The ratio table below shows the relationship between the number of packages of gum and the total pieces of gum.
How many pieces of gum are in 4 packages of gum?

9514 1404 393

Answer:

  (d)  $775.50

Step-by-step explanation:

The parallelogram on the left has an area of ...

  A = bh = (4 yd)(2 yd) = 8 yd²

The rectangle in the middle has an area of ...

  A = lw = (6 yd)(4 yd) = 24 yd²

The triangle on the right has an area of ...

  A = 1/2bh = 1/2(1 yd)(2 yd) = 1 yd²

The total area of the carpet is ...

  (8 + 24 + 1) yd² = 33 yd²

__

At $23.50 per square yard, the cost is ...

  ($23.50/yd²)(33 yd²) = $775.50 . . . . . matches the last choice

Answer:

The volume of the sphere is \(V\approx101.212 \:in^3\).

Step-by-step explanation:

A sphere is a 3-D figure in which all of the points in a plane are the same distance from a given point, the center of the sphere.                      

A sphere with radius r has a volume of

                                                          \(V=\frac{4}{3} \pi r^3\)

and a surface area of

                                                         \(S=4\pi r^2\)

To find the volume of the sphere we use the fact that the surface area of the sphere is 105 \(in^2\) and we use it to find the radius.

\(105=4\pi r^2\\\\4\left(\pi \right)r^2=105\\\\r^2=\frac{105}{4\pi }\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\r=\sqrt{\frac{105}{4\pi }},\:r=-\sqrt{\frac{105}{4\pi }}\)

The radius cannot be negative. Therefore,

\(r=\sqrt{\frac{105}{4\pi }}=\frac{\sqrt{105}\sqrt{\pi }}{2\pi }\approx 2.891 \:in\)

Now, that we know the radius we can find the volume

\(V=\frac{4}{3} \pi (2.891)^3=\frac{96.65053\dots \pi }{3}=\frac{303.63661\dots }{3}\approx101.212 \:in^3\)

Answer:

HMMM. LET ME THINK everything will be okay

At least you ate a nice healthy meal.

Also, if you can find some fresh pants or you can go to the bathroom and grab paper and wet it and it may take out the stain

REMEMBER EVERYONE HAS BAD DAY INCLUDING MYSELF

HAVE A NICE DAY :)

Step-by-step explanation:

Answer:

Explained below.

Step-by-step explanation:

The random variable X follows an exponential distribution with λ = 5.

The probability density function of X is:

\(f_{X}(x)=\lambda\cdot e^{-\lambda\cdot x};\ 0<x<\infty\)

\(P(X\leq x)=1-e^{-\lambda\cdot x}\\\\P(X\geq x)=e^{-\lambda\cdot x}\)

(a)

Compute the value of P (X ≤ 0) as follows:

\(P(X\leq 0)=1-e^{-\lambda\cdot x}\)

               \(=1-e^{-5\times 0}\\\\=1-1\\\\=0\)

Thus, the value of P (X ≤ 0) is 0.

(b)

Compute the value of P (X ≥ 2) as follows:

\(P(X\geq 2)=e^{-5\times 2}=4.54\times 10^{-5}\approx 0\)

Thus, the value of P (X ≥ 2) is approximately 0.

(c)

Compute the value of P (X ≤ 1) as follows:

\(P(X\leq 0)=1-e^{-\lambda\cdot x}\)

               \(=1-e^{-5\times 1}\\\\=1-0.00674\\\\=0.99326\)

Thus, the value of P (X ≤ 1) is 0.99326.

(d)

Compute the value of P (1 ≤ X ≤ 2) as follows:

\(P(1<X<2)=\int\limits^{2}_{1} {5\times e^{-5x}} \, dx \\\\=5\times [\frac{e^{-5x}}{-5}]^{2}_{1} \\\\=5\times [\frac{0-0.00674}{-5}]\\\\=0.0067\)

Thus, the value of P (1 ≤ X ≤ 2) is 0.0067.

(e)

Compute the value of x such that P (X < x) = 0.05 as follows:

\(P(X<x)=0.05\\\\\int\limits^{x}_{0} {5\times e^{-5x}} \, dx =0.05\\\\5\times [\frac{e^{-5x}}{-5}]^{x}_{0} =0.05\\\\1-e^{-5x}=0.05\\\\-e^{-5x}=0.95\\\\-5x=\ln(0.95)\\\\-5x=-0.05\\\\x=0.01\\\\\)

Thus, the value of x is 0.01.

The maximum displacement is 5 centimeters.

The time required for one oscillation is π seconds.

The frequency is 1 / π Hz.

Equation to model the motion of the object is x(t) = 5 × cos(2t)

The maximum displacement from equilibrium can be determined by observing that the object is pulled down 5 centimeters from its rest position.

In simple harmonic motion, the amplitude represents the maximum displacement from equilibrium.

The period of oscillation is given as π seconds.

The period (T) is the time required for one complete oscillation.

The frequency (f) is the reciprocal of the period and represents the number of oscillations per unit time.

Thus, the frequency is the inverse of the period: f = 1 / T.

To model the motion of the object, we can use the equation for simple harmonic motion:

x(t) = A×cos(ωt + φ)

A = 5 centimeters (maximum displacement),

T = π seconds (period),

f = 1 / π Hz (frequency).

To find ω, we can use the relation ω = 2π / T:

ω = 2π / π = 2 radians/second.

The equation to model the motion of the object is:

x(t) = 5 × cos(2t)

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Answer: it is 4:2

Step-by-step explanation: because it is a ratio, both sides can be divided by the same number and still have the same meaning. btw in this case both divided by 2

Step-by-step explanation:

Based on the information given, we have a diagram with two sides labeled as 13.3 mm and 5.5 mm, and another side labeled as X mm.

To find the length of X, we can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

Perimeter = 13.3 mm + 5.5 mm + X mm

The perimeter is the total distance around the triangle. Since we have three sides, the perimeter is the sum of the lengths of those sides.

To find X, we can subtract the sum of the known sides from the perimeter:

X mm = Perimeter - (13.3 mm + 5.5 mm)

Since the value of X is not given, we cannot calculate it without the perimeter value. If you provide the perimeter value, I can help you find the length of X.

Answer:

a) There is an integer a such that  \(\frac{a-1}{a}\) is  an integer

b) False

Step-by-step explanation:

Statement : ∀a ∈ Z,    (a − 1) a is not an integer

A) The correct negation will be :

There is an integer a such that  \(\frac{a-1}{a}\) is  an integer

B) The Given statement is FALSE because

when we assume the value of a = 1

( a - 1 ) / a = (1 - 1 ) / 1 = 0   ;  which is an integer

Answer:

B

Step-by-step explanation:

The figure has rotational symmetry is figure B.

Symmetry According to the definition of mathematics, "symmetry is a mirror image." Symmetry occurs when a picture appears identical to the original image after the shape has been twisted or flipped. It exists in the form of patterns. In everyday life, you may have heard the term "symmetry."

We know in rotational symmetry the plane figure is rotated by angle(radians) about a certain point on the plane to coincide with the original figure, This figure is called a rotational symmetry figure.

Here, the figure that satisfies the rotational symmetry is figure B.

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Considering the definition of parallel and perpendicular line, you get:

A linear equation o line can be expressed in the form y = mx + b

where

Parallel lines are two lines that are always at the same distance from each other.

Two lines are parallel if they have the same slope and different y-intercepts.

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

The line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If you multiply the slopes of two perpendicular lines, you get –1, the slope perpendicular line can be calculated as:

5/8× slope perpendicular line= -1

slope perpendicular line= (-1)÷ 5/8

slope perpendicular line= -8/5

So, the perpendicular line has a form of: y= -8/5x + b

The line passes through the point (8, 4). Replacing in the expression for perpendicular line:

4= -8/5×8 + b

4= -64/5 + b

4 + 64/5= b

84/5= b

Finally, the equation of perpendicular line is y= -8/5x + 84/5.

In this case, the line is y= 5/8x -4, with a value of slope m of 5/8 and ordinate to the origin b of -4.

If two lines are parallel if they have the same slope, the parallel line has a slope of 5/8 and has a form of: y= 5/8x + b

The line passes through the point (8, 4). Replacing in the expression for parallel line:

4= 5/8×8 + b

4= 5 + b

4 -5 = b

-1 = b

Finally, the equation of parallel line is y= 5/8x - 1

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Answer:

(0,7)

Step-by-step explanation:

28

Step-by-step explanation:

Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

Answer:

Ellipse

Step-by-step explanation:

From the given information:

Suppose the plane cuts the cone in such a manner that the plane is neither perpendicular nor parallel to the axis and also the angle of intersection is greater than the generator angle.

Then the conic section formed is an Ellipse.

The Conic Section that is formed from the intersection of the central axis at an angle between 40° and 90° will be An Ellipse.

Let us consider that the plane cuts the cone in such a manner that the plane is neither perpendicular nor parallel to the axis and also the angle of intersection is greater than the generator angle.

Thus, we can say that when the plane intersects the double-napped cone in such a manner that the angle between the vertex and the angle is greater than the vertex angle.

Then the resulting conic section formed is an Ellipse.

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The rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

The volume of the liquid in the bowl is given by the following integral:

\(V = \int\limitsx_{0}^{h} \, \pi r^{2}(y) dy\)

where r = radius of the bowl and y = height of the liquid.

The radius of the bowl is equal to the distance from the curve y = (4/(8-x)) - 1 to the y-axis. This can be found using the following equation:

r = √{(4/(8-x)) - 1}² + 1²

The height of the liquid is equal to the distance from the curve y = (4/(8-x)) - 1 to the x-axis. This can be found using the following equation:

h = (4/(8-x)) - 1

Substituting these equations into the volume integral:

\(V = \int\limitsx_{0}^{h } \, \pi {\sqrt{(4/(8-x)) - 1)^{2} + 1^{2} (4/(8-x))} - 1 dy\)

Evaluate this integral using the following steps:

Expand the parentheses in the integrand.

Separate the integral into two parts, one for the integral of the square root term and one for the integral of the linear term.

Integrate each part separately.

The integral of the square root term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, dx \sqrt{x} dx = 2/3 (x^{3/2}) |^{b}_{a}\)

The integral of the linear term can be evaluated using the following formula:

\(\int\limits^{b} _{a} \, {x} dx = (x^{2/2}) |^{b}_{a}\)

Substituting these formulas into the integral:

V = π { 2/3 (4/(8-x))³ - 1/2 (4/(8-x))² } |_0^h

Evaluating this integral:

V = π { 16/27 (8-h)³ - 16/18 (8-h)² }

The rate of change of the volume of the liquid is given by:

dV/dt = π { 48/27 (8-h)² - 32/9 (8-h) }

The rate of change of the volume of the liquid is 7π cm³ s⁻¹. Also the depth of the liquid is one-third of the height of the bowl. This means that h = 2/3.

Substituting these values into the equation for dV/dt:

dV/dt = π { 48/27 (8-2/3)² - 32/9 (8-2/3) } = 7π

Solving this equation for the rate of change of the depth of the liquid:

dh/dt = 7/(48/27 (8 - 2/3)² - 32/9 (8 - 2/3)) = 1.25 cm s⁻¹

Therefore, the rate at which the depth of the liquid is increasing when the depth of the liquid reaches one-third of the height of the bowl is 1.25 cm s⁻¹.

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Answer:

Step-by-step explanation:

81 texts in 9 hours

So you do 81 divided by 9

Which givrs you 9 text an hour

The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.

To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

Scale factor = Length of corresponding side in D' / Length of corresponding side in D

For the corresponding sides, we have:

Scale factor = 6/18 = 1/3

Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.

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The coefficient of the second term, 6x⁴, is 6.

The terms of the polynomial are:

-4y⁵, 6x⁴, 9w³, -4w, -1

The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.

The coefficient is 6.

Therefore, the list of terms is:

-4y⁵, 6x⁴, 9w³, -4w, -1

Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.

The coefficients indicate the scalar value by which each term is multiplied.

The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.

Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.

There is a 6 coefficient.

As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.

Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.

The scalar value by which each phrase is multiplied is shown by the coefficients.

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310,763,136 in word form is Three hundred and ten million, Seven hundred and Sixty-three thousand, One Hundred and Thirty-six

Nine digits are in hundreds of million, six digits in hundreds of thousand and three digits hundred hence the figure in words.

Let's assume that the number of diners at the Italian restaurant is "x" and the number of diners at the Mexican restaurant is "y". Then, we can write the following equations based on the given information:

Italian restaurant:

Donation = $462 + $1 per diner

Donation = $462 + $1x

Mexican restaurant:

Donation = $235 + $2 per diner

Donation = $235 + $2y

Since both restaurants will donate the same total amount, we can set their donations equal to each other:

$462 + $1x = $235 + $2y

Simplifying this equation, we get:

$2y - $1x = $227

We know that the number of diners has to be a whole number, so we can try different values of x and see which one gives us a whole number for y.

For example, if we try x = 200, then we can solve for y:

$2y - $1(200) = $227

$2y = $427

y = 213.5

Since y is not a whole number, we need to try a different value of x. If we try x = 250, then we get:

$2y - $1(250) = $227

$2y = $477

y = 238.5

Again, y is not a whole number, so we try another value of x. If we try x = 300, then we get:

$2y - $1(300) = $227

$2y = $527

y = 263.5

Still not a whole number, so we try x = 350:

$2y - $1(350) = $227

$2y = $577

y = 288.5

Finally, we get a whole number for y, so we have our solution:

Italian restaurant: x = 350 diners, donation = $812

Mexican restaurant: y = 289 diners, donation = $812

Therefore, 350 diners promised to participate and each restaurant would donate $812.

Answer:

\(\boxed{22n^8-16n^7-140n^4+112n^3-98}\)

Step-by-step explanation:

\((7n^4-14 - 5n^3) (7-8n^3 + 11n^4)\)

According to the distributive property, each term multiplies each of the terms in the other equation. Therefore, we can do the following:

\(\begin{aligned}\Rightarrow &7n^4 (7-8n^3 + 11n^4)= 49n^4-56n^3 n^4+77n^4n^4 \\&=49n^4-56n^7+77n^8 \end{aligned}\)

\(\begin{aligned}\Rightarrow &-14 (7-8n^3 + 11n^4)\\& = -98+112n^3-154n^4 \end{aligned}\)

\(\begin{aligned}\Rightarrow &-5n^4 (7-8n^3 + 11n^4)= -35n^4+40n^3n^4-55n^4n^4 \\&=-35n^4+40n^7-55n^8 \end{aligned}\)

Next, we combine all the terms of the plynomial equation:

\(49n^4-56^7+77n^8-98+112n^3-154n^4-35n^4+40n^7-55n^8\)

common factor:

\(22n^8-16n^7-140n^4+112n^3-98\)

By this, we have solved the exercise.

\(\text{-B$\mathfrak{randon}$VN}\)

Answer:

B. 120 m²

Step-by-step explanation:

To find the surface area of the composite solid, we would need to calculate the area of each solid (square pyramid and square prism), then subtract the areas of the sides that are not included as surface area. The sides not included as surface area is the side the pyramid and the prism is joint together.

Step 1: find the surface area of the pyramid:

Surface area of pyramid with equal base sides = Base Area (B) + ½ × Perimeter (P) × Slant height (l)

Base area = 4² = 16 m

Perimeter = 4(4) = 16 m

Slant height = 3 m

Total surface area of pyramid = 16 + ½ × 16 × 3

= 16 + 8 × 3 = 16 + 24

= 40 m²

Step 2: find the area of the prism

Area = 2(wl + hl + hw)

Area = 2[(4*4) + (5*4) + (5*4)]

Area = 2[16 + 20 + 20]

Area of prism =  2[56] = 112 m²

Step 3: Find the area of the sides not included

Area of the sides not included = 2 × area of the square base where both solids are joint

Area = 2 × (4²)

Area excluded = 2(16) = 32 m²

Step 4: find the surface area of the composite shape

Surface area of the composite shape = (area of pyramid + area of prism) - excluded areas

= (40m²+112m²) - 32m²

= 152 - 32

Surface area of composite solid = 120 m²

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.

(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

The next step is to combine like terms within each parentheses:

= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

Finally, we can add the two expressions:

= (56x - 3x² + 7) + (-8x + 2x³ + 3)

= 56x - 3x² - 8x + 2x³ + 3 + 7

= 56x - 3x² - 8x + 2x³ + 10

The final answer is 56x - 3x² - 8x + 2x³ + 10.

Answer:

whatever 42 times 10 equals, it also equals what ten minus 4 times seventy is

Step-by-step explanation:

so both 42 × 10

and 10 – 4 × 70

EQUAL

420

(pffft 420....sorry its funny)

Answer:

Associative properties

Step-by-step explanation:

42 x 10 = 420

(10-4)=6

6 x 70 = 420

The equation to show the perimeter of the rectangle is P = 2(2w + 5)

From the question, we have the following parameters that can be used in our computation:

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

0?

Step-by-step explanation:

i think?

Answer:

First point : (0, -3)

Second point : (2, 0)

Y-intercept : -3

Step-by-step explanation:

To tackle a question like this, the first thing you want to do is put the equation into y = mx + b form.

1.) 3x - 2y = 6

2.) -2y = -3x + 6 (bring 3x to the other side, using inverse operations)

3.) y = 1.5x - 3 (divide -2 on both sides, to isolate the variable y)

Now that you have the y-intercept (-3), you have your y value. Finally, just substitute the variable y from the original equation to solve for the x value.

1.) 3x - 2(-3) = 6

2.) 3x + 6 = 6 (multiply (-2) and (-3))

3.)3x = 0 (subtract 6 on both sides using inverse operations)

4.) x = 0

Now you have your first point which is (0, -3)!

To get your last point, just substitute your y coordinate from the original equation to get x.

1.) 3x - 2(0) = 6

2.) 3x - 0 = 6

3.) 3x = 6

4.) x = 2

Then, substitute the x coordinate from above in the original equation to get the y coordinate.

1.) 3(2) - 2y = 6

2.) 6 - 2y = 6

3.) -2y = 0

4.) y = 0

Second coordinate : (2, 0)

I hope this explanation was helpful!

For the linear equation 3x + y = 9 we have:

Here we want to find the two intercepts for the linear equation:

3x + y = 9

First, the x-intercept is the point that we get when we evaluate on y = 0.

3x + 0 = 9

3x = 9

x = 9/3

x = 3

Then we get: x-intercept (3, 0)

And for the y-intercept we need to evaluate in x = 0.

3*0 + y = 9

y = 9

Then the y-intercept is (0, 9).

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Answer:

19 6/8 or 19 3/4

I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

\(w(x)=14\cdot 1.08^{x}\)

w(25) =

\(w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96\)

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves