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Answer:

8

Step-by-step explanation:

Answer: B. 26

Step-by-step explanation:

The options are:

A. 21

B. 26

C. 9

D. 15

Let the third side of the triangle be x.

Since the two sides of a triangle measure 17 inches and 9 inches, therefore we can form a triangle inequality with the figures given. This would be:

x + 9 > 17

x > 17 - 9

x > 8

Also,

x < 9 + 17

x < 26

Therefore, 8 < x < 26

Therefore, the answer is 26.

Answer:

see below

Step-by-step explanation:

The 95% confidence interval for the mean weight of salt in packages marked 500g is (498.59g, 503.41g).

To calculate the confidence interval, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard deviation / sqrt(sample size))

First, we need to calculate the sample mean, which is the average of the weights:

Sample Mean = (498 + 502 + 505 + 503 + 495 + 499 + 501 + 502 + 505 + 499 + 503) / 11 = 501.36g

Next, we need to calculate the standard deviation of the sample. We can use the formula for the sample standard deviation:

Sample Standard Deviation = sqrt((sum of (weight - sample mean)^2) / (sample size - 1))

Plugging in the values, we get:

Sample Standard Deviation = sqrt(((498-501.36)^2 + (502-501.36)^2 + ... + (503-501.36)^2) / (11-1)) = 3.21g

The critical value for a 95% confidence interval can be obtained from the t-distribution table or using statistical software. For a sample size of 11 and a confidence level of 95%, the critical value is approximately 2.228.

Finally, we can calculate the confidence interval:

Confidence Interval = 501.36g ± (2.228 * 3.21g / sqrt(11)) ≈ (498.59g, 503.41g)

This means that we are 95% confident that the true mean weight of salt in packages marked 500g lies between 498.59g and 503.41g.

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The average rate of change is -0.1295, under the condition the given exponential decay function is f (t) = 2(0. 95).

In order to find the average rate of change from x=0 to x=4 for the given exponential decay function \(f(t) = 2(0.95)^{t}\), we need to find the slope of the line that passes through the points (0,f(0)) and (4,f(4)).

f(0) = 2(0.95)⁰ = 2

f(4) = 2(0.95)⁴ ≈ 1.482

The slope of the line passing through these two points is:

(f(4) - f(0))/(4 - 0)

= (1.482 - 2)/4

≈ -0.1295

Therefore, the average rate of change from x=0 to x=4 is approximately -0.1295.

An exponential decay function is a form of a function that reduces at a constant rate over time. It is a type of  mathematical model used to present many real-world phenomena such as radioactive decay, population growth, and the depreciation of assets.

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Answer:

Your just going to keep adding 3 and the 2 is there because you had negative -1 and then you added 3 so hope this helps probably not what you looking for but hope this helps. Have a good day.

Step-by-step explanation:

Answer:

i know right? It's so difficult till I'm brainless when I try to solving it

Answer:

same tbh

Step-by-step explanation:

Answer:

I dont see any question

Step-by-step explanation:

Answer:

where is the question????

Answer:

A.

Step-by-step explanation:

Using the exterior angle theorem of a triangle, the value of x is 6

From the question, we are to determine the value of x in the given triangle

From one of triangle theorems, we have that

"In a triangle, the exterior angle is always equal to the sum of the interior opposite angle"

In the given diagram,

The exterior angle is (17x - 23)°

and

The two interior angles are (8x -4)° and (3x + 17)°

Thus,

From the theorem, we can write that

(17x - 23)° = (8x -4)° + (3x + 17)°

Now, solve for x

17x - 23 = 8x -4 + 3x + 17

Collect like terms

17x - 8x - 3x = -4 + 17 + 23

6x = 36

x = 36/6

x = 6

Hence, the value of x is 6

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If x<y and z>x then the solution is true.

Boolean operators are straightforward words (AND, OR, NOT, or AND NOT) that are used as conjunctions in searches to combine or exclude terms, producing more specialized and useful results.

An expression that may only be evaluated as true or false is called a boolean expression (after mathematician George Boole). Let's examine some examples in everyday language: Pink is one of my favorite colors. I'm apprehensive about programming computers.

From the above theory we can say that

if x=5, y=3 and z=8

and if the conditions are x<y or z>x

Then it is true

as one of them is correct.

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The dimensions of the box that maximize the volume are x = √700 and h = 100 / √700.

To find the largest possible volume of the box, we need to optimize the dimensions of the box. Let's denote the length of each side of the square base as x and the height of the box as h.

The surface area of the box consists of the area of the square base (x^2) and the four sides of the box (4xh). Since the box has an open top, we do not consider the top surface. The total surface area is given as 2100 square centimeters, so we have:

x^2 + 4xh = 2100

To maximize the volume, we need to express the volume of the box (V) in terms of a single variable. The volume of a rectangular prism is given by V = x^2h.

We can rewrite the equation for the surface area to solve for h:

h = (2100 - x^2) / (4x)

Now we can substitute this expression for h in the volume equation:

V = x^2 * [(2100 - x^2) / (4x)]

Simplifying, we have:

V = (1/4) * (2100x - x^3)

To find the maximum volume, we need to find the critical points of this function. We take the derivative of V with respect to x and set it equal to zero:

dV/dx = 2100/4 - (3/4)x^2 = 0

Solving this equation, we find:

2100/4 = (3/4)x^2

x^2 = 700

x = √700

Substituting this value back into the equation for h, we find:

h = (2100 - 700) / (4 * √700) = 1400 / (4 * √700) = 100 / √700

Therefore, the largest possible volume of the box is:

V = (1/4) * (2100 * √700 - 700 * √700) = 350√700 cubic centimeters.

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tan (0.9269428)

Decimal form=1.33235488...

Answer:

the answer is 2.4 .

Step-by-step explanation:

plug in arccos(5/13) in the calculator and u will get 67.380, then plug that value in for tan and you will get 2.4.

Answer:

800 dolls

Step-by-step explanation:

Step one:

given  data

we are told that the ratio of the number of male dolls to the number of female dolls is 3:5 , i.e male dolls to female dolls is 3 to 5

given that there are 500 female dolls, let the number of male dolls be x

Step two:

3/5= x/500

cross multiply we have

3*500=5x

1500=5x

divide both sides by 5

x=1500/5

x=300

hence there are 300 male dolls

The total dolls is 300+500= 800 dolls

Answer:

04x=24

Step-by-step explanation:

04x=24

divide both sides by 4 to let x stand alone

04x÷4=24÷4

x=6

Using the graph and the table given: A) Car 1 will go farther.

In the image given, the table represents the relationship between amount of fuel (x) and distance covered (y) for car 1, while the graph shows that for car 2.

Using any point on the table, (10, 370), find the unit rate for car 1:

Unit rate for car 1 = 370/10 = 37 miles per gallon.

Therefore, for 25 gallons, we would have:

37 × 25 = 925 miles

Car 1 will go 925 miles.

Using any point on the graph, (2, 52), find the unit rate for car 2:

Unit rate for car 2 = 52/2 = 26 miles per gallon.

Therefore, for 25 gallons, we would have:

26 × 25 = 650 miles

Car 2 will go 650 miles.

In conclusion, Car 1 will go farther

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(a) The translational speed of the X-ray source is approximately 8.95 m/s. (b) The angular speed of the X-ray source is approximately 17.98 rad/s. (c) The magnitude of the centripetal force on the X-ray source is approximately 13,872 N. (d) The X-ray source turns approximately 0.634 degrees in 100 milliseconds. (e) The frequency of the rotation of the X-ray source is approximately 10 Hz.

(a) The translational speed of the X-ray source can be calculated using the formula v = d/t, where d is the circumference of the circular ring (2πr) and t is the time it takes to capture one sliced image (350 milliseconds). Substituting the values, we get v = (2π * 40 cm) / (0.35 s) ≈ 8.95 m/s.

(b) The angular speed of the X-ray source can be calculated using the formula ω = θ/t, where θ is the angle covered by the X-ray source in one rotation (360 degrees or 2π radians) and t is the time it takes to capture one sliced image (350 milliseconds). Substituting the values, we get ω = (2π) / (0.35 s) ≈ 17.98 rad/s.

(c) The centripetal force on the X-ray source can be calculated using the formula Fc = mω²r, where m is the mass of the X-ray source (38 kg), ω is the angular speed (17.98 rad/s), and r is the radius of the circular ring (40 cm or 0.4 m). Substituting the values, we get Fc = (38 kg) * (17.98 rad/s)² * (0.4 m) ≈ 13,872 N.

(d) The angle covered by the X-ray source in 100 milliseconds can be calculated using the formula θ = ωt, where ω is the angular speed (17.98 rad/s) and t is the given time (100 milliseconds or 0.1 s). Substituting the values, we get θ = (17.98 rad/s) * (0.1 s) ≈ 1.798 radians. To convert to degrees, we multiply by (180/π), so the angle is approximately 0.634 degrees.

(e) The frequency of rotation can be calculated using the formula f = 1/t, where t is the time it takes to capture one sliced image (350 milliseconds or 0.35 s). Substituting the value, we get f = 1 / (0.35 s) ≈ 10 Hz.

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Answer:

We conclude that option A is true as x = 1 is the root of the polynomial.

Step-by-step explanation:

Given the polynomial

\(f\left(x\right)\:=\:x^2\:+\:2x^2\:-\:x-2\)

Let us determine the root of the polynomial shown below.

\(\:0=\:x^2\:+\:2x^2\:-\:x-2\)

\(0=3x^2-x-2\)

switch sides

\(3x^2-x-2=0\)

as

\(3x^2-x-2=\left(3x+2\right)\left(x-1\right)\)

so the equation becomes

\(\left(3x+2\right)\left(x-1\right)=0\)

Using the zero factor principle

\(3x+2=0\quad \mathrm{or}\quad \:x-1=0\)

solving

\(3x+2=0\)

\(3x=-2\)

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

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

and

\(x-1=0\)

\(x=1\)

The possible roots of the polynomial will be:

\(x=-\frac{2}{3},\:x=1\)

Therefore, from the mentioned options, we conclude that option A is true as x = 1 is the root of the polynomial.

The lengths of the sides are 3 inches, 10 inches, 40 inches, and 17 inches.

To find the lengths of the sides of the quadrilateral, we need to set the sum of the equations equal to the perimeter and solve for x. The equation will be:

X-5 + X+2 + X^2-3x + 2x+1 = 70

Simplifying the equation:

X^2 + X - 72 = 0

We can use the quadratic formula to solve for x:

X = (-b ± √(b^2-4ac))/(2a)

Where a = 1, b = 1, and c = -72

X = (-1 ± √(1^2-4(1)(-72)))/(2(1))
X = (-1 ± √(289))/(2)
X = (-1 ± 17)/(2)
X = 8 or X = -9

Since the length of a side cannot be negative, we will use X = 8. Now we can plug X back into the equations to find the lengths of the sides:

X-5 = 8-5 = 3 inches
X+2 = 8+2 = 10 inches
X^2-3x = 8^2-3(8) = 40 inches
2x+1 = 2(8)+1 = 17 inches

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Answer:

x<11

Step-by-step explanation:

x−4(|−2|)<3

Simplifies to:

x−8<3

Let's solve your inequality step-by-step.

x−8<3

Step 1: Add 8 to both sides.

x−8+8<3+8

x<11

The iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ is 84

The term iterated triple integrals means the result of applying integrals to a function of more than one variable (for example or ) in a way that each of the integrals considers some of the variables as given constants.

Here we have to write six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane XYZ and then we have to evaluate the first integral.

Here in this case we will integrate with respect to y first.

Therefore, the iterated integral that we need to compute is,

∬6xy²dA=∫⁴₂∫₁²6xy²dydx

When we per the first stage integral, then we get,

=> ∫⁴₂ (2xy³)₁²dydx

When we expand it then we get,

=> ∫⁴₂ [16x - 2x] dx

=>  ∫⁴₂ 14x dx

Then we further integrate this one, then we get.,

=>  ∫⁴₂ 14x dx = [7x²]₂⁴

=> [7(4)² - 7(2)²]

=> 112 - 28

=> 84

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The area inside the ellipse can be computed using Green's theorem, which relates the area of a region to a line integral over its boundary.

To apply Green's theorem, we need to parameterize the boundary of the ellipse. Using x(t) = 13cos(t), we can express y in terms of t as y(t) = 6sin(t).

Next, we compute the derivatives dx/dt and dy/dt:

dx/dt = -13sin(t)

dy/dt = 6cos(t)

Substituting these values into the line integral formula, we have:

(1/2) ∫∂D (-ydx + xdy) = (1/2) ∫₀²π (-6sin(t)(-13sin(t)) + 13cos(t)(6cos(t))) dt

= (1/2) ∫₀²π (78sin²(t) + 78cos²(t)) dt

= (1/2) ∫₀²π 78(dt)

= 39π

Thus, the area inside the ellipse, computed using Green's theorem, is 39π square units.

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Answer: 3/5 cm

Step-by-step explanation:

Let the length of the base be x. Then, using the formula for the area of a triangle,

\(\frac{3}{25}=\frac{1}{2} \cdot \frac{2}{5} x\\\\\frac{3}{25}=\frac{1}{5}x\\\\x=\frac{3}{5}\)

The equation that represents the graph is y = -(2/3)x + 6 .

The X- intercept is defined as the point at which the line crosses the x axis.

The Y- intercept is defined as the point at which the line crosses the y axis.

When a and b are the x and y intercept of a line then

the equation of line in intercept form is x/a + y/b = 1 .

Form the graph in the question

we can see that the graph crosses the x axis at 9, so it's x intercept is 9.

and the graph crosses the y axis at 6, so it's y intercept is 6.

So the intercept form of the line will be given by

x/9 + y/6 = 1

taking LCM of 6 and 9 as 18 ,

and solving further we get ,

2x/18 + 3y/18 = 1

(2x + 3y)/18 = 1

2x + 3y = 18

3y = 18 - 2x

Dividing both sides by 3 , we get

y = 18/3 - (2/3)x

y = 6 - (2/3)x

y = -(2/3)x + 6

Therefore , the equation that represents that represents the graph is                  y = -(2/3)x + 6 .

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Answer:

Step-by-step explanation:

Let the equation of the line representing relation between the euros and dollars is,

E = mD + b

Where 'E' = Number of euros

D = Number of dollars

m = slope of the line

b = y-intercept

Slope of a line which passes through two points (120, 90) and (400, 300) will be,

m = \(\frac{y_2-y_1}{x_2-x_1}\) = \(\frac{300-90}{400-120}\)

m = 0.75

Equation of the line passing through (120, 90),

90 = 0.75(120) + b

b = 90 - 90 = 0

Therefore, equation of the line will be,

E = mD

E ∝ D

Here m = Proportionality constant

And the relation between the numbers of Euros and US dollars is a proportional relationship.

Answer:

\(f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)

Step-by-step explanation:

Let f(x) = y

Interchange x and y so

\(x = \frac{1}{\sqrt{y^{3} + 9 } }\)

\(x\sqrt{y^{3} + 9} = 1\)

\(\sqrt{y^{3} + 9 } = \frac{1}{x}\)

\(y^{3} + 9 = \frac{1}{x^{2} }\)

\(y^{3} = \frac{1}{x^{2} } - 9\) = \(\frac{1 - 9x^{2} }{x^{2} }\)

\(y = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)

\(f^{-1} (x) = \sqrt[3]{\frac{1 - 9x^{2} }{x^{2} } }\)

Answer:

8x³ - 22x² + 3x +15

Step-by-step explanation:

I do quick mathz

Answer:

B. rotation

Step-by-step explanation:

A reflection would mean that the shape would be mirrored across the y-axis or the x-axis. A translation means that nothing about the shape changes except for the location. A dilation (not an answer option but still helpful to know) is the change in size of the shape. And finally, the correct answer for this problem, a rotation means that the shape is rotated at a specific point.

I included a picture that uses a shape to help explain this idea. I hope this helps! Have a lovely day!! :)