Im thinking of a number , multiply it by 4 and add 5 to the product, you get 41. Find the number
a) 9
b) 10
c) 11
d) 12

Answer:

12 kilograms costs $14.40.

The first statement is true

Step-by-step explanation:

They all can be simplyfied to 3/4 including 12/16

The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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Answer:

No solution.

Step-by-step explanation:

It only leads into another equation, that being \(3(4x+9)\). And if you try solving that, you'll just get \(12x + 27\) again. Therefore, there is no visible solution to this problem.

The probability of the total being less than or equal to 4 when rolling two six-sided fair dice is 1/12.

To calculate the probability, we need to determine the favorable outcomes and the total number of possible outcomes. The favorable outcomes are the combinations that result in a total less than or equal to 4: (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1). The total number of possible outcomes is 6 x 6 = 36, as each die has 6 sides. Therefore, the probability is calculated as the ratio of favorable outcomes to total outcomes: 6/36 = 1/6. However, since we want the total to be less than or equal to 4, we exclude (3, 3) from the favorable outcomes.

Hence, the final probability is 5/36. The probability of the total being less than or equal to 4 when rolling two six-sided fair dice is 1/12 or approximately 0.0833.

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Answer:

200 grams

Step-by-step explanation:

Let us represent

The number of grams of

30% smarties = x

20% smarties = y

Hence:

x + y = 500

x = 500 - y

Hence:

30% × x + 20% × y = 24% × 500

0.3x + 0.2y = 120

Substitute 500 - y for x

Hence:

0.3(500 - y) + 0.2y = 120

150 - 0.3y + 0.2y = 120

Collect like terms

- 0.3y + 0.2y = 120 - 150

- 0.1y = -30

y = -30/0.1

y = 300

Solving for x

x = 500 - y

x = 500 - 300

x = 200

Hence,

The number of grams of

30% smarties = x = 200 grams

20% smarties = y = 300 grams

Therefore:

the mass of the 30% mix is required to make a 500 gram mixture that will have 24% Smarties by mass is 200 grams

Answer:

x = 10

y = 10√2 = 14.142

Step-by-step explanation:

Since we are given 2 angles 45° and 90° and the three angles of  a triangle add up to `180° the third angle included by x and y must be
180-(90 + 45) = 45

So we have a triangle which has two angles equal i.e. an isosceles triangle.

Hence x = 10

y = √(10² + 10²) by the Pythagorean formula:
y = √200

= √100√2

= 10√2

= 14.142

Answer:

x = 10, y = 20

Step-by-step explanation:

angles in a triangle add up to 180°

so 90° + 45° + a = 180°

a = 180° - 90° - 45°

a = 45°

so the unknown angle in the triangle is 45°

90/y = 45/10

90×10 = 45×y

45y = 900

45y/45 = 900/45

y = 20

45/x = 45/10

45 × x = 45 × 10

45x = 450

45x/45 = 450/45

x =10

The magnitude of the resultant force acting on the object is 340 N.

To find the resultant force, we need to resolve each given force into its horizontal and vertical components.

For F1, the horizontal component is F1h = F1 * cos(42°) and the vertical component is F1v = F1 * sin(42°).

For F2, the horizontal component is F2h = F2 * sin(11°) (since it is given as an angle West of North) and the vertical component is F2v = F2 * cos(11°).

For F3, the horizontal component is F3h = F3 * cos(23°) and the vertical component is F3v = F3 * sin(23°).

Next, we add up the horizontal components (F1h, F2h, and F3h) and the vertical components (F1v, F2v, and F3v) separately.

The resultant horizontal component (Rx) is the sum of the horizontal components, and the resultant vertical component (Ry) is the sum of the vertical components.

Finally, we can calculate the magnitude of the resultant force (R) using the Pythagorean theorem: R = sqrt(Rx^2 + Ry^2).

After calculating the values, we find that the magnitude of the resultant force is 340 N.

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Answer:

there are two different, real roots.  

Step-by-step explanation:

The coefficients of this quadratic are {1, -7, -8}.  Let's find the discriminant, b^2 - 4ac.  In this case a = 1, b = -7 and c = -8 and so the discriminant value is

(-7)^2 - 4(1)(-8), or 49 + 32, or 81.

Because the discriminant is positive, we know immediately that there are two different, real roots.  

We are not asked to find the roots, but let's do it anyway:

      -(-7) ± √81

x = ------------------ => x = 8 and x = -2 (which are real and different from

              2                                           one another).

The surface area of a rectangular prism is found as 150 square inches.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.

Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.

Calculation for the surface area of rectangular prism-

Height of a rectangular prism => H = 4 inches

Width of a rectangular prism => B = 9 inches

Length of a rectangular prism => L = 3 inches

Surface area of a rectangular prism = 2(LB + BH + HL)

                                                           = 2(9×3 + 9×4 + 4×3)

                                                           = 150

Therefore, the surface area of a rectangular prism is found as  150 square inches.

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The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).

In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).

The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.

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Answer:

∠ 6 = 38°

Step-by-step explanation:

∠ 6 and 38° are vertically opposite angles and are congruent , then

∠ 6 = 38°

12.41% of the trucks logged more than 57,060 but less than 58,280 miles. It is unlikely that one truck was above 5 stdevs above the mean. The probability is almost 0.

A data collection with a normal distribution is put up so that the majority of the values cluster around the middle of the range and the remaining values taper off symmetrically in either direction. Because the probability density graph of the normal distribution resembles a bell, it is frequently referred to as the bell curve. In honor of the German mathematician Carl Gauss, who first described it, it is also referred to as the Gaussian distribution.

Here,

(a) z(57060) = (57060-60000)/2000 = -1.47

z(58280) = (58280-60000)/2000 = -0.86

prob(-1.47 < z < -0.86) from a table:

=12.41%

(b) z(70000) = (70000-60000)/2000

= 5

It is unlikely that one truck was above 5 stdevs above the mean. The prob is almost 0.

More than 57,060 but fewer than 58,280 miles were done by 12.41% of the vehicles. One vehicle being more than 5 stdevs above the mean is improbable. The likelihood is almost 0.

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The amount you could save per month would be 25% of your discretionary money.

Discretionary income is the money you have left over after paying taxes and necessary cost-of-living expenses.

The formula for discretionary money is: Discretionary money = Realized income - Fixed expenses. Inputting data, we have: Discretionary money = $3,543.22 - Fixed expenses

Amount to be saved = 25% of discretionary money

Amount to be saved = 0.25 * (Realized income - Fixed expenses)

Therefore, the amount savable is calculated as 0.25 times the difference between your realized income and fixed expenses.

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To express the quadratic function f(x) = x^2 - 18x + 63 in standard form, we need to complete the square.

First, we can factor out the coefficient of x^2, which is 1: f(x) = 1(x^2 - 18x + 63), Next, we want to find the value that completes the square for the expression inside the parentheses,

which is (-18x + 63). To do this, we take half of the coefficient of x, which is -9, square it, and add it to both sides: f(x) = 1(x^2 - 18x + 81 - 81 + 63).

Notice that we added and subtracted 81 inside the parentheses, which is the value we got from (-9)^2. This allows us to write the expression as a perfect square trinomial, which can be factored as: f(x) = 1[(x - 9)^2 - 18].

Finally, we can simplify this expression by distributing the 1 and adding 63 outside the brackets: f(x) = (x - 9)^2 - 18 + 63, So the quadratic function f(x) in standard form is: f(x) = (x - 9)^2 + 45.

Note that standard form for a quadratic function is usually written as ax^2 + bx + c, where a, b, and c are constants. In this case, we factored out the coefficient of x^2, which is why our standard form expression doesn't have an "a" term.

A quadratic function in standard form is written as f(x) = a(x - h)^2 + k, where a, h, and k are constants. Our goal is to rewrite the given function in this format. So, the standard form of the given quadratic function is: f(x) = (x - 9)^2 - 18

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. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

Answer:

5x

Step-by-step explanation:

4x plus 1x equals 5x.

Hope this helped, have a nice day! :)

Answer:

5x

Step-by-step explanation:

4x+1x

=x+x+x+x+x

Answer:

I attached the photo below, but two points are (0,-1), (3,-2)

Step-by-step explanation:

3y=-x-3

x|        y|

0        -1

3        -2

Answer:

the last option is the correct answer.

The dimensions for the maximum possible area that is 6.25 m² are L = 2.5 m and W = 2.5 m.

Area is the measure of the surface enclosed by a closed two-dimensional figure. It is typically measured in square units, such as square meters, square feet, or square inches. The formula for finding the area of various shapes depends on their geometrical structure. For example, the area of a rectangle is given by multiplying its length and width, the area of a triangle is given by multiplying its base and height and dividing by 2, and the area of a circle is given by π times the square of its radius.

Here,

To find the maximum area of the rectangular exercise area, we need to use the given amount of fencing to enclose the largest possible area.

a) Let the length of the rectangle be L and the width be W. We know that the perimeter of the rectangle is 10 m, so:

2L + 2W = 10

Simplifying, we get:

L + W = 5

We want to maximize the area of the rectangle, which is given by:

A = LW

Using the equation L + W = 5, we can solve for L in terms of W:

L = 5 - W

Substituting into the area equation, we get:

A = (5 - W)W = 5W - W²

To find the maximum area, we need to take the derivative of A with respect to W, set it equal to zero, and solve for W:

dA/dW = 5 - 2W = 0

Solving for W, we get:

W = 2.5

Substituting this value back into the equation L + W = 5, we get:

L = 2.5

So the maximum possible area is:

A = LW = (2.5)(2.5) = 6.25 square meters

b. To find the dimensions of the maximum possible area, we can use the fact that the maximum area occurs when the rectangle is a square.

Let x be the length and y be the width of the rectangle. We know that the perimeter is 10m, so:

2x + 2y = 10

Simplifying this equation, we get:

x + y = 5

To maximize the area, we want to find the values of x and y that satisfy this equation and also make the area as large as possible. Since we know that the rectangle is a square, we can set x = y:

x + y = 5

x + x = 5

2x = 5

x = 2.5

Therefore, the dimensions of the maximum possible area are 2.5m by 2.5m.

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Verify each equation

option A

For x=3 ------> y=216(3^3)=

For the required value of the given complex numbers z₁z₂ = 32(cos 255° + isin 255°).

Complex numbers are those that expand on the idea of real numbers by incorporating an illogical element.

The formula for a complex number is "a + bi," where "a" and "b" are real numbers and "i" is the imaginary unit, which is equal to the square root of -1.

"A" stands for the complex number's real component, and "b" stands for the imaginary component.

We multiply the magnitudes of two complex numbers and add their arguments to determine their product.

Let's compute z₁z₂ with the supplied values.

Given:

z₁ = 8(cos 45° + isin 45°)

z₂ = 4(cos 210° + isin 210°)

We add the arguments and multiply the magnitudes to find z₁z₂:

Magnitude of z₁ = 8

Magnitude of z₂ = 4

Argument of z₁ = 45°

Argument of z₂ = 210°

Now, let's calculate z₁z₂:

Magnitude of z₁z₂ = (Magnitude of z₁) × (Magnitude of z₂) = 8 × 4 = 32

Argument of z₁z₂ = (Argument of z₁) + (Argument of z₂) = 45° + 210° = 255°

Therefore, z₁z₂ = 32(cos 255° + isin 255°).

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The correct question =

Given z₁ = 8(cos 45° + isin 45°) and z₂ = 4(cos 210° + isin 210°), what is z₁z₂?

Answer:

6 : 11

Step-by-step explanation:

12 : 22

reduce

6 : 11

Answer:

6:11

Step-by-step explanation:

Bunnies: dogs

12           :  22

Divide by 2

12/2      :22/2

6         : 11

Answer:

Step-by-step explanation:

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.  And know that the square root of 2 is irrational.

Hope this helps! ^^

Answer:

x=4

y= -1

Step-by-step explanation:

(3x-2y=14)×3

(7x+3y=25)×2

9x-6y= 42

14x + 6y =50

9x-42=6y

-14x+50=6y

9x-42= -14x+50

23x = 92

x=4

3(4)-2y=14

12-2y =14

-2y=2

y= -1

Answer:

Pretty sure its C). 90

Step-by-step explanation:

Answer:

x=90°

Step-by-step explanation:

.....................90°...........

Part (a) states that for finite sets A and B with the same cardinality, any injective function from A to B must also be surjective. However, in part (b), we can find examples of infinite sets A and B along with an injective function from A to B that is not surjective.

In part (a), we consider finite sets A and B with the same cardinality. Since the function ƒ is injective, it means that each element in A is mapped to a unique element in B. Since both A and B have the same number of elements, and each element in A is assigned to a distinct element in B, there cannot be any elements in B left unassigned. Therefore, every element in B has a corresponding element in A, and the function ƒ is surjective.

However, in part (b), we can find examples of infinite sets A and B where an injective function from A to B is not surjective. For instance, let A be the set of natural numbers (1, 2, 3, ...) and B be the set of even natural numbers (2, 4, 6, ...). We can define a function ƒ from A to B such that ƒ(n) = 2n. This function is injective since each natural number n is mapped to a unique even number 2n. However, since B consists only of even numbers, there are elements in B that do not have a preimage in A. Therefore, the function ƒ is not surjective.

In conclusion, part (a) holds true for finite sets, where an injective function from A to B must also be surjective. However, part (b) demonstrates that this statement does not hold for infinite sets, as there can exist injective functions from A to B that are not surjective.

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Answer:

V=96 mi/h

Step-by-step explanation:

We know that the velocity is equal to displacement over the time.

So V=S/T

We change the minutes to hours.

V= 40/(25/60)

V=96 mi/h