Find the value of x.
93
2x + 12

Answer:

4

Step-by-step explanation:

The principal square root is the positive square root

sqrt(16) = ±4

taking the positive square root

4

Answer:

B

Step-by-step explanation

This is because the 'principal square root' means the positive square root of a certain number, and so √16 = 4 × 4, making 4 the answer. This has a certain term for it as √16 could equal -4 also (-4 × -4 = 16).

Answer:

Step-by-step explanation:

1.89/14= .135

estimating to the nearest cent would be .14

Answer:

(9q + 5r)(9q - 5r)

Step-by-step explanation:

Given :-

81q² - 25r²

To Find :

Factors

Formula :-

a² - b² = (a + b)(a - b)

Solution :-

(9q + 5r)(9q - 5r)

Answer:

wx+10=20 20-10 =10

Step-by-step explanation:

because wx=? when the side change of any equation sign is change

After how many miles is the total charge for each vehicle the​ same is 400 miles.

Let x represent the number of miles

Let Car cost =240+.25x

Let Van cost =180+.40x

Formulate the equation

$240 + $0.25x = $180 + $0.40x

Rearrange

60 = .15x

Divide both side by .15x

x=60/.15

x=400 miles

Inconclusion after how many miles is the total charge for each vehicle the​ same is 400 miles.

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Answer:

r=10%

I=1149.60

P=2874

t=(I×100)/(p×r)

(1149.60×100)/(2874×10)

114960÷28740

4 years

\(r = 10\%\)

\(p = 2874\)

\(l = 1149.60\)

the numbers of year's needed for the investment.

\(t = \frac{l \times 100}{p \times r} \)

\(t = \frac{1149.60 \times 100}{2874 \times 10} \)

\(t = \frac{114960}{28740} \)

\(t = 4\)

therefore, 4 years is needed for the investment.

Answer:

distance of the rocket from the pine high school ≈ 344 miles

Step-by-step explanation:

The illustration forms a triangle with 2 right angle triangle in it. The western high school angle of elevation  is 41° and the pine high school angle of elevation is 23°. The distance between the 2 school is 512 miles .The distance of the rocket from the pine school is the adjacent side of one of the right angle triangle .

The full triangle has angle of 23°, 41° and the last angle will be 180 - 23 - 41 = 116°. The hypotenuse side of the right angle triangle representing the pine high school triangle can be solved using sine formula.

p/sin 41° = 512/sin 116°

p/0.65605902899 = 512/0.89879404629

cross multiply

0.89879404629 p = 335.902222843

divide both sides by 0.89879404629

p = 335.902222843 /0.89879404629

p = 373.725464949

p ≈ 373.70 miles

using cosine ratio the adjacent side of the triangle can be found.

cos 23° = adjacent/hypotenuse

cos 23° = adj/373.70

cross multiply

adjacent = 0.92050485345  × 373.70

adjacent = 343.992663735

distance of the rocket from the pine high school = 343.992663735

distance of the rocket from the pine high school ≈ 344 miles

Answer:

El saldo que el Sr. Rodríguez debe pagar cuando vence el pagaré es de $ 370

Step-by-step explanation:

Los parámetros dados del préstamo son;

El monto principal del préstamo, P = $ 675

La duración del préstamo, T = 8 meses = 2/3 años

La tasa de interés aplicada al préstamo, R = 10%

La cantidad que paga el Sr. Rodríguez en el segundo mes = $ 150

La cantidad que paga el Sr. Rodríguez en el cuarto mes = $ 200

Interés simple = P · R · T / 100 = 675 × 10 × 2/3/100 = 45

El interés simple del préstamo, I = $ 45

La cantidad total que el Sr. Rodríguez tiene que pagar, A = P + I = 675 + 45 = 720

La cantidad de reembolso que realiza el Sr. Rodríguez, R = 150 + 200 = 350

El saldo que debe pagar el señor Rodríguez, B = 720 - 350 = 370

El saldo que el señor Rodríguez debe pagar cuando el pagaré no vence, B = $ 370

Al vencerse el pagaré el señor Rodríguez deberá pagar $370.

Dado que el señor Rodríguez firma un pagaré por $675 a 8 meses de plazo y al 10%, si efectúa dos pagos antes del vencimiento, uno por $150 a los 2 meses, y otro por $200 a los 4 meses, para determinar cuál es el saldo que debe pagar al vencerse el pagaré se debe realizar el siguiente cálculo:

Por lo tanto, al vencerse el pagaré el señor Rodríguez deberá pagar $370.

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Answer:

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side c

Using Pythagoras theorem we have

c² = b² + a²

where

c is the hypotenuse

So we have

\( {c}^{2} = {5}^{2} + {3}^{2} \\ c = \sqrt{ {5}^{2} + {3}^{2} } \\ c = \sqrt{ 25 + 9} \\ c = \sqrt{34} \: \: \: \: \: \: \: \: \\ = 5.83095189...\)

We have the final answer as

Hope this helps you

The term "content loaded in a test of the hypotheses" refers to the data and information used to perform the hypothesis test, which in this case resulted in a calculated p-value of 0.03.

Based on the information provided, the calculated p-value of 0.03 is less than the level of significance of 2%. This means that the null hypothesis can be rejected and the alternative hypothesis can be accepted.

Therefore, the decision is to reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis.

The term "content loaded in a test of the hypotheses" refers to the data and information used to perform the hypothesis test, which in this case resulted in a calculated p-value of 0.03.

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200 meters is equal to 0.124275 miles. both are unit of measurement of distance.

The conversion factor for converting meters to miles is 0.000621371. So, to convert 200 meters to miles, you need to multiply 200 by 0.000621371, which results in 0.124275 miles.

It's important to note that the mile is a unit of length commonly used in the United States, while the meter is the standard unit of length in the International System of Units (SI).

For converting small lengths, it is sufficient to use this conversion factor, but for larger or more precise measurements, it is important to use a more accurate conversion method.

It's also worth noting that converting between different units of measurement can sometimes result in slight differences in the values obtained through conversion due to rounding.

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The area of the given composite shape, can be found to be 430. 58 square feet

There are two semi circles in the figure so to find the area of the figure, you need to find the surface areas of these two semi - circles and then sum them up.

Area of first semi circle :

= π x radius ²

= π x ( 22 / 2 ) ²

= π x 11 ²

= 380 . 29 square feet

Area of second semi circle :

=  π x radius ²

= π x ( ( 30 - 22 ) / 2 ) ²

= 50. 29 square feet

The area of the composite shape is :

= 380 . 29 + 50. 29

= 430. 58 square feet

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To determine whether quality is associated with the source of the shipments, we need to test the competing hypotheses.

The competing hypotheses are as follows:

H0: Quality and source of shipment (vendor) are independent.
HA: Quality and source of shipment (vendor) are dependent.

To test these hypotheses, we can use a chi-square test for independence. The test statistic is calculated by comparing the observed frequencies with the expected frequencies under the assumption of independence.

b-1. To calculate the test statistic, we first need to create a contingency table with the observed frequencies of quality and source of shipment. Each cell in the table represents the count of shipments from a specific vendor with a specific quality.

For example, the table could look like this:

            | Vendor A | Vendor B | Vendor C
--------------------------------------------
Good Quality |   10     |   15     |   12
--------------------------------------------
Poor Quality |   20     |   25     |   18

Next, we calculate the expected frequencies assuming independence. The expected frequency for each cell is calculated by multiplying the row total by the column total and dividing by the total number of observations.

Finally, we calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies divided by the expected frequencies for each cell.

b-2. Once we have the test statistic, we can find the p-value associated with it. The p-value represents the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

To find the p-value, we need to consult the chi-square table or use a statistical software. The p-value will indicate the strength of evidence against the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis.

Based on the given options, the p-value falls within the range of 0.01 ≤ p-value < 0.025. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that quality and source of shipment are dependent.

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The double integral of f(x, y) = 55xy over the domain D is to be computed. D is bounded by x = y and x = y².

The double integral represents the integral of a function of two variables over a region in a two-dimensional plane.

The most fundamental tool for finding volumes under surfaces or areas on surfaces in three-dimensional space is the double integral.

The formula for computing double integral over a region of integration can be written as:

∬f(x,y)dA, where f(x,y) is the integrand,

dA is the area element, and

D is the region of integration of the variables x and y.

In the present problem, f(x,y) = 55xy and D is bounded by x = y and x = y².

Thus the double integral is given by ∬D55xydA.

It can be written as:

∬D55xydA = ∫0¹dx ∫\(\sqrt{x}\)xdy

55xy = 55 * ∫0¹dx ∫\(\sqrt{x}\) xdy xy

∬D55xydA = 55 * ∫0¹dx ∫\(\sqrt{x}\)xdy xy

Now,

∫x^(1/2)xdy = xy|_(\(\sqrt{x}\), x)

                 = x(x) - \(\sqrt{x}\) x∫x^(1/2)xdy

                 = x² - \(x^{\frac{3}{2} }\)

Thus,∬D55xydA = 55 * ∫0¹dx ∫\(\sqrt{x}\)xdy xy

∬D55xydA = 55 * ∫0¹dx (x² - \(x^{\frac{3}{2} }\))

∬D55xydA = 55 * [x³/3 - (2/5)\(x^{\frac{5}{2} }\)]|

0¹ = 55(1/3 - 0) - 55(0 - 0)

    = 55/3.

Therefore, the value of the double integral of f(x, y) = 55xy over the domain D, bounded by x = y and x = y²,  is 55/3.

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The mean, variance, and standard deviation for the given probability density function over the interval [6, 13] are:

Mean (μ) = 9.50, Variance (σ²) = 2.993, Standard Deviation (σ) = 1.73

The mean (μ) represents the average value of the probability density function within the given interval. In this case, the mean is calculated as 9.50. It indicates the central tendency of the distribution and provides a measure of the "typical" value.

The variance (σ²) measures the spread or dispersion of the probability density function. It quantifies how far the values are from the mean. For the given function, the variance is determined to be 2.993.

The standard deviation (σ) is the square root of the variance and provides a more easily interpretable measure of the spread. In this case, the standard deviation is 1.73, which indicates that the values of the function within the interval tend to deviate from the mean by approximately 1.73 units on average.

The mean, variance, and standard deviation of the given probability density function provide insights into its central tendency, spread, and the typical deviation from the mean. These measures help us understand the characteristics and behavior of the function over the specified interval.

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Answer:

The average rate of change is: 0.25

Step-by-step explanation:

Given

See attachment for graph

Required

The average rate of change between 1930 and 1950

Average rate of change (m) is calculated as:

\(m = \frac{f(b) - f(a)}{b - a}\)

In this case,

\([a,b] = [1930,1950]\)

So, we have:

\(m = \frac{f(1950) - f(1930)}{1950 - 1930}\)

\(m = \frac{f(1950) - f(1930)}{20}\)

From the attached graph;

\(f(1950) = 45\)

\(f(1930) = 40\)

So, we have:

\(m = \frac{45- 40}{20}\)

\(m = \frac{5}{20}\)

\(m = 0.25\)

Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S and q is _____ the force exerted between S and p

a. 1/2

b. 2 times

c. 1/4

d. 4 times

Answer:

4 times

Step-by-step explanation:

Given the following :

Distance between q and S (r) = 1 unit

Distance between P and S (r) = 2 × 1 unit = 2

According to coliumbs law:

F = Ke(q1q2) /r^2

Where F = electrostatic force, Ke = coloumbs constant

q1,q2 = charges, r = distance between two charges

For q and S :

Fsq = Ke(q1q2) / 1^2

Fsq = Ke(q1q2) - - - - - equation 1

For P and S :

Fsp = Ke(q1q2) / 2^2

Fsp = Ke(q1q2) / 4 - - - - - equation 2

Dibiding equation 1 by equation 2

Fsq/Fsp = Ke(q1q2) / Ke(q1q2)/4

Fsq / Fsp = Ke(q1q2) × 4 / Ke(q1q2)

Fsq / Fsp = 4 / 1

Using cross multiplication

Therefore, Fsq = 4 × Fsp

Answer:

Step-by-step explanation:

Answer:

Find the indicated sum for each geometric series.

{1875+750+300+⋯+3.072}

Answer: 3122.952

Step-by-step explanation:

{1875+750+300+⋯+3.072}

r=0.4 3.072=1875(0.4)n−1

0.0016384=(0.4)n−1

7=n−1→n=8

Sn=1875(1−(0.4)8)1−0.4=3122.952

I think is like this.

Answer:

2.5×10 to the sixth power

Step-by-step explanation:

6÷2.4=2.5

10^9÷10^3=6

Answer:

\(x=14\)

Step-by-step explanation:

\(\angle TPR=8x+7-75=360-150-91-75\\8x=112\\x=14\)

In order to determine which of the potential employees should be offered the job, we need to compare their scores in relation to the mean and standard deviation of their respective versions of the aptitude test.

Vincent scored 83.5 on his version of the test, which has a mean of 68.2 and a standard deviation of 9. This means that Vincent's score is 1.72 standard deviations above the mean (z-score = (83.5-68.2)/9).
Kaitlyn scored 251.2 on her version of the test, which has a mean of 238 and a standard deviation of 22. This means that Kaitlyn's score is 0.6 standard deviations above the mean (z-score = (251.2-238)/22).

Reyna scored 8.04 on her version of the test, which has a mean of 7.2 and a standard deviation of 0.7. This means that Reyna's score is 1.2 standard deviations above the mean (z-score = (8.04-7.2)/0.7).
Based on these calculations, it is clear that Kaitlyn performed the best on the aptitude test, as her score was the furthest above the mean in terms of standard deviations. Therefore, if the company prefers to fill the position with the applicant who performed best on the aptitude test, Kaitlyn should be offered the job.

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Answer:

x-3y-7=0

Step-by-step explanation:

2x-6y=14

2x-6y-7=0

x-3y-7=0

Answer:

50 of 300 times

Step-by-step explanation:

Answer:

Step-by-step explanation:

The No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases.

In statistics, the No Information Rate (NIR) is a measure of the accuracy of a classification model that predicts the most frequent class as the outcome for all cases. It represents the accuracy rate that can be achieved by simply guessing the most frequent outcome without using any predictive model or variable.

The NIR is commonly used as a benchmark for evaluating the performance of classification models, as any model that performs worse than the NIR is considered to be poorly performing. Conversely, a model that performs better than the NIR is considered to have some predictive power beyond simply guessing the most frequent outcome.

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============================================

Explanation:

On that diagram, the unmarked angle above the (6x-8) is equal to (5x+12). This is because the unmarked angle and the angle marked with (5x+12) are corresponding angles. Corresponding angles must be congruent if you want line m to be parallel to line n.

From here we add up (5x+12) and (6x-8) and set that sum equal to 180. Solve for x

We get the following:

(5x+12)+(6x-8) = 180

5x+12+6x-8 = 180

(5x+6x)+(12-8) = 180

11x+4 = 180

11x = 180-4

11x = 176

x = 176/11

x = 16

The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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The supplied returns' variance is around 0.02495.

To calculate the variance, we need to follow these steps:

Step 1: Calculate the average return (mean) of the given returns.

Step 2: Calculate the squared differences between each return and the mean.

Step 3: Calculate the average of the squared differences, which gives us the variance.

Let's perform these calculations:

Step 1:

Average return (mean) = (16% + 6% - 25% - 3%) / 4 = -6%

Step 2:

Squared differences:

(16% - (-6%))² = (22%)² = 0.0484

(6% - (-6%))² = (12%)² = 0.0144

(-25% - (-6%))² = (-19%)² = 0.0361

(-3% - (-6%))² = (3%)² = 0.0009

Step 3:

Average of the squared differences:

(0.0484 + 0.0144 + 0.0361 + 0.0009) / 4 = 0.0998 / 4 = 0.02495

Therefore, the variance of the given returns is approximately 0.02495.

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Answer:

53 (seconds)

Step-by-step explanation:

Let's calculate each of the boy's time to reach the destination and subtract them from each other to get our answer.

Bill:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + (500+150)^2 = c^2

90000 + 650^2 = c^2 (you're gonna want a calculator)

90000 + 422500 = c^2
512500= c^2

Take the square root of both sides, isolating the variable c:
c= 715.891053 m
round it off: 716 m
c stands for the distance that Bill has to walk. If he is walking at 3 meters per second, we can divide to get the number of seconds:

716 / 3 = 238.666667 seconds to get to the playground
round it off: 239

Ted:
Using the Pythagorean Theorem, a^2 + b^2 = c^2
Plugging in:
300^2 + 500^2 = c^2

90000 + 250000 = c^2

340000=c^2

Take the square root of both sides, isolating the variable c:
c= 583.095189 m
round it off: 583 m
c stands for the distance that Ted has to walk. If he is walking at 2 meters per second, we can divide to get the number of seconds:

583 / 2 = 291.5 seconds to get to the playground
round it off: 292

Lastly, subtract the number of seconds it took Ted to the number of seconds it took Bill because Ted took a longer amount of time, and that will be your answer:
292-239= 53

The shorter route 53 seconds faster