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Step-by-step explanation:

Answer:

Step-by-step explanation:

The distance between Afia's school and her babysitter's house is 16 units.

Distance is a measurement of how far away two things or locations are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.

The distance between two points in a coordinate plane can be found using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points, and d is the distance between them.

In this case, the coordinates of Afia's school are (-8, -3) and the coordinates of her babysitter's house are (8, -3).

Plugging these values into the distance formula:

d = √((8 - (-8))^2 + (-3 - (-3))^2)

d = √((8 + 8)^2 + (0)^2)

d = √(16^2)

d = √(256)

d = 16 units

Therefore, the distance between Afia's school and her babysitter's house is 16 units.

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=> n-4<5

=> n-4+4<5+4

=> n<9

After integrating the expression  [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex] we will get the value as: [tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]

Integration by parts, also known as partial integration, is a technique used in calculus and more widely in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.

The integration of the result of two functions is the integration by parts. Typically, the two functions are shown as f(x) and g. (x). The first function, f(x), is chosen from the two functions in such a way that its derivative formula exists, while the second function, g(x), is chosen in such a way that its integral formula exists.

∫ f(x).g(x).dx = f(x) ∫ g(x).dx - ∫(f'(x) ∫g(x).dx).dx + C

We have, [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]

We know that

[tex]\frac{1}{x}=arccot(x) \\I=5 \int_1^{\sqrt{3}} arccot(x) dx[/tex]

Integrating by parts

[tex]$$\int f g^{\prime}=f g-\int f^{\prime} g$$[/tex]

let  us assume that,

[tex]$\quad f=\cot ^{-1}(x) \quad g^{\prime}=1$[/tex]

[tex]$I=5 \int_1^{\sqrt{3}} \cot ^{-1}(x) d x$[/tex]

[tex]$I=5\left[x \cot ^{-1}(x)-\int \frac{-x}{x^2+1} d x\right]$[/tex]

[tex]$I=5\left[x \cot ^{-1}(x)+\frac{1}{2} \ln \left|x^2+1\right|\right]_1^{\sqrt{3}}$[/tex]

[tex]$I=5\left[\left(\sqrt{3} \cot ^{-1}(\sqrt{3})+\frac{1}{2} \ln |4|\right)-\left(\cot ^{-1}(1)+\frac{1}{2} \ln |2|\right)\right]$[/tex]

[tex]$I=5\left[\frac{\sqrt{3} \pi}{6}+\ln 2-\frac{\pi}{4}-\frac{1}{2} \ln |2|\right]$[/tex]

[tex]$I=\left(\frac{5 \sqrt{3}}{6}-\frac{5}{4}\right)^\pi+\frac{5}{2} \ln |2|$[/tex]

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The correct question should be:

Evaluate the integral [tex]$$I=\int_1^{\sqrt{3}} 5 \arctan \left(\frac{1}{x}\right) d x$$[/tex]

By finding the unit rates for the two jars, we will see that the better option is the 28-ounce jar.

To find wich option is the better buy, we need to find the unit rate for each of these jars.

To get the unit rate, we need to take the quotient between the cost of each jar and the volume of peanut butter that each jar has.

We know that the jar of 28 ounces has a cost of $4.29, then its unit rate is:

U =  ($4.29)/28 oz = $0.153 per oz.

This means that with this jar, each ounce costs $0.153

For the 16 ounce jar, the cost is $2.49, then the unit rate is:

U' = $2.49/16 oz = $0.156 per oz.

So here the cost per ounce is larger, then the better option is the 28-ounce jar.

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Answer:

Below

Step-by-step explanation:

Point -4, 6    slope = - 3

Point slope form of the line :      ( y-y1) = m (x - x1)

(y-6) = -3 (x - -4)

y - 6 = -3 (x+4)

Answer:

8, 3

Step-by-step explanation:

28, 23, 18, 13

Subtract each term from the next term.

23 - 28 = -5

18 - 23 = -5

13 - 18 = -5

All differences are equal. When all differences are equal, you have an arithmetic sequence. The equal differences are called the "common difference." To find a new term, add the common difference to the previous term.

13 + (-5) = 13 - 5 = 8

8 + (-5) = 8 - 5 = 3

Answer: 8, 3

The Pythagorean theorem and the above information can be used to deduce that the diagonal SU has a length of 13.

Given :

It is known that RS=12 and ST=5 in the rectangle RSTU.

The steps listed below can be used to calculate the diagonal SU's length:

The Pythagorean theorem can be used to calculate the diagonal SU's length in step 1.

Step 2 - The following is the Pythagorean theorem:

H² = B² + P²

Where B is the base, P is the perpendicular, and H is the hypotenuse.

Step 3: Replace the known terms' values in the aforementioned expression.

SU² = 12² + 5²

Step 4: Condense the previous expression.

SU = √144 + 25

SU = 13

So, the length of the diagonal SU is 13.

The complete question is:

In rectangle RSTU it is known that RS=12 and ST=5. What is the length of diagonal SU?

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Using the law of cosines we know that the outfielder throws the ball 169.26 feet away.

The law of cosines in trigonometry establishes a relationship between a triangle's side lengths and the cosine of one of its angles.

According to the Law of Cosines, c2=a2+b22ab cosC.

With the exception of the third component, which equals zero if C is a straight angle and the Pythagorean Theorem results, this is similar to the Pythagorean Theorem.

So, here, the pitcher's mound is 60.5 feet away from home plate.

Additionally, the ball traveled 216 feet when it was struck by the bat.

Allow the outfielder to toss the ball x feet away.

According to the diagram below:

x² = 216² + 60.5² - 2 * 216 * 60.5 * cos34°

x = 169.258748677 ⇒ 169.26 feet

Therefore, using the law of cosines we know that the outfielder throws the ball 169.26 feet away.

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Correct question:

Use the law of cosines to solve the problem. On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher's mound. an outfielder catches the ball and throws it to the pitcher. how far does the outfielder throw the ball?

Answer:20

Step-by-step explanation: 5+5+5+5

Answer:

4 times 5 is equal to 20.

Step-by-step explanation:

If in rectangular park that is 63 yards by 16 yards, a dog began in the northwest corner and ran south along the length of the park and Finally, the dog ran back to the northwest corner. The dog ran 65 yards.

Distance can be defined as how far an object is from another object.

Using the Pythagoreans theorem to find the distance

c² = √a² + b²

Let plug in the formula

c² = √63² + 16²

c² = √3,969 + 256

c = √4,225

c = 65 yards

Therefore the distance is 65 yards.

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So on solving the provided question we can say that here, coefficient of x² in 3x³+ 2x² -x+ 1 is 2

A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include:  The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example  Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.

here,

coefficient of x² in 3x³+ 2x² -x+ 1 is 2

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Answer:

  a.  x²

  b.  144 cm²

Step-by-step explanation:

You want to know an expression for the area of the four white triangles in the given figure, and you want to know that area when x = 12 cm.

If you draw horizontal and vertical lines through the middle of the figure, you can see that for each white triangle there is a matching shaded triangle. That is, the shaded area is equal to the white area.

The shaded area is the square of the length of the side of the shaded square, so is ...

  shaded area = x²

The white area is the same, so is ...

  white area = x²

Using x = 12 cm, the formula from part (a) tells us ...

  white area = (12 cm)² = 144 cm²

The total area of the four white triangles is 144 cm².

__

Additional comment

The relation between the side lengths of the shaded area and the side length of the total area is ...

  2x/√2 = x+6

This has one solution: x = 6/(√2 -1) ≈ 14.485281 (cm).

The figure cannot be drawn to scale for any other value of x, so it is impossible for x=12 cm, unless the outside length is (x+4.97056...)

If you take the white triangles to be isosceles right triangles, each will have an area of A = 1/2bh = 1/2(x/√2)(x/√2) = x²/4. The four of them will have an area of 4(x²/4) = x². If you take the white area to be the overall area less the area of a square of side length x, then the area of the four triangles will be (x+6)² -x² = 12x+36. You will notice that these expressions give different values of the area of the white triangles when x=12. (See the previous comment about the value of x.)

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Answer:

x = 50

Step-by-step explanation:

These two angles are supplementary angles which means their sum is equal to 180°.

We can write the following equation based on this information:

3x+5+x-25 = 180

4x - 20 = 180

4x = 200

x = 50

So on solving the provided question we cans ay that by unitary method earns 47 hours = 15.34375 * 47 = $721.15625

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

so here,

She earns a fixed salary for the first  = 40hours.

he worked  and earned $613.75

earns per hour = 613.75/40 = 15.34375

earns 47 hours = 15.34375 * 47 = $721.15625

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The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.

The values of variables that satisfy the given quadratic equation are known as its roots. In other words, x = α is a root of the quadratic equation f(x) if f(α ) = 0. The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersects the x-axis.

To find  sum and the product we first need to find roots/zeroes of the quadratic equation 2x² − 6x + 1 = 0, i.e.

⇒ 2x² − 6x + 1

⇒ 2x²−6x + 1

Putting them in quadratic equation

[tex]$ \Rightarrow x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}[/tex]

[tex]$ \Rightarrow x={\frac {-(-6)\pm {\sqrt {(-6)^{2}-4(2)(1)}}}{2(2)}}[/tex]

[tex]$ \Rightarrow x = \frac{3 -\sqrt{7} }{2}[/tex], [tex]$ \Rightarrow x_2 = \frac{3 +\sqrt{7} }{2}[/tex]

⇒ x = 0.177124,  x₂ = 2.822876

⇒ x = 0.18,  x₂ = 2.82

The sum of the equation roots of 2x² − 6x + 1 = 0 is

0.18 + 2.82 = 3

The Product of the equation roots of 2x² − 6x + 1 = 0 is

0.18 × 2.82 = 0.5076

Thus, The sum of the roots of 2x² − 6x + 1 = 0 is 3 and the product is 0.5076.

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Yes, 4x is an exponential function. An exponential function is one where there is a constant being raised to a variable.

Exponential functions involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round. if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function. The exponential function is a type of mathematical function which are helpful in finding the growth or decay of population, money, price that are growing or decay exponentially. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. it can be extended to the complex numbers or generalized to other mathematical objects like matrices.

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he system of equations used to represent this scenario is y = –x + 10 and y = 4x, where x and y are the two numbers.

To find the larger number, we can solve the system of equations by setting y = 4x in the first equation and solving for x.

y = –x + 10

4x = –x + 10

3x = 10

x = 10/3

So the smaller number is 10/3. To find the larger number, we know that it is 4 times the smaller number, which is 4(10/3) = 40/3.

Therefore, the larger number is 40/3.

Answer:

The larger number = 8

Step-by-step explanation:

Below is the system of equations:

y = -x + 10

y = 4x

Since both equations equal "y", we can set them equal to each other:

4x = -x + 10

4x + x = 10

5x = 10

x = 2              

This means that at x = 2, the y-values of both equations are the same and is when the criteria of "the sum of two numbers are 10 and the larger number is 4 times the smaller number" is met

"x" is the smaller number. To find the bigger number, input "x" into either one of the equations in the system:

y = 4(2) = 8

Hence option b is the correct option i.e The sample mean's sampling distribution will be roughly normal.

The appropriate response to the question about Sampling Distributions is The sample mean will have a sampling distribution mean that is identical to the population mean.

The sampling distribution must then resemble the normal distribution as the sample size grows.

According to this, if the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or any other distribution.

A bell-shaped, symmetrical distribution known as a normal distribution has fewer observations the farther out from its center.

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Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.

Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.

given

consider the triangles ABC and ACD

from the figure

∠DAC = 36°

∠CAB = 68°

AD = 35 m

we have to find the height of the cliff i.e. he length BC

i.e. the length BC

cosθ = adjacent side / hypotenuse

cos36° = 35 / AC

AC = 43.21 m

tan68° = BC / 43.21

BC = 43.21 * 2.47 = 106.73 m

Ann and Byron set up shop 35 meters apart on one side of a creek, with the height of the cliff on the other side of the stream being 106.73 meters.

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The mean of Evelyn’s scores based on the information will be 138.

From the information, Robin and Evelyn are playing a target game, the object of the game is to get an object as close to the center as possible and each player’s score is the number of centimeters away from the center.

It should be noted that Robin and Evelyn’s results from five rounds are shown. The mean simply means the average of the numbers.

The mean of Evelyn’s scores based on the information will be:

= (125 + 137 + 138 + 145 + 145) / 5

= 690/5

= 138

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Answer:

  p:q:r = 12:15:10

Step-by-step explanation:

Given p:q = (2/3):(5/6) and q:r = (3/4):(1/2), you want p:q:r.

We can turn each ratio into a ratio of integers by multiplying by the least common denominator.

  p:q = 4:5 . . . . . . . multiply the given ratio by 6

  q:r = 3:2 . . . . . . . multiply the given ratio by 4

Now, we need to have q be represented in each ratio by the same number. That number will be the least common multiple of its representations in these ratios: LCM(5, 3) = 15.

Multiplying the first ratio by 3, we have ...

  p : q = 12 : 15

Multiplying the second ratio by 5 gives ...

  q : r = 15 : 10

Now, we can write the ratio of interest:

  p : q : r = 12 : 15 : 10

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Since ​14​ is equivalent to 8x, that number must be 14 ÷ 8. Then ​14 ÷ 8 = x, because of the inverse relationship between multiplication and division.

There are 4 basic mathematical operations which are addition, subtraction, division and multiplication.

Multiplication and division are inverse operations because multiplication undoes division and also division undoes multiplication.

We want to find the quotient of 14 and 8. This is expressed as 14 ÷ 8.

Now, we are told to consider that some number times 8 equals ​14. Let the number be x and as such we have;

8x = 14

Now, since 14 is equal to 8x, then that number must be gotten by using the inverse relationship by multiplying both sides by 1/8 to get;

x = 14/8

Finally, ​14÷8 = x because of the inverse relationship between multiplication and division.

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Answer:

m∠1 = 32

Step-by-step explanation:

∠WXZ = 115

m∠2 = m∠1 + 51

x + x + 51 = 115

2x + 51 = 115

2x = 64

x = 32

The given statement "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)" is true.

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the x-axis is (x, -y).

The given statement is "If point (x, y) is reflected over the x-axis, the resulting point is (-x, y)".

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Therefore, the given statement is true.

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The midline theorem claims that cutting along the midline of a triangle creates a segment that is parallel to the base and half as long.

The condition for the midline theorem is that the two triangles must have the same size and shape, so all three sides have the same length, and all three angles have the same measure.

For the theorem, we draw a line through two points on either side of the triangle and then we prove that the line divides the sides into equal halves. Once proven that the sides are in two equal halves using congruency it is proved that the base and midline are parallel.

Since the base and midline are parallel to each other using the SAS rule of congruency therefore according to the theorem the segment is half as long as the base.

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The exponential of 16, also known as [tex]e^{16[/tex], is the value of the mathematical constant e (approximately equal to 2.71828) raised to the power of 16.

To calculate e^16, we would use the following formula:

[tex]e^{16[/tex] = e x e x e x e x e x e x e x e x e x e x e x e x e = 8.222838 x [tex]10^6[/tex]

So, the exponential of 16 is approximately 8.222838 x [tex]10^6[/tex].

It's important to note that the exponential value of any number is a real number, the value of e is raised to the power of that number. The mathematical constant e, also known as Euler's number, is an important number in mathematics and is used in various branches such as calculus, statistics and probability. It has also been used in physics and engineering, it appears naturally in many processes such as radioactive decay, natural growth and decay of populations, and more.

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Answer:

Step-by-step explanation: v = 1/3π[tex]r^{2}[/tex]h

[tex]\frac{1}{3}[/tex]π([tex]1.5^{2}[/tex]) x 15

[tex]\frac{1}{3}[/tex]π x 2.25 x 15

=35.34291