Solve by using a system of equations.

A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?

The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

The total surface area of the can is therefore:

A = 2πr² + 2πrh

We know that the volume of the can is 810 cm³, which is given by:

V = πr²h

We can solve this equation for h to get:

h = V/(πr²)

Substituting this expression for height h into the equation for the surface area, we get:

A = 2πr² + 2πr(V/(πr²))

Simplifying, we get:

A = 2πr² + 2V/r

Now we have an equation for the surface area of the can in terms of the radius, r.

To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.

dA/dr = 4πr - 2V/r² = 0

Solving for radius r, we get:

[tex]r = (810/\pi)^1^/^3[/tex]

r=∛810/3.14

r=6.35 cm

Now find h:

h = 810/πr²

h=810/3.14×6.35²

h=810/126.6

h=6.39 cm

Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

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Tasheena's grade percentage in the class so far is approximately 71.00935%.

The percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.

To compute Tasheena's grade percentage in the class so far, we can calculate the weighted average of her scores based on the weightage of each component of the final grade.

Given:

Quizzes: 15% weightage

Exams: 55% weightage

Projects: 25% weightage

Attendance: 5% weightage

Tasheena's scores:

Quizzes: 117 out of 150 points

Exams: 74, 86, and 91 on the first three exams (each worth 100 points)

Projects: 29 out of 25 possible points

Attendance: Perfect attendance

Let's calculate Tasheena's grade percentage:

Quizzes:

Tasheena's quiz score percentage = (117 / 150) * 100 = 78%

Exams:

Tasheena's exam average = (74 + 86 + 91) / 3 = 83.67

Tasheena's exam score percentage = (83.67 / 100) * 55 = 46.017%

Projects:

Tasheena's project score percentage = (29 / 25) * 100 = 116%

Attendance:

Tasheena's attendance score percentage = 100% (since she had perfect attendance)

Now, let's calculate the weighted average of Tasheena's scores:

Weighted average = (Quizzes weightage * Quiz score percentage) + (Exams weightage * Exam score percentage) + (Projects weightage * Project score percentage) + (Attendance weightage * Attendance score percentage)

= (15% * 78%) + (55% * 46.017%) + (25% * 116%) + (5% * 100%)

= 11.7% + 25.30935% + 29% + 5%

= 71.00935%

Hence, Tasheena's grade percentage in the class so far is approximately 71.00935%.

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The slope of the relation with the equation 5x - 3y = 4 is 5/3

To find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.

First, we'll subtract 5x from both sides:

-3y = -5x + 4

Next, we'll divide both sides by -3 to isolate y:

y = (5/3)x - 4/3

Now we can see that the slope of the line is 5/3.

So the correct answer is: 5/3

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Answer:

The answer is A

Step-by-step explanation:

Trust me

Therefore, the coordinates of  [tex]S'[/tex] are  [tex](-2, -1)[/tex] .

A series of numbers called coordinates is used to describe a point's location in a two- or three-dimensional space.

Typically, coordinates in a two-dimensional space are expressed as a pair of integers (x, y), where x denotes the point's horizontal location (also known as the abscissa) and y denotes its vertical position (also known as the ordinate).

Coordinates are commonly expressed as a triplet of numbers (x, y, z) in a three-dimensional space, where x, y, and z stand for the locations along the x, y, and z axes, respectively.

In order to describe the location of objects or points in space, coordinates are often employed in a variety of disciplines, including mathematics, physics, engineering, and computer graphics.

To rotate a point 180° about the origin, we need to negate the x-coordinate and the y-coordinate of the point.

So to find the coordinates of S', we can apply this rule to the coordinates of S:

x-coordinate of   [tex]S' = -x-[/tex] coordinate of [tex]S = -(2) = -2[/tex]

y-coordinate of  [tex]S' = -y-[/tex]  coordinate of  [tex]S = -(1) = -1[/tex]

Therefore, the coordinates of S' are [tex](-2, -1).[/tex]

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The TRUE statement about Alexander's deposit of $3,200 into a savings account that has a simple interest rate of 1% calculated quarterly is a. He will earn $8 in interest each quarter, totaling $32 in interest for the year.

Simple interest describes an interest system that does not compound the interest.

Compounding involves charging interest on both interest and principal.

For the simple interest system, the interest amount is computed only on the principal, using the following SI formula.

Principal deposit, P = $3,200

Interest rate, R = 1%

Interest period, P = 1 year

Interest system = Simple interest quarterly

Simple interest (SI) formula = P x R x T

Simple interest for each quarter = $8 ($3,200 x 0.01 x 1/4)

Simple interest for the year = $32 ($3,200 x 0.01)

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The time taken by the runner is equal to 9.064 hours.

In this problem we find the case of runner taking a time (t), in hours, to run a certain distance (d), in miles, at constant speed (v), in miles per hour. The kinematic equation is now introduced:

v = d / t

Now we proceed to determine the missing time:

(26.2 mi) / (4.75 hours) = (50 mi) / t

t = 9.064 h

The runner takes a time of 9.064 hours to run a distance of 50 miles.

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The value of 11 3/8 -7/8 is 10 1/2

Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60

Solving 11 3/8 -7/8

= 91/8 - 7/8

= (91-7)/8

= 84/8

= 21/2

= 10 1/2

Therefore the value of 11 3/8 -7/8 is 10 1/2

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The values of the matrices operations are [tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex] and [tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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

[tex]G = \left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right][/tex]

Also, we have

[tex]F = \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Using the above as a guide, we have

[tex]4G + 2F = 4\left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right] + 2 \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]

Evaluate the sum

[tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex]

Next, we have

[tex]D = \left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right][/tex]

Also, we have

[tex]B = \left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

The matrix expression is then represented as

[tex]4D - 3B= 4\left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right] - 3\left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]

Evaluate

[tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]

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Answer: 5

Step-by-step explanation:

They are the points

Answer:

-----------------------------

AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.

Hence this is a right triangle.

Its area is:

The probability of getting blue or green is 1/3, the probability of getting blue is 3/4 and there are 8 blue marbles.

a) If the probability of getting a yellow marble is 2/3, then the probability of getting a blue or green marble is:

P(blue or green) = 1 - P(yellow) = 1 - 2/3 = 1/3

b) If the probability of getting a green marble is 1/4, then the probability of getting a blue marble is:

P(blue) = 1 - P(green) = 1 - 1/4 = 3/4

c) The total number of marbles in the bag is 24. Let x be the number of blue marbles. Then the number of yellow marbles is 2x, and the number of green marbles is 24 - x - 2x = 24 - 3x. We know that:

2x/24 = 2/3 (probability of getting a yellow marble is 2/3)

=> x = 8

Therefore, there are 8 blue marbles in the bag.

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Explanation:

The paragraph explains how TERFs have alienated many feminists from radical feminism and why TERF is a harmful and anti-trans movement.

Some other possible sentences are:

Answer:

n = 20/3

Step-by-step explanation:

Theory about the discriminant, and how solutions are acquired via the quadratic formula

One variable quadratic equations in the form [tex]0=ax^2+bx+c[/tex] have exactly one solution when the discriminant [tex](b^2-4ac)=0[/tex].

This is because for quadratic equations of the original form, the two solutions are given by the quadratic formula:

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

which is equivalent to [tex]x=\dfrac{-b}{2a}\pm \dfrac{\sqrt{b^2-4ac}}{2a}[/tex].

The [tex]x=\dfrac{-b}{2a}[/tex] is the axis of symmetry, and the [tex]\dfrac{\sqrt{b^2-4ac}}{2a}[/tex] part is how much the solutions deviate from the axis of symmetry.  If the deviation is zero, then the two solutions are both ON the axis of symmetry, and are the same number, giving exactly one solution.

Addressing the given equation

Putting it into standard form

Given the given equation...

[tex](n-4)u^2+6=8u[/tex]

subtract 8u from both sides to obtain an equation that looks like the standard form equal to zero...

[tex](n-4)u^2-8u+6=0[/tex]

The variable here is "u" instead of "x", so the solutions to this equation would be [tex]u=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex], where [tex]a=n-4[/tex], [tex]b=-8[/tex], and [tex]c=6[/tex].

Identifying the discriminant

The discriminant then, with values of a, b, and c, substituted, becomes:

[tex]Discriminant=(-8)^2-4(6)(n-4)[/tex]

If we want the discriminant to equal zero (so that there is exactly one solution for "u"), substitute zero on the left side of the equation, and solve for n.

Solving for n

[tex]0=(-8)^2-4(6)(n-4)[/tex]

[tex]0=64-4(6)(n-4)[/tex]

[tex]0=64-24(n-4)[/tex]

Add -24(n-4) to both sides...

[tex]24(n-4)=64[/tex]

Divide both sides by 24...

[tex]n-4=\dfrac{64}{24}[/tex]

Reduce the right hand side...

[tex]n-4=\dfrac{8}{3}[/tex]

Add 4 to both sides...

[tex]n=\dfrac{8}{3}+4[/tex]

Find a common denominator...

[tex]n=\dfrac{8}{3}+\dfrac{12}{3}[/tex]

Find a common denominator...

[tex]n=\dfrac{20}{3}[/tex]

So, if [tex]n=\dfrac{20}{3}[/tex], then the equation [tex](n-4)u^2+6=8u[/tex] has exactly one solution.  Furthermore, this is the only value of "n" for which the equation has exactly one solution, because it is the only value of "n" for which the discriminant is zero.

The woman's gross income, adjusted income and taxable income are:

The gross income to the woman is:

= Wages + interest

= 33, 900 + 2, 600

= $ 36, 500

The adjusted gross income :

= Gross income - Retirement plan contribution

= 36, 500 - 3, 600

= $ 32, 900

The taxable income ;

= AGI - Personal exemption - Deductions

= 32, 900 - 3, 500 - 5, 440

= $ 23, 960

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The expression of the function which is represented by the given graph is given by,

xy = -8

The given figure is a rectangular hyperbola.

So the equation of the given graphed curve be, xy = c, where c is a constant.

We can clearly see that the curve passes through the point with coordinates (-2, 4). So it must satisfy the equation of the curve.

Substituting the point (-2, 4) in the equation of the curve xy = c we get,

(-2)*4 = c

c = -8

Hence the expression for the graph the function represents is given by,

xy = -8.

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The expression of angle in radian is -0.071.

Angles can be measured in two units: degrees and radians.

Radian is a unit of measurement for angles, and it is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle.

To be more precise, an angle of one radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

The expression of angle in radian is calculated as follows;

θ = tan⁻¹ (-0.071)

θ = -0.071

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Answer:

x=2

Step-by-step explanation:

f(x) is 89

f(x)=41x+7

89=41x+7

41x+7=89

41x=89-7

41x=81

x=81/41

x=2

Answer:

False

Step-by-step explanation:

you have to save at least 20 percent

Question: What are the two possible angles of a triangle with sides of 100 and 75 with a 40° as marked in the triangles above? Solution: Use the law of sines formula where the 75 length is opposite of 40°, and 100 is opposite of θ. Answer: The two possible angles for this triangle is 58.97° and 121.03°.

Answer:

can i get a picture\

Step-by-step explanation:

thanks

Answer:

Step-by-step explanation:

1:4

Applying the Intersecting Secants and Tangents Theorem, the measures are: CD = 19.5 units;     UZ = 12.8 units

a. Apply the intersecting secant-tangent theorem to create the equation below:

EG² = EC * ED

Plug in the values:

13² = 6.5 * (6.5 + CD)

169 = 42.25 + 6.5CD

169 - 42.25 = 6.5CD

126.75/6.5 = CD

CD = 19.5 units

b. Apply the intersecting secants theorem to create the equation below:

UX * UY = UZ * UW

Plug in the values:

8 * 64 = UZ * 40

512/40 = UZ

UZ = 12.8

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The probability that Brent draws mismatched socks is approximately 31/153.

After adding 2 identical black socks, Brent has a total of 18 socks in his drawer. The probability of drawing a white sock on the first draw is 16/18 (since there are 16 white socks out of 18 total socks).

After drawing a white sock on the first draw, there are 15 white socks and 2 black socks left in the drawer. The probability of drawing a black sock on the second draw is 2/17 (since there are 2 black socks out of 17 total socks left). So the probability of drawing a white sock followed by a black sock is;

(16/18) × (2/17) = 32/306

Similarly, the probability of drawing a black sock followed by a white sock is;

(2/18) × (15/17) = 30/306

However, the probability of drawing mismatched socks is;

32/306 + 30/306 = 62/306

= 31/153

Therefore, the probability will be 31/153.

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Answer:

A.) Newly married couples tend to have two earners.

Step-by-step explanation:

When newly married couples first start off marriage, they tend to both work to make stable income since they recently had to work to make money for only their selves, which is why they both tend to have two earners.

Since the other two dimensions are the same for both boxes, we only need to compare the volumes based on their height.

Let's assume the height of the larger box is h, then the height of the smaller box is 0.8h.

The volume of the larger box is:

V1 = lwh = (8)(11)(h) = 88h

The volume of the smaller box is:

V2 = lwh = (8)(11)(0.8h) = 70.4h

Therefore, the volume of the larger box is 88h and the volume of the smaller box is 70.4h.

Using the given matrix, the value of -10(T) is

[tex]-10(T) = \left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]

From the question, we are to carry out the matrix multiplication

From the given information,

The given matrices is:

[tex]T =\left[\begin{array}{cc}23&-38\\17&-6\end{array}\right][/tex]

Now, we are to determine -10(T)

To achieve this, we will multiply each of the element in the given matrix by -10

That is,

-10 ×23 = -230

-10 × -38 = 380

-10 × 17 = -170

-10 × -6 = 60

Thus,

The result of the multiplication will be:

[tex]\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]

Hence, the value of -10(T) is

[tex]-10(T) = \left[\begin{array}{cc}-230&380\\-170&60\end{array}\right][/tex]

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Answers:

[tex]z=12\sqrt{3} \\y=12\\x=12\sqrt2[/tex]