Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of longest side is unknown.

What is the smallest possible whole-number length of the unknown side?

The complete equation is:

-75 ÷ 15 = (-75 ÷ 15) + (-30 ÷ -0.1333)

To fill in the missing numbers, let's solve the equation step by step.

We start with:

-75 ÷ 15 = ( ÷ 15) + (-30 ÷ )

First, let's simplify the division:

-75 ÷ 15 = -5

Now we have:

-5 = ( ÷ 15) + (-30 ÷ )

To find the missing numbers, we need to make the equation true.

Since -5 is the result of -75 ÷ 15, we can replace the missing number in the first division with -75.

-5 = (-75 ÷ 15) + (-30 ÷ )

Next, let's simplify the second division:

-30 ÷ = -2

Now we have:

-5 = (-75 ÷ 15) + (-2)

To find the missing number, we need to determine what value divided by 15 equals -2.

Dividing -2 by 15 will give us:

-2 ÷ 15 ≈ -0.1333 (rounded to four decimal places)

Therefore, the missing number in the equation is approximately -0.1333.

The complete equation is:

-75 ÷ 15 = (-75 ÷ 15) + (-30 ÷ -0.1333)

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The integral ∫213cos(x)dx evaluates to 106.5sin(x)cos(x) + C, where C is the constant of integration.

Given, we need to first make a substitution and then use integration by parts to evaluate the integral ∫213cos(x)dx.Let's make the substitution u = sin x, then du = cos x dx.So, the integral becomes ∫213cos(x)dx = ∫213 cos(x) d(sin(x)) = 213 ∫sin(x)d(cos(x))Using integration by parts, let u = sin x, dv = cos x dx, then du = cos x dx and v = sin x213 ∫sin(x)d(cos(x)) = 213(sin(x)cos(x) - ∫cos(x)d(sin(x)))= 213(sin(x)cos(x) - ∫cos(x)cos(x)dx)= 213(sin(x)cos(x) - ∫cos²(x)dx)So, ∫cos²(x)dx = 213(sin(x)cos(x) - ∫cos²(x)dx)Or, 2∫cos²(x)dx = 213sin(x)cos(x)Or, ∫cos²(x)dx = 1/2 . 213sin(x)cos(x)Now, substituting u = sin x, we get213 sin(x)cos(x) = 213 u . √(1 - u²)Therefore,∫213cos(x)dx = 1/2 . 213sin(x)cos(x) + C= 1/2 . 213u. √(1 - u²) + C= 106.5 sin(x)cos(x) + C. Hence, the correct option is +C.

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Answer:

Step-by-step explanation:

= > (122°F − 32) × 5/9

= > 50°C...ans

The value of 122°F in °C is 50°C

Temperature is the degree of hotness or coldness in a place. There are different temperature scales such as Celsius, Fahrenheit etc.

To convert from Fahrenheit to Celsius, use:

C = (F - 32) * 5/9

Given that F = 122, hence:

C = (122 - 32) * 5/9 = 50°

The value of 122°F in °C is 50°C

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Answer:

32

Step-by-step explanation:

Pythagorean theorem

\(a^{2} + b^{2} =c^{2}\)

a = perpendicular

b = base

c = hypotenuse

we have to find the hypotenuse

so,

\(13^{2} + 29.25^{2} = c^{2} \\169 + 855.6 = c^{2}\\1024.6 = c^{2}\\\sqrt{1024.6} = \sqrt{c^{2}} \\c = 32\)

Step-by-step explanation:

it's answer is 72 percent

Answer:

the median of th given data is 243

In order to make a the subject of this equation , we need to get a by itself .

The current equation is :

v = u + at

Subtract u on both sides :

v-u=at

Now, divide by t on both sides :

v-u/t=a

\(\boxed{\\\begin{minipage}{3cm}Equation \\ a=$\displaystyle\frac{v-u}{t} $ \\ \end{minipage}}\)

hope helpful ~

Answer:

h=3v/\(\pi\)r

Step-by-step explanation:

Answer:

182

Step-by-step explanation:

152

+31

---------

182

Option (b) is correct that the y-intercept in a regression equation is not represented by Y hat. Here, we will discuss the concept of the y-intercept, regression equation, and Y hat.

Regression analysis is a statistical tool used to analyze the relationship between two or more variables. It helps us to predict the value of one variable based on another variable's value. A regression line is a straight line that represents the relationship between two variables.

Thus, Y hat is the predicted value of Y. It's calculated using the following formulary.

hat = a + bx

Here, Y hat represents the predicted value of Y for a given value of x. In conclusion, the y-intercept is not represented by Y hat. The y-intercept is represented by the constant term in the regression equation, while Y hat is the predicted value of Y.

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Answer:

  5.7y^2 +2y +2

Step-by-step explanation:

You want to simplify the expression 4.7y^2+5.3+4y-3.3-2y+y^2.

Identify like terms and combine their coefficients:

  4.7y^2+5.3+4y-3.3-2y+y^2

  = (4.7 +1)y^2 +(4 -2)y +(5.3 -3.3)

  = 5.7y^2 +2y +2

The number that is a surd is the number that is irrational. The given numbers are being classified as either surd or not a surd below.

A surd is defined as the representation that is made up of square root or cube root for numbers that are not a perfect square or that are irrational.

For example, √7, √3, and √5 is a surd while √4 and √25 is not a surd.

The following numbers are classified as surd or no surd:

√80 = surd.

√2 × √6 = √ 12 = Surd

√216 = surd

2√3× √27 = 2√ 3× 27 = 2√ 81 = 2 × 9 = 18 = Not sure

2√28 = surd

√96 - √ 54 = √ 96-54 = √42 = surd

4√169 = 4× 13 = 52 = Not surd

√108 - 2√27 = 2√108-27 = 2√ 81 = 2*9 = 18 = Not surd

√30/√6 = √5= Surd

2/3√45 + 1/2√80 = surd

√75/√3 = √25 = 5 = Not surd

√126/√7-√162 = Surd

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Answer: 102

Step-by-step explanation:

Answer:

The translation corresponds to a translation of 13 units to the right

Step-by-step explanation:

Translation of a Graph

If the graph of

y=f(x) is translated a units horizontally, then the equation of the translated graph is

y =f(x - a)

The value of a is considered positive for translations to the right.

The parent function is

y = x

and the given function is

y = x - 13

The translation corresponds to a translation of 13 units to the right

Answer:

h(4)= -2

Step-by-step explanation:

plug in 4 into the x:

h(4)=-4+2=-2

Answer:

Step-by-step explanation:

5:6

6=384

5=

5×384÷6=320

Boys =302

Answer:

5n - 2

Step-by-step explanation:

8 subract 3 is 5

5 minus 3 is 2

5n - 2

Answer:

A”(-3, -18) B” (0, -27) C” (-12, -30)

Step-by-step explanation:

Two transformations have been listed beneath the graph. Complete them in order to get the solution.

The first transformation is a translation. A translation involves moving the shape across the graph without altering its form. To receive the coordinates for this. Add the <-3, -8> given to coordinates A, B, and C. Which should result in the following: A (-1, -6) B (0, -9) C (-4, -10)

Now complete the second transformation, which is a dilation. Dilations happen when a shape is either made smaller or larger by a set number. To complete the second transformation: take the number given: “3” and multiply each number in the coordinate sets you got after the first transformation by this number.

Which should result in: A”(-3, -18) B” (0, -27) C” (-12, -30)

(a) The limit lim(x→2) (\(x^2\) - 2x)/(x - 2) leads to the indeterminate form 0/0. Evaluating the limit gives 2.

(b) The limit lim(x→0) h[(1 + h)\(^2\) - 1] leads to the indeterminate form 0/0. Evaluating the limit gives 0.

(c) The limit lim(h→0) (h(a + h) - (a + 1))/(\(h^2\) + 1) leads to the indeterminate form 0/0. Evaluating the limit gives 0.

(d) The limit lim(x→-3) (x + 3)/(x + 4)\(^(-1)\) leads to the indeterminate form 0/0. Evaluating the limit gives 0.

(a) To evaluate the limit, we substitute 2 into the expression (\(x^2\) - 2x)/(x - 2). This results in (\(2^2\) - 2(2))/(2 - 2) = 0/0, which is an indeterminate form. However, after simplifying the expression, we find that it is equivalent to 2. Therefore, the limit is 2.

(b) Substituting 0 into the expression h[(1 + h)\(^2\)- 1] yields 0[(1 + 0)^2 - 1] = 0/0, which is an indeterminate form. By simplifying the expression, we obtain 0. Hence, the limit evaluates to 0.

(c) By substituting h = 0 into the expression (h(a + h) - (a + 1))/(h\(^2\) + 1), we get (0(a + 0) - (a + 1))/(0\(^2\) + 1) = 0/1, which is an indeterminate form. Simplifying the expression yields 0. Thus, the limit is 0.

(d) Substituting -3 into the expression (x + 3)/(x + 4)\(^(-1)\), we obtain (-3 + 3)/((-3 + 4)\(^(-1)\)) = 0/0, which is an indeterminate form. After evaluating the expression, we find that it equals 0. Hence, the limit evaluates to 0.

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The true statement about the linear functions is the last one:

The x-intercept of g(x) is twice the x-intercept of h(x), so the correct option is the last one.

Here we have the two linear functions:

h(x) = -3x + 2

g(x) = 3x - 4

Remember that the general linaer function is:

f(x) = ax + b

Where a is the slope and b is the y-intercept.

We can see that the slope of h(x) is the -1 times the slope of g(x), so the graphs don't have the same slope.

The x-intercepts are:

h(x) = 0 = -3x + 2

        -2 = -3x

        -2/-3 = x

         2/3 = x

g(x) = 0 = 3x - 4

         4 = 3x

         4/3 = x

So we can see that the x-intercept of g(x) is twice the x-intercept of h(x), so the correct option is the last one.

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Answer: Quotient 142

Remainder 12

Step-by-step explanation:

The quotient is 142 and  the remainder is 12.

The long division method is as follows :

                                             \(142\)

                                      \(39\sqrt{5550}\)  

                                          -39                        

                                             165                       (3rd 5 taken down )

                                           -156    

                                                 90                     ( 0 taken down )

                                                -78  

                                                  12

step 1 : take the first two digits (55) of the divident , now multiply 39 with such a number that the product of those two must not go above 55 but should be closest to it.

step 2 : write the number on top and subtract the answer from 55.

step 3 :  Now bring down the third 5 and write it after the answer of the subtraction. So the number becomes 165.

step 4 : Again multiply 39 with such a number that the product of those two must not go above 165 but should be closest to it.

step 5 : write that number on top after the previous number and subtract the answer from 165.

step 6 : Now bring down the 0 and write it after the answer of the subtraction. So the number becomes 90.

step 7 : Again multiply 39 with such a number that the product of those two must not go above 90 but should be closest to it.

step 8 : write that number on top after the previous number and subtract the answer from 90.

We have to repeat these steps until all the digits from the divident are used and the remainder comes out to less than the divisor.

Here all the digits of divident are used and the remainder (12) is also less than the divisor (39), so we stopped.

Hence the quotient is 142 and the remainder is 12.

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The long term rate is defined by r = 3/2.

Probability deals with the likelihood of an event or phenomena occurring and is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurrence and 1 denotes the certain outcome of an event. Joint probability refers to a statistical measure that determines the probability of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs. Hence, joint probability is a measure of two events happening at the same time and can only be applied to situations where more than one observation can occur at the same time.

A random variable with probability density function is f(x) = 2x, 0 <x<1.

Let Xi denote the life-time of the ith component , then Sn = ∑Xi represents the time of the nth failure. The long-term rate failures occur, is defined by

\(r = \lim_{n \to \infty} \frac{n}{S_n}\)

Let Xi denote the ith component and understand that X1, X2,.., is a sequence of independent and similarly distributed random variables, with finite mean.

\(Mean = E[Xi] = \int\limits^0_1 {xf(x)} \, dx = \int\limits^0_1 {2x^{2} } \, dx = \frac{2}{3}\)

So,

\(r = \lim_{n \to \infty} \frac{n}{S_n} = \frac{1}{Mean} = \frac{3}{2}\)

Thus, the long term rate is defined by r = 3/2.

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The long term rate is defined by r = 3/2.

Probability deals with the likelihood of an event or phenomena occurring and is quantified as a number between 0 and 1 inclusive, where 0 indicates an impossible chance of occurrence and 1 denotes the certain outcome of an event. Joint probability refers to a statistical measure that determines the probability of two events occurring together and at the same point in time. Joint probability is the probability of event Y occurring at the same time that event X occurs. Hence, joint probability is a measure of two events happening at the same time and can only be applied to situations where more than one observation can occur at the same time.

A random variable with probability density function is f(x) = 2x, 0 <x<1.

Let Xi denote the life-time of the ith component , then Sn = ∑Xi represents the time of the nth failure. The long-term rate failures occur, is defined by

\(r = \lim_{n \to \infty} \frac{n}{S_n}\)

Let Xi denote the ith component and understand that X1, X2,.., is a sequence of independent and similarly distributed random variables, with finite mean.

\(Mean = E[X_i] = \int\limits^0_1 {x} f(x) \, dx =\int\limits^0_1 {2x^2} \, dx =\frac{2}{3}\)

So,

\(r = \lim_{n \to \infty} \frac{a_n }{S_n} = \frac{1}{mean} = \frac{3}{2}\)

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Let's assume the number of boys in Stephen's class is B. According to the given information, the number of girls in the class exceeds the number of boys by 8. Therefore, the number of girls would be B + 8.

The total number of pupils in the class is given as 36. We can write this as an equation:

B + (B + 8) = 36

Simplifying the equation, we have:

2B + 8 = 36

2B = 36 - 8

2B = 28

B = 28/2

B = 14

So, there are 14 boys in Stephen's class. Since the number of girls exceeds the number of boys by 8, the number of girls would be 14 + 8, which is equal to 22.

Therefore, there are 14 boys and 22 girls in Stephen's class.

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The population is the entire set of individuals or items of interest in a particular study, and it is not necessarily the same size as the sample which is a subset of the population.

Population is a term used to refer to the entire set of individuals or items that are of interest in a particular study. Population size is not necessarily the same as sample size. Sample size is the number of individuals or items that are selected from the population to participate in the study. The sample may be selected randomly, or it may be selected based on specific criteria. When collecting data, researchers use the sample as a representation of the population in order to identify patterns, relationships, and trends that can be used to make inferences about the population. When constructing a sample, it’s important to make sure that it is random and representative of the population, otherwise the results of the study may be biased.

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Answer: 1067/10000 is a fraction in simplest form. where, 0.1067 is a decimal, 10.67% is a percentage.

Step-by-step explanation:

Answer:

Dad=35, Son=15

Step-by-step explanation:

Well since the dad is 20 year older then the son we can call the son x and the dad x+20. Now five years ago the father was 3 times older then the so we construct the following equation:

x+20−5=3(x−5)

x+15=3x-15

x=15

So now we know that the sons age is 15 meanimg that since the dads 20 years older then him, his age is 20+15 which is 35!

Answer:

B

Step-by-step explanation:

the absolute value function always gives a positive result

However, the value inside can be positive or negative, that is

5x + 30 = 10x or - (5x + 30) = 10x

solving both

5x + 30 = 10x (subtract 5x from both sides )

30 = 5x ( divide both sides by 5 )

6 = x

or

- (5x + 30) = 10x

- 5x - 30 = 10x ( add 5x to both sides )

- 30 = 15x ( divide both sides by 15 )

- 2 = x

As a check

substitute these values into the equation and if both sides are equal then it is a solution.

x = 6

left side = | 5(6) + 30 | = | 30 + 30 | = | 60| = 60

right side = 10(6) = 60

Then x = 6 is a solution

x = - 2

left side = | 5(- 2) + 30 | = | - 10 + 30 | = | 20 | = 20

right side = 10(- 2) = - 20 ≠ 20

Thus x = - 2 is an extraneous solution

Answer:

a)  The intercepts of the graph are (-75, 0), (75, 0), (0, -75) and (0, 75).

b)  The radius is 75 miles.

c)  The area of the region is 17,671 square miles (to the nearest square mile).

Step-by-step explanation:

The x-intercepts are the points at which the graph crosses the x-axis, so when y = 0. Therefore, to find the x-intercepts, substitute y = 0 into the given equation.

\(\implies x^2+y^2=5625\)

\(\implies x^2+(0)^2&=5625\)

\(\implies x^2&=5625\)

\(\implies x&=\sqrt{5625}\)

\(\implies x&=\pm75\)

The y-intercepts are the points at which the graph crosses the y-axis, so when x = 0. Therefore, to find the y-intercepts, substitute x = 0 into the given equation.

\(\implies x^2+y^2=5625\)

\(\implies (0)^2+y^2&=5625\)

\(\implies y^2&=5625\)

\(\implies y&=\sqrt{5625}\)

\(\implies y&=\pm75\)

Therefore, the intercepts of the graph are:

\(\hrulefill\)

The general equation of a circle is:

\((x-h)^2+(y-k)^2=r^2\)

where (h, k) is the center and r is the radius of the circle.

By comparing the given equation with the general equation:

Take the positive square root of r² to find the radius of the circle (since length cannot be negative):

\(\implies r=\sqrt{5625}\)

\(\implies r=75\)

Therefore, the radius of the circle is 75 miles.

\(\hrulefill\)

The formula for the area of a circle is:

\(A=\pi r^2\)

where r is the radius.

To find the area of the region in which the broadcast from the station can be picked up, find the area of the circle with the radius from part b, r = 75:

\(\implies A= \pi \cdot 75^2\)

\(\implies A=5625 \pi\)

\(\implies A=17671.4586...\)

Therefore, the area of the region is 17,671 square miles (to the nearest square mile).

Answer:

Step-by-step explanation:

To find:-

Answer:-

The given equation of the circle is ,

\(:\sf\implies x^2 + y^2 = 5625 \\\)

\(\rule{200}2\)

G R A P H : -

\(\setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\vector(1,0){6}}\put(0,0){\vector(-1,0){6}}\put(0,0){\vector(0,1){6}}\put(0,0){\vector(0,-1){6}}\put(.2,2.5){$\sf (0,75)$}\put(.2, - 2.7){$\sf (0,-75)$}\put(2.5,0.2){$\sf (75,0)$}\put( - 4.2,.2){$\sf ( - 75,0)$}\put(4,4){$\bigstar \: \: \sf Centre = (0,0) $}\put(4,3){$\bigstar \: \: \sf Radius = 75\ miles $}\put(4,-4){$\boxed{\bf \textcopyright \: \: Tony Stark }$}\end{picture}\)

\(\rule{200}2\)

Answer a :-

The intercepts are the points at which the circle cuts the x-axis and y-axis . At x intercept , the value of y coordinate becomes 0 and at y intercept the x coordinate becomes 0 .

So for finding x intercept , plug in y = 0 , in the given equation of circle, as ;

\(:\sf\implies x^2 + (0)^2 = 5625 \\\)

\(:\sf\implies x^2 = 5625 \\\)

\(:\sf\implies x =\sqrt{5625} \\\)

\(:\sf\implies x =\pm 75 \\\)

\(:\sf\implies \red{ x = +75 , -75} \\\)

Hence the circle cuts the x-axis at (75,0) and (-75,0).

To find out y intercept plug in x = 0 in the given equation of the circle as ,

\(:\sf\implies (0)^2 + y^2 = 5625 \\\)

\(:\sf\implies y^2 = 5625 \\\)

\(:\sf\implies y=\sqrt{5626}\\\)

\(:\sf\implies y = \pm 75 \\\)

\(:\sf\implies \red{ y = +75,-75} \\\)

Hence the circle cuts the y-axis at (0,75) and (0,-75).

\(\rule{200}2\)

Answer b :-

Next we are interested in finding out the radius of the circle, for that we need to compare the given equation of circle to the standard equation of circle .

Standard equation of circle :-

\(:\sf\implies \red{ (x-h)^2 + (y-k)^2 = r^2}\)

where ,

We can rewrite the given equation of circle as ,

\(:\sf\implies (x-0)^2 + (y-0)^2 = 5625 \\\)

\(:\sf\implies (x-0)^2+(y-0)^2 = 75^2\\\)

On comparing to the standard form, we have;

\(:\sf\implies \red{ radius = 75\ miles } \\\)

Hence the radius of the circle is 75miles .

\(\rule{200}2\)

Answer c :-

To find out the area we can use the formula of area of circle , which is ;

\(:\sf\implies \red{Area=\pi(radius)^2} \\\)

We already got the radius to be 75 miles in the previous part of the question. Plugging in that value would give us the area , as ;

\(:\sf\implies Area =\pi (75\ miles )^2 \\\)

\(:\sf\implies Area = \dfrac{22}{7}\times 5625\ miles^2\\\)

\(:\sf\implies \red{ Area = 17678.57 \ miles^2 } \\\)

Hence the area of the circle is 17678.57 miles² .

The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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