43x+ 67y = -24 and 67x + 43y = 24 solve

Answer:

Step-by-step explanation:

Binomial is a factor of the polynomial.

Answer:

The zeros are {-2, 3}

Step-by-step explanation:

Set each of these factors equal to zero, in turn, set each factor = to 0 and solve the resulting equation for x:

x + 2 = 0 yields x = -2;

x - 3 = 0 yields x = 3

The zeros are {-2, 3}

The total price that Bryce got charged to his credit card is $120.54  .

In the question ,

it is given that the

price for Shorts = $14.00

price for Soccer Ball = $25.00

price for Shin guard = $10.00

price for Cleats = $60.00

the total price for all the items = 14+25+10+60 = $109  

Given that the sales tax is 6% of the total price .

So , the sales tax = 6% of 109 = 0.06×109 = $6.54

According to the question

total price = price + sales tax + shipping cost

= 109 + 6.54 + 5

= 120.54

Therefore , the total price that Bryce got charged to his credit card is $120.54  , the correct option is (D) $120.54   .

The given question is incomplete , the complete question is

Bryce orders the following items from a catalog. What is the total price he charges to his credit card if the sales tax is 6 percent and nontaxable shipping costs $5 for the order? Round to the nearest cent if necessary. Shorts=$14.00 ,Soccer ball=$25.00 ,Shin guards=$10.00 ,Cleats=$60.00 .

(A) $104.94

(B) $109.94

(C) $115.54

(D) $120.54

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Answer:

(5, 3 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ) , thus

(- 3, 5 ) → (5, 3 )

Answer:

(-5,-3)

Step-by-step explanation:

Answer:

x=1/25

Step-by-step explanation:

Answer: -25

Step-by-step explanation:

You would have to divide both sides by 3/5 which is the same as multiplying by 5/3.

x = -15*5/3

x = -75/3 = -25

The probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

If the average number of units rented per week is 2.3 and the distribution is Poisson, then the parameter lambda is also equal to 2.3.

The probability of renting exactly three apartments in a week is given by the Poisson probability function:

\(P(X = 3) = (e^(-lambda) * lambda^x) / x!\)

Substituting the values, we get:

\(P(X = 3) = (e^(-2.3) * 2.3^3) / 3!\)

P(X = 3) = (0.09963 * 12.167) / 6

P(X = 3) = 0.2018

Therefore, the probability of renting exactly three apartments in a week is approximately 0.2018 or 20.18%.

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Using the z-distribution, we have that:

a) The 90% confidence interval for the proportion of all U.S. adults who could name all three branches of government is (0.339, 0.381). It means that we are 90% sure that the true population proportion is within these values.

b) The entire confidence interval is below 50%, which means that it provides convincing evidence that less than half of all U.S. adults could name all three branches of government.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

Item a:

For the parameters, we have that:

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 - 1.645\sqrt{\frac{0.36(0.64)}{1416}} = 0.339\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 + 1.645\sqrt{\frac{0.36(0.64)}{1416}} = 0.381\)

The 90% confidence interval for the proportion of all U.S. adults who could name all three branches of government is (0.339, 0.381). It means that we are 90% sure that the true population proportion is within these values.

Item b:

The entire confidence interval is below 50%, which means that it provides convincing evidence that less than half of all U.S. adults could name all three branches of government.

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In the table that shows the length, in inches, of fish in a pond, there are no outlier.

we know, a value that differs significantly from the other values in a dataset is an outlier in mathematics. Measurement errors, data entry errors, or extreme results that are actually outliers from the majority of the data can all lead to outliers.

Here according to question,

A box-and-whisker plot, which depicts the distribution of a dataset by presenting the minimum, first quartile, median, third quartile, and maximum values, is one method for identifying outliers.

Thus, there are no outlier.

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Answer:

x^2 (x^2 + 6x - 27)(x+5) + 81/3(x+5)

Step-by-step explanation:

1) Use this rule: a/b x c = ac/b.

(x^2 + 6x - 27)/3 + 27/x + 5

2) Regroup terms.

x^2 (x^2 + 6x - 27)/3 + 27/x+5

3) Rewrite the expression with a common denominator.

x^2 (x^2 + 6x - 27) (x + 5) 27 x 3/ 3(x + 5)

4) Simplify 27 x 3 to 81.

x^2 (x^2 + 6x - 27)(x+5) + 81/3(x+5)

Thanks

Answer:

Step-by-step explanation:

The slope of the line passing through two given points:  \(m=\dfrac{y_2-y_1}{x_2-x_1}\)

(-2, 8)   ⇒   x₁ = -2,  y₁ = 8

(-22, 8)   ⇒     x₂ = -22,  y₂ = 8

So, the slope:

                     \(m=\dfrac{8-8}{-22-(-2)}=\dfrac{0}{-20}=0\)

Answer:

Check pdf

Step-by-step explanation:

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

A stone arch can be twice as wide as a stone lintel because an arch distributes the weight of the structure vertically down its curve to the columns (piers) on either side while a lintel distributes the weight horizontally along the length of the stone.

It requires only a small fraction of the arch's width to support itself while a lintel requires the full width of the structure that it spans. Thus, a stone arch can span a larger gap than a stone lintel and be twice as wide while using the same material.

For example, the Roman Colosseum uses an arch to span the entrances and exits while the walls supporting the upper levels use a series of stone lintels to support the structure.

Moreover, the arc prevents the need for a central support structure, which would be in the way of any events taking place in the structure. The technology of arches made them fundamental to ancient Roman architecture. For example, the arches were used to construct aqueducts, which provided a steady supply of water to the city of Rome.

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The items and the contained that best describes them between unit rate and rate include:

Rate:

Unit Rate:

A rate is a ratio that compares two different types of quantities, often with different units. A unit rate, on the other hand, is a specific type of rate that compares a quantity to one unit of another quantity.

1 page for every 4 students is a rate because it compares pages (one type of quantity) to students (a different type of quantity). 1 sheet per 4 paragraphs is also a rate because it compares sheets (one type of quantity) to paragraphs (a different type of quantity).

40 pages for each booklet is a unit rate because it compares pages (one type of quantity) to a single unit of another quantity, which in this case is 1 booklet.

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The critical value for constructing a 98% confidence interval for a mean from a sample size of n = 15 is 2.602.

The range of values that is likely to contain the population parameter with a specific degree of certainty is known as the confidence interval. It is the range of values in which a population parameter is predicted to exist based on a sample of data. In statistical research, confidence intervals are frequently used to indicate the accuracy of an estimate or the variability of a particular statistic.

The critical value is the number used to determine if the null hypothesis should be accepted or rejected in a statistical hypothesis test. It is frequently determined using a table of critical values that corresponds to a specific level of significance and degrees of freedom.

The significance level is typically established at 5% or 0.05.

The formula to compute the critical value for a confidence interval is as follows:

Critical value = Zα/2, where Zα/2 is the Z-score associated with a level of significance of α/2.

In this case, the critical value for constructing a 98% confidence interval for a mean from a sample size of n = 15 is 2.602.

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The critical value for constructing a 98% confidence interval for a mean from a sample size of n = 15 can be found using the t-distribution table. Here are the steps to find the critical value:

1. Determine the degrees of freedom (df) for your sample size: df = n - 1 = 15 - 1 = 14.
2. Identify the confidence level: 98%.
3. Find the corresponding t-value in the t-distribution table for 98% confidence level and 14 degrees of freedom.

Upon looking up the t-distribution table, the critical value (t-value) for a 98% confidence interval with 14 degrees of freedom is approximately 2.977.

So, the critical value for constructing a 98% confidence interval for a mean from a sample size of n = 15 is 2.977.

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Answer:

y=1/5x

That's the answer with the other point at (0,0)

Step-by-step explanation:

The directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

To get the directional derivative of the function f(x, y) = 3(e^x) sin y at the point (0, π/3) in the direction of the vector v = <-6, 8>, follow these steps:       Compute the gradient of the function:
∇f(x, y) = (df/dx, df/dy) = (3(e^x) sin y, 3(e^x) cos y)
Evaluate the gradient at the given point (0, π/3):
∇f(0, π/3) = (3(e^0) sin(π/3), 3(e^0) cos(π/3)) = (3(1)(√3/2), 3(1)(1/2)) = (3√3/2, 3/2)
Normalize the direction vector v:
||v|| = √((-6)^2 + 8^2) = √(36 + 64) = √100 = 10
u = v/||v|| = (-6/10, 8/10) = (-3/5, 4/5)
Compute the directional derivative D_u f(0, π/3) by taking the dot product of the gradient at the given point and the normalized direction vector:
D_u f(0, π/3) = ∇f(0, π/3) · u = (3√3/2, 3/2) · (-3/5, 4/5) = (-3/5)(3√3/2) + (4/5)(3/2) = (-9√3/10) + (6/5)
So, the directional derivative D_u f(0, π/3) is equal to (-9√3/10) + (6/5).

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When there is a multiplication between a term with parenthesis and another term we apply the distributive property:

It says that the parenthesis indicates that the term outside will multiply each of the terms inside it.

For the first parethesis:

- 3(2x + 4) = (-3) · 2x + (-3) · 4

since

(-3) · 2x = -6x

(-3) · 4 = -12

then

- 3(2x + 4) = (-3) · 2x + (-3) · 4

- 3(2x + 4) = -6 x - 12

For the second

– (2x + 4) ​= – 1 (2x + 4)

= ​(-1) · 2x + (-1) · 4

=-2x -4

We can see in this case that both parenthesis are the same, then it is the common factor of - 3(2x + 4) and – (2x + 4) ​,

We can factor it by separating it of each term and letting the remaining terms inside a parenthesis

- 3(2x + 4) – (2x + 4) ​= (2x + 4) ( -3 -1)

= (2x + 4) ( -4)

= -4 (2x + 4)

The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.

Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.

Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.

Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.

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a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Answer:

What are you talking about

Step-by-step explanation:

I dont speak confusing

-4z plus 3 equal is to 6 plus 2z

Answer will be 3=-2z

Answer:

x

Step-by-step explanation:

-3x + 4x =x

-7 + 7 = 0

x

(a) False. The radial probability function does not represent the positions of individual electrons, but rather the probability of finding an electron at a particular distance from the nucleus. (b) False. The radial probability function and probability density do not go to zero at the same distance. (c) True. For an ns orbital, the number of radial nodes is equal to the principal quantum number.

(a) The radial probability function represents the probability of finding an electron at a specific distance from the nucleus. It does not indicate the positions of individual electrons. The function may have maxima or peaks at certain distances, but it does not imply that each electron is located at those specific distances. Therefore, the statement is false.

(b) The radial probability function and probability density are related but represent different aspects. The radial probability function describes the probability of finding an electron at a particular distance, while the probability density represents the probability of finding an electron within a small volume around a point in space. They do not go to zero at the same distance from the nucleus. The radial probability function typically goes to zero at larger distances, while the probability density decreases but does not necessarily reach zero at the same distance. Therefore, the statement is false.

(c) The number of radial nodes in an orbital is indeed equal to the principal quantum number (n). For an ns orbital, where the angular momentum quantum number (l) is 0, the number of radial nodes is equal to n - 1. This means that an ns orbital with a principal quantum number of 2 (n = 2) will have one radial node. So the statement is true.

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Calculating a relationship between college admission scores and freshman gpa requires the  Correlational statistics type of statistics. Correlational statistics are used to measure the strength of the relationship between two variables.

This type of statistic is used when attempting to determine the relationship between college admission scores and freshman GPA. By measuring the correlation between the two variables, it can be determined if there is a correlation between college admission scores and freshman GPA. Correlational statistics can measure the direction, strength, and significance of the relationship between two variables.

This type of statistics can provide information such as the degree to which two variables move together and the extent to which one variable changes as the other variable changes. Correlational statistics can also provide information on how much of the variability in one variable is explained by the other variable. Correlational statistics can be used to determine if there is a correlation between the two variables and, if so, the strength of that correlation.

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From the given figure we can see a vertical line intersected the x-axis at point (2, 0)

Since the equation of the vertical line that passes through the point (a, b) is

Where a is the x-coordinate of any point on the line

Then the equation of the given line that passes through the point (2, 0) is

Since the line is solid and the shading area is right the line, then

The sign of inequality should be >=

Then the inequality that represented the line is

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

The building is 13.91 m tall

Step-by-step explanation:

The parameters given are;

Angle of elevation to the top of the building = 71°

Angle of depression to the bottom of the building = 26°

Height of the man = 2  m

Therefore, the sight of the man, the man's height, and the distance of the man from the building forms a triangle where:

The hypotenuse side = The sight of the man to the bottom of the building

Hence;

In ΔABC, A being at the eye level or head level of the man, B at the foot and C at the bottom of the building

∴ ∠A + Angle of depression to the bottom of the building = 90°

∠A = 90° - 26° = 64°

∠B = 90° and ∠C = 26° (Sum of angles in a triangle)

\(Tan(C) = \frac{AB}{BC}\)

Distance of the man from the building = BC

\(Tan(26) = \frac{2}{BC}\)

\(BC= \frac{2}{ Tan(26) } = 4.1 \, m\)

Given that the angle of elevation to the top of the building = 71°, we have;

ΔAET

Where:

A is at the head level of the man,

E is the point on the building directing facing the man and

T is the top of the building

Hence AE = BC and ∡TAE = 71°

TE + AB= The height of the building

\(Tan(TAE) = \dfrac{TE}{AE}\\\\Tan(71) = \dfrac{TE}{4.1}\)

∴ TE = tan(71°) × 4.1 = 11.91 m

Hence the height of the building = 11.91 + 2 = 13.91 m.

According to the question, the four consecutive numbers can be written as :

First = \(x\); Second = \(x+2\);  Third = \(x+4\); Fourth = \(x+6\)

As per the question, the final expression is :

\(2((x+2)+(x+4)) = 3(x)+32\)

\(4x+12 = 3x+32\)

\(x = 20\)

Therefore, the four values can be calculated by substituting the above value:

\(x=20; x+2=22; x+4=24; x+6=26\)

The four consecutive numbers are: \(20,22,24,26\)

Substitute the calculated values in the final expression, to check whether the answer is correct or not.

\(2(22+24) = 3(20)+32\)

\(92=92\)

Therefore, the calculated values are correct.

What are consecutive terms?

Consecutive terms are those terms which follow one sequential order.

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