere with a radius of 8. 8 cm, rounded to the nearest tenth of a cubic centimeter, is approximately 1436.8 cubic centimeters.

To find the volume of a hemisphere with a radius of 8.8 cm, you can use the formula:

Volume = (2/3)πr³

where r is the radius of the hemisphere. Plugging in the given radius:

Volume = (2/3)π(8.8)³ ≈ 1436.8 cubic centimeters

So, the volume of the hemisphere is approximately 1436.8 cubic centimeters, rounded to the nearest tenth of a cubic centimeter.

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The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.

According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.

Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.

Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.

Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.

Therefore, Choice C correctly represents the interpretation of the relationship between the variables.

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In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable, which is manipulated in order to observe its effect on the dependent variable.

In the analysis of variance procedure (ANOVA), factor refers to:
b. the independent variable

In ANOVA, a factor is an independent variable that is manipulated or controlled to investigate its effect on the dependent variable. Different levels of a factor represent the variations in the independent variable being tested. The different levels of a treatment are often created by manipulating the factor.
In contrast, independent variables are not considered dependent on other variables in various experiments. [a] In this sense, some of the independent variables are time, area, density, size, flows, and some results before the affinity analysis (such as population size) to predict future outcomes (dependent variables).

In both cases it is always a variable whose variable is examined through a different input, statistically also called a regressor. Any variable in an experiment that can be assigned a value without assigning a value to another variable is called an independent variable.

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Answer:

this is the answer−6x^2 +10x+7

Answer:

139

Step-by-step explanation:

If x=-5

then

5*-5^2-(-5)+9

5*25+5+9

139

Answer: 139

Concept:

Here, we need to understand the idea of evaluation.  

When encountering questions that gave you an expression with variables, then stated: "If x = a, y = b, z = c" (a, b, c are all constants), this means you should substitute the value given for each variable back to the expression.

Solve:

Given information

5x² - x + 9

x = -5

Substitute value into the expression

=5(-5)² - (-5) + 9

Simplify exponents

=5 (25) + 5 + 9

Simplify by multiplication

=125 + 5 +9

Simplify by addition

=\(\boxed {139}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

225/4 sqrt(3) in ^3

Step-by-step explanation:

The volume is found by

V = Bh

The B is the triangle

B = s^2 sqrt(3)/4

  = 5^2 sqrt(3)/4

  25/4  sqrt(3)

We know the height is 9

V =  25/4  sqrt(3) *9

V = 225/4 sqrt(3)

this is approximately 97.42785793 in^3

Answer:

I don't understand

Step-by-step explanation:

Answer:

number of beads to be made x 10

x×10=

The correct statement is: 'A one-variable data table has input values that are listed either down a column (column-oriented) or across a row (row-oriented). '

The correct answer is an option (a)

We know that a one-variable data table contain its input values either in a single column (column-oriented), or across a row (row-oriented).

And any formula in this data table must refer to only one input cell.

Whereas we se a two-variable data table to see how different values of two variables in one formula will change the formula results.

Custom data tables are used for: Building data-driven services that can easily be updated without modifying it and storing the results.

And the pre-formatted data tables stored as building blocks in galleries that can be accessed any time and be reused any number of times you want.

Therefore, the correct answer is an option (a)

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The complete question is:

A ________ data table has input values that are listed either as column-oriented or roworiented.

A) one-variable

B) two-variable

C) custom

D) pre-formatted

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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Answer: 500 people don't read both.

Step-by-step explanation:

Answer:

6x + 10

Step-by-step explanation:

3x + 5 + 3x + 5

6x + 10

Answer:

b = 81

Step-by-step explanation:

given a² and b are directly proportional then the equation relating them is

a² = kb ← k is the constant of proportionality

to find k use the condition a = 2 when b = 9 , then

2² = 9k

4 = 9k ( divide both sides by 9 )

\(\frac{4}{9}\) = k

a² = \(\frac{4}{9}\) b ← equation of proportion

when a = 6 , then

6² = \(\frac{4}{9}\) b

36 = \(\frac{4}{9}\) b ( multiply both sides by 9 to clear the fraction )

324 = 4b ( divide both sides by 4 )

81 = b

The sample variances (s²) and expected variances of the sample means (V( \(\bar{y}\))) for all possible samples are as follows,

Sample 1: s² = 0.5, V( \(\bar{y}\)) = 0.25

Sample 2: s² = 2, V( \(\bar{y}\)) = 1

Sample 3: s² = 2, V( \(\bar{y}\)) = 1

Sample 4: s² = 4, V( \(\bar{y}\))= 2

Sample 5: s² = 0.5, V( \(\bar{y}\)) = 0.25

Sample 6: s² = 1, V( \(\bar{y}\))= 0.5

Sample 7: s² = 2.5, V( \(\bar{y}\)) = 1.25

Sample 8: s² = 0.5, V( \(\bar{y}\))= 0.25

Sample 9: s² = 2, V( \(\bar{y}\)) = 1

Sample 10: s² = 0.5, V( \(\bar{y}\))= 0.25

Let's calculate s² for the population and V( \(\bar{y}\)) for the sample using the given population {0, 1, 2, 3, 4} and a sample size of n = 2.

For the population,

To calculate the population variance, we need the population mean (μ),

μ = (0 + 1 + 2 + 3 + 4) / 5

  = 2

Now calculate the population variance (s²),

s² = (Σ(x - μ)²) / N

= ((0 - 2)² + (1 - 2)² + (2 - 2)² + (3 - 2)² + (4 - 2)²) / 5

= (4 + 1 + 0 + 1 + 4) / 5

= 10 / 5

= 2

So, the population variance (s²) is 2.

For the sample,

Let's calculate s² and V(\(\bar{y}\)) for each sample,

Sample 1: {0, 1}

Sample mean (X) = (0 + 1) / 2

                             = 0.5

Sample variance (s²) = (Σ(x - X)²) / (n - 1)

= ((0 - 0.5)² + (1 - 0.5)²) / (2 - 1)

= (0.25 + 0.25) / 1

= 0.5

V( \(\bar{y}\))

= s² / n

= 0.5 / 2

= 0.25

Sample 2: {0, 2}

Sample mean (X) = (0 + 2) / 2

                            = 1

Sample variance (s²) = (Σ(x - X)²) / (n - 1)

= ((0 - 1)² + (2 - 1)²) / (2 - 1)

= (1 + 1) / 1

= 2

V( \(\bar{y}\))= s² / n

= 2 / 2

= 1

Perform similar calculations for the remaining samples,

Sample 3: {0, 3}

Sample mean (X) = (0 + 3) / 2

                            = 1.5

Sample variance (s²) = 2

V( \(\bar{y}\)) = 1

Sample 4: {0, 4}

Sample mean (X) = (0 + 4) / 2 = 2

Sample variance (s²) = 4

V( \(\bar{y}\)) = 2

Sample 5: {1, 2}

Sample mean (X) = (1 + 2) / 2

                            = 1.5

Sample variance (s²) = 0.5

V( \(\bar{y}\)) = 0.25

Sample 6: {1, 3}

Sample mean (X) = (1 + 3) / 2 = 2

Sample variance (s²) = 1

V( \(\bar{y}\)) = 0.5

Sample 7: {1, 4}

Sample mean (X) = (1 + 4) / 2 = 2.5

Sample variance (s²) = 2.5

V( \(\bar{y}\))= 1.25

Sample 8: {2, 3}

Sample mean (X) = (2 + 3) / 2 = 2.5

Sample variance (s²) = 0.5

V( \(\bar{y}\))= 0.25

Sample 9: {2, 4}

Sample mean (X) = (2 + 4) / 2 = 3

Sample variance (s²) = 2

V( \(\bar{y}\)) = 1

Sample 10: {3, 4}

Sample mean (X) = (3 + 4) / 2 = 3.5

Sample variance (s²) = 0.5

V( \(\bar{y}\)) = 0.25

Therefore, the sample variances (s²) and expected variances of the sample means (V( \(\bar{y}\))) for all possible samples are as follows,

Sample 1: s² = 0.5, V( \(\bar{y}\)) = 0.25

Sample 2: s² = 2, V( \(\bar{y}\)) = 1

Sample 3: s² = 2, V( \(\bar{y}\)) = 1

Sample 4: s² = 4, V( \(\bar{y}\))= 2

Sample 5: s² = 0.5, V( \(\bar{y}\)) = 0.25

Sample 6: s² = 1, V( \(\bar{y}\))= 0.5

Sample 7: s² = 2.5, V( \(\bar{y}\)) = 1.25

Sample 8: s² = 0.5, V( \(\bar{y}\))= 0.25

Sample 9: s² = 2, V( \(\bar{y}\)) = 1

Sample 10: s² = 0.5, V( \(\bar{y}\))= 0.25

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The above question is incomplete , the complete question is:

List all possible simple random samples of size n = 2 that can be selected from the population {0, 1, 2, 3, 4}. calculate s2 for the population and V(y) for the sample.

Answer:

1/9

Step-by-step explanation:

I'm assuming the equation you mean is y = (x/9)  -- if so, parentheses aren't really required.

The equation for the constant of proportionality is y=kx. So, we will want to find the value of k, which is the constant. The y and x variables are in both equations already, and there is only the 1/9, which is k.

Therefore, the constant of proportionality is 1/9. We can check this answer by putting 1/9 back into the equation. y = 1/9 (x)    or    y=  x/9.

Answer:

1/9

Step-by-step explanation:

None. Just trust me.

Answer: The distance between these two points is 5.

Step-by-step explanation:

Yay! Love doing distance formula questions!

Okay, so first off, the distance formula goes as follows:

d = \(\sqrt(x^{2} - x^1)^2 + (y^{2}-y^1)^2\)

Basically you just plug in your coordinates to the formula.

Step 1:

\(\sqrt(-5 + 5)^{2} + (2-7)^{2}\)

Step 2: Distribute the exponent to both parenthesis to get \(\sqrt{25}\).

Step 3: Factor the number, which would result in \(\sqrt{5^2}\).

As a result of this, your answer would be 5.

To determine if any flavours of gum are more popular than others, the hypotheses for the company to test are:
Null hypothesis (H0): All flavours of gum are equally popular.
Alternative hypothesis (H1): At least one flavour of gum is more popular than the others.

B) To calculate the P-value, you need to perform a Chi-Square test on the given data. First, calculate the expected frequency for each flavour if they were equally popular. Since there are 80 people in the sample and 4 flavours, the expected frequency for each flavour is 80/4 = 20.
Now, compute the test statistic using the Chi-Square formula:
Χ² = Σ[(observed - expected)² / expected]
Χ² = [(25-20)²/20 + (19-20)²/20 + (22-20)²/20 + (14-20)²/20] = 3.25
With 3 degrees of freedom (number of flavors - 1), the P-value can be found using a Chi-Square distribution table or calculator. For this test statistic, the P-value is approximately 0.354.
C) To test the claim at a 1% significance level, compare the P-value to the significance level (alpha). Since the P-value (0.354) is greater than the significance level (0.01), we fail to reject the null hypothesis.
In conclusion, there is not enough evidence at the 1% significance level to suggest that any flavour of gum is more popular than the others.

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False.

The given statement "If a sample of n=5 scores has EX= 10 and EX2 = 100, then SS= 80" is a true statement.

Here is how we can prove it:

To calculate SS, we can use the formula below:

SS = \sum_{i=1}^{n}x_{i}^{2} - \frac{(\sum_{i=1}^{n}x_{i})^2}{n}

Given n = 5, EX = 10, and EX2 = 100

We know that:

EX = \frac{\sum_{i=1}^{n}x_{i}}{n}

Putting the given value of EX = 10, we can find out the value of sum of all n scores.

sum = EX \times n sum = 10 \times 5 sum = 50

Now,

we can use EX2 to find the value of sum of squares of all n scores.

EX2 = \frac{\sum_{i=1}^{n}x_{i}^{2}}{n}

Putting the given value of EX2 = 100, we can find out the value of sum of squares of all n scores.

sum of\;squares = EX2 \times n sum of\;squares = 100 \times 5

sum of\;squares = 500

Now, we can substitute the values of sum and sum of squares in the formula of SS.  

SS = \sum_{i=1}^{n}x_{i}^{2} - \frac{(\sum_{i=1}^{n}x_{i})^2}{n}

SS = 500 - \frac{50^2}{5}

SS = 500 - 500

SS = 0

Therefore, the value of SS is 0 which is not equal to 80.

Hence, the statement "If a sample of n=5 scores has EX= 10 and EX2 = 100, then SS= 80" is false.

False.

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