-3x - 7y=2
x + 3y = -2
solving systems by elimination

Find the amount of the increase and divide that by the original amount:

7.70 - 7.00 = 0.70 increase

0.70 / 7.00 = 0.1

Multiply by 100 to get the percentage:

0.1 x 100 = 10 %

The increase was 10 %

Theatre should conclude that majority of patrons were dissatisfied with performance quality.

Here, we have to use one sample z test for a population proportion.

Null hypothesis: H0: No majority of patrons are dissatisfied with performance quality.

Alternative hypothesis: Ha: The majority of patrons are dissatisfied with performance quality.

H0: p ≤ 0.5 versus Ha: p > 0.5

This is an upper-tailed or right-tailed test.

We assume a level of significance as α = 0.05.

The test statistic formula for this test is given as below:

Z = (p ^ - p)/sqrt(pq/n)

Where, p^ = Sample proportion, p is population proportion, q = 1 - p, and n is the sample size

n = sample size = 100

p^ = x/n = 0.70

p = 0.50

q = 1 - p = 0.50

Z = (p^- p) / sqrt ( p q / n)

Z = (0.70 – 0.50) / sqrt(0.50*0.50/100)

Z = 4.00

P-value = 0.00 (by using z-table)

P-value < a = 0.05

So, we reject the null hypothesis.

Therefore theatre should conclude that majority of patrons were dissatisfied with performance quality.

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The average number of viewers over the two weeks is  4. 85  x 10^5. Option D

Average is simply a number taken as the representative of a list of numbers.

It is determined by taking the sum of the numbers divided by the number of listed numbers.

Given the number of viewers as;

5.6 x 105 viewers  and 4.1 x 105 viewers

Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2

Average = 9. 7  x 10^5 / 2

Average = 4. 85  x 10^5

The average number of viewers over the two weeks is  4. 85  x 10^5

Thus, the average number of viewers over the two weeks is  4. 85  x 10^5. Option D

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Hence, the probability that an aircraft entering the area is detected by more than two radar sets is approximately 0.998816, or about 99.88%.

To calculate the probability that an aircraft is detected by more than two radar sets, we need to consider the different combinations of radar sets that can detect the aircraft.

Let's analyze the possibilities:

If the aircraft is detected by all three radar sets:

Probability = (probability of detection) * (probability of detection) * (probability of detection)

= (0.98) * (0.98) * (0.98)

= 0.941192

If the aircraft is detected by exactly two radar sets:

There are three possible combinations of two radar sets that can detect the aircraft: (1st and 2nd), (1st and 3rd), (2nd and 3rd).

Probability for each combination = (probability of detection) * (probability of detection) * (probability of failure to detect) = (0.98) * (0.98) * (0.02) = 0.019208.

Total probability = 3 * 0.019208 = 0.057624.

Therefore, the probability that an aircraft is detected by more than two radar sets is the sum of the probabilities from the two cases above:

Probability = 0.941192 + 0.057624

= 0.998816

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Answer:y

=

4

3

x

−

9

Explanation:

Given -

x

1

=

6

y

1

=

−

1

Slope

m

=

4

3

Given the slope and a point, the formula for the straight line equation is

(

y

−

y

1

)

=

m

(

x

−

x

1

)

y

−

(

−

1

)

=

4

3

(

x

−

6

)

y

+

1

=

4

3

x

−

6

.

4

3

y

+

1

=

4

3

x

−

8

y

=

4

3

x

−

8

−

1

y

=

4

3

x

−

9

The expression of (x-9)(x+6) as a trinomial is x²  -3x - 54

A trinomial is an algebraic expression that has three non-zero terms.

In a simpler terms, the definition of a trinomial is a math equation that has three terms which are connected by plus or minus notations.

Therefore, let's express  (x-9)(x+6) as a trinomial.

Hence,

(x-9) (x+6) = x²  + 6x - 9x - 54

Finally,

x²  + 6x - 9x - 54 = x²  -3x - 54

Therefore, the trinomial form of (x-9)(x+6)  is  x²  -3x - 54

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The Mean Absolute Deviation over Months 3-6 is 5.

Correct answer is option C) 5

To calculate the Mean Absolute Deviation (MAD) over Months 3-6, we need to follow these steps:

Identify the errors for Months 3-6: The errors for Months 3-6 are 3, -5, 4, and -8.

Calculate the absolute value of each error: Taking the absolute value of each error gives us 3, 5, 4, and 8.

Find the sum of the absolute errors: Add up the absolute errors: \(3 + 5 + 4 + 8 = 20.\)

Divide the sum by the number of errors: Since there are 4 errors, we divide the sum (20) by 4 to get the average: 20/4 = 5.

Determine the Mean Absolute Deviation: The MAD is the average of the absolute errors, which is 5.

Therefore, the Mean Absolute Deviation over Months 3-6 is 5.

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Answer:

1. $22.50 2. $11.70

Step-by-step explanation:

Cause 30% of 75 is 22.5 and 65% of 18 is 11.7

Answer:

Its B

Step-by-step explanation:

28.4x

&

3x

&

9.5x

Answer:

12 months

Explanation:

Given the function that models the total chacrge of a company as T = 35.00 + 18.75m where;

T is the total charges,

m is the number of months of storage

Given

T = $260.00

we are to find the value of m

Substitute

260 = 35 + 18.75m

18.75m = 260 - 35

18.75m = 225

m = 225/18.75

m = 12

Hence it will take 12 months to cost a new custimer $260.00

Step-by-step explanation:

Use z-score table to find the z-score that corresponds to .7000   ( 70%)

approx   .525   s.d.  above the mean

  .525  * 10 =  5.25  points above 100   = 105.25

The real rate of interest that you are paying is 3.5%.

The rate of interest, often referred to as the interest rate, is the percentage or proportion of the principal amount that is charged or earned over a certain period of time. It represents the cost of borrowing money or the return on investment. The rate of interest is typically expressed as an annual percentage, but it can also be calculated for shorter or longer time periods depending on the context.

The real rate of interest is calculated by subtracting the inflation rate from the nominal interest rate. In this case, the nominal interest rate is 6.5% per year, and the inflation rate is 3% per year.

Real Rate of Interest = Nominal Interest Rate - Inflation Rate

Real Rate of Interest = 6.5% - 3%

Real Rate of Interest = 3.5%

Therefore, the real rate of interest that you are paying is 3.5%.

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9514 1404 393

Answer:

  d.  76(cos(3π/16) +i·sin(3π/16))

Step-by-step explanation:

To form the product of 38cis(π/8) and 2cis(π/16), multiply the magnitudes and add the angles:

  38cis(π/8) × 2cis(π/16) = (38×2)cis(π/8 +π/16) = 76cis(3π/16)

___

In this context, a·cis(b) ≡ a(cos(b) +i·sin(b))

Answer:

y = 20x

Step-by-step explanation:

For members

y = 1/2x + 6

Where,

y = yearly cost in dollars

x = total game tokens purchased

1/2 = cost of each game token

6 = yearly fee

For non members: without yearly fee

A nonmember pays $20 per game token

y = 20x represents the yearly cost for a nonmember at the same video game arcade based on the total number of game tokens purchased in a year

Answer:

B,C,E

Step-by-step explanation:

Got it right on Edge

Answer:

13 containers of coleslaw

12 teammates

13÷12= 1,08 containers of coleslaw per teammate

The solution to the equation is C. 4/9

Logarithm is the exponent or power to which a base must be raised to yield a given number. It is also the inverse of exponents.  

How to determine this using the law of Logarithm,

㏒3 (4x) - 2㏒3 x = 2

Using the division rule which states;

The division of two logarithmic values is equal to the difference of each logarithm.

Logb (m/n)= logb m – logb n

So, ㏒3 (4x) - ㏒3 \(x^{2}\) = 2

㏒3 4x/\(x^{2}\) = 2

So, 4x/\(x^{2}\) = 3^2

4x/\(x^{2}\) = 9

Cross multiply

4x = 9x^2

divides through by 9x

4x/9x = 9x^2/9x

4/9 = x

x = 4/9

Therefore, the solution for the equation is 4/9

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Answer:

14 rabbits.

Step-by-step explanation:

Since there are 87 animals in total, add 41 and 32, which is 74. Now subtract 74 from 87, which would be give you 14, so the answer is 14.

Answer

8:28 Hope this helps.

Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: \((y-y_1)=m(x-x_1)\).

m= the slope.

\((x_1,y_1)\)= the coordinate of a point.

For the given example: m=1 and b=19.

The question gives: y + 2 = 3(x - 1). Therefore,

y + 2 = 3(x - 1)

y=3x-3-2

y=3x-5

If y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:

m= the slope. It can be calculated for Δy/Δx.

b= the constant term that represents the y-intercept

Thus, the slope is 3 and the y-intercept is -5.

For this, you should do a table with points

x     y= 3x-5

-2   y=3*(-2)-5=-6-5= -11

-1    y=3*(-1)-5=-3-5= -8

0   y=3*(0)-5=0-5= -5

1    y=3*(1)-5=3-5= -2

2    y=3*(2)-5=6-5= 1

Draw a graph from these points, see the attached image.

The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.

y= 3x-5, for x=0

y=3*0-5

y=0-5

y=-5

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The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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Answer:

D

Step-by-step explanation:

brainliest

hello

to solve this question, we just have to follow thr instructions as it is

the answer to this question is 6t/s

Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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The phrase \(f (x)\) denotes a formula with \(x\) serving as its input variable. Not multiply f and x, though!

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable .

The x in \(f(x)\) is referred to the argument of the function or simply the argument in function notation. Therefore, the response is just 2 if they ask for a argument and give you the equation \(f(2)\).

Hence,  the phrase \(f (x)\) represents a formula with \(x\) serving as its input variable.

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The conjugate of x - √2 is as follows:

(x + √2).

A pair of entities connected together is referred to as being conjugate. For instance, the two smileys—smiley and sad—are identical save from one set of characteristics that is essentially the complete opposite of the other. These smileys are identical, but you'll see if you look closely that they have the opposite facial expressions: one has a smile, and the other has a frown. Similar to this, the term "conjugate" in mathematics designates either the conjugate of a complex number or the conjugate of a surd when the number only undergoes a sign change with respect to a few constraints.

Here in the question,

The binomial is given as:

x - √2

The negative of this or when the operation sign is changed in the binomial, we get the conjugate as:

x + √2

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a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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Answer:

x = - 3

Step-by-step explanation:

Given

5x - 4 = x - 16 ( subtract x from both sides )

4x - 4 = - 16 ( add 4 to both sides )

4x = - 12 ( divide both sides by 4 )

x = - 3

Answer:

\( \huge{ \fbox{ \sf{x = -3}}}\)

Step-by-step explanation:

\( \star{ \sf{ \: 5x - 4 = x - 16}}\)

\( \text{Step \: 1 \: : \sf{ \: Move \: x \: to \: left \: hand \: side \: and \: change \: its \: sign.}}\)

\( \hookrightarrow{ \sf{5x - x - 4 = - 16}}\)

\( \text{Step \: 2 \: : \sf{ \: Move \: 4 \: to \: right \: hand \: side \: and \: change \: its \: sign.}}\)

\( \hookrightarrow{ \sf{ 5x - x = - 16 + 4}}\)

\( \text{Step \: 3 \: : \sf{Collect \: like \: terms}}\)

\( \hookrightarrow{ \sf{ 4x = - 16 + 4}}\)

\( \text{Step \: 4 \: : \sf{Calculate}}\)

\( \text{ \underline{Remember! : }} \sf{ \: The \: \: negative \: and \: positive \: integers \: are \: always \: subtracted \: but \: posses \: the \: sign \: of \: the \: bigger \: integer.}\)

\( \hookrightarrow{ \sf{ 4x = - 12}}\)

\( \text{Step \: 4 \: : Divide \: both \: sides \: by \: - 6}\)

\( \hookrightarrow{ \sf{ \frac{ 4x}{ 4} = \frac{ - 12}{ 4}}} \)

\( \text{Step \: 5 \: : Calculate}\)

\( \hookrightarrow{ \sf{x = -3}}\)

The value of x is -3 .

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

Answer:

128

Step-by-step explanation: