Bronze is a mixture of copper and tin. The copper and tin are mixed in the ratio 9:1 by weight.

a. How much copper is there in a bronze brooch weighing 360 g?

b. Another bronze brooch contains 670.5g of copper.

How much does it weigh altogether?

Answer:

{y l y > 9}

Step-by-step explanation:

Given function:

[tex]f(x)=3^x+9[/tex]

The given function is an exponential function.

The parent function is the basic equation before the function has undergone any transformation(s).  Therefore, the parent function of the given function is:

The range of the parent function is restricted to positive real numbers as it never takes a negative value.  Furthermore, it never reaches zero (although it approaches y = 0 as x → -∞).  Therefore, the range of the parent function is {y | y > 0}.

As the given function has been translated up 9 units (by the addition of "+ 9"), the range of the given function is translated 9 units up.  So as x approaches negative infinity, y approaches (but never reaches) 9. Therefore, the range of the given function is:

As per the ratio, the number of men on the sight-seeing tour is 4.

In the given sight-seeing tour, we are told that there were 14 people in total. We are also given the ratio of women to children, which is 5 to 2. This means that for every 5 women on the tour, there were 2 children.

To find the number of men on the tour, we need to first find the number of women and children. We can do this by dividing the total number of people by the ratio of women to children.

Let's use a variable to represent the number of sets of 5 women and 2 children. We'll call this variable "x".

So, the number of women on the tour is 5x and the number of children is 2x.

Now, we can set up an equation to find the value of x:

5x + 2x = 14

This equation represents the total number of women and children on the tour, which is equal to 14.

Simplifying the equation, we get:

7x = 14

Dividing both sides by 7, we get:

x = 2

This means that there were 2 sets of 5 women and 2 children on the tour. So, the number of women is:

5x = 5(2) = 10

The number of children is:

2x = 2(2) = 4

Now, we can find the number of men by subtracting the number of women and children from the total number of people:

14 - 10 = 4

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The rounded number to the nearest thousands place is 9,910,000

To change a number into an approximation having fewer significant digits is called rounding a number.

Given that, a number 9,909,937 we are asked to round it,

9,909,937 in words =

nine million nine hundred nine thousand nine hundred thirty-seven

Therefore, to round to the nearest thousand;

You rounded to the nearest thousands place. The 9 in the thousands place rounds up to 10 because the digit to the right in the hundreds place is 9.

Because the thousands place was rounded up from 9 to 10, the thousands place becomes 0 and the ten thousands place is increased by 1. When a 9 is rounded up to 10, that place value becomes 0, and we add 1 to the previous place value.

9,910,000

When the digit to the right is 5 or greater we round away from 0. 9909937 was rounded up and away from zero to 9,910,000

Hence, the rounded number to the nearest thousands place is 9,910,000

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Answer:

The possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Step-by-step explanation:

The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.  

Expand the cubed part by using the (a + b)³ formula:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Therefore:

[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]

So:

[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]

To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:

[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]

[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]

Therefore, the expression for the coefficient of x² is:

[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]

Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:

[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]

Therefore the possible values of the constant b are:

[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]

Answer: x=92x=−7

Step-by-step explanation:x=−b±b2−4ac2a=−±2−4√2Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

Answer:it’s 3

Step-by-step explanation:

so what u do is multiply

The best describes EB is diameter of circle because it is a chord of circle which passes through the center.

A circle is a two-dimensional object made up of points that are spaced out from a given point (centre) on the plane by a fixed or constant distance (radius). The fixed point is referred to as the circle's origin or centre, and the fixed distance between each point and the origin is referred to as the radius.

The following components make up a circle:

Circumference: Also known as a circle's perimeter, circumference is the distance a circle travels around its circumference.

Radius: The radius is the distance a circle's center is from any point on its edge.

A diameter is a straight line that links two places on the circle's edge and passes through the center.

So that EB is describes as diameter of circle because it is a chord of circle which passes through the center.

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The dot product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex]  in terms of the positive scalar quantities a, b, c, and d is:

[tex]\vec{A}.\vec{B}=-ab[/tex]

The scalar product of two vectors [tex]\vec{A}[/tex] and [tex]\vec{B}[/tex] is given by the formula:

[tex]\vec{A}.\vec{B}=(a_1*b_1) + (a_2*b_2) + (a_3*b_3)[/tex]

Where a₁, a₂, and a₃ are the components of vector [tex]\vec{A}[/tex] and b₁, b₂, and b₃ are the components of vector [tex]\vec{B}[/tex].

In this case, vector A = (ai - bk) and vector B = (- cj + dk), so the components of vector A are a₁ = a, a₂ = 0, and a₃ = -b, and the components of vector B are b₁ = 0, b₂ = -c, and b₃ = d.

Plugging these values into the formula for the dot product, we get:

[tex]\vec{A}.\vec{B}=(a*0) + (0*-c) + (-d*b)\\\\\vec{A}.\vec{B}= 0 + 0 + (-bd) \\\\\vec{A}.\vec{B}=-bd[/tex]

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Inequality for the number of weeks lily will need to save to have at least $300 is 40 + 65*x >= 300  and  4 week needed to buy the cellphone.

The phenomenon of an unfair and/or unequal distribution of opportunities and resources among the people who make up a society is referred to as inequality. To different people and in various contexts, the word "inequality" may mean different things. Additionally, inequality has distinct yet overlapping social, economic, and geographic dimensions. The conflict between the normative concept of "deservingness" and the moral ethics of equity and social justice, on the one hand, and on the other, further complicates discussions about inequality. Inequalities that can be seen both within and between social groups have come to the forefront of public consciousness in recent years. The growing realization that inequality is systemic and ingrained in various socioeconomic and political structures is the result of this awareness. The contributions of geographers to the subject.

she needs to save at least $300 before she is able to buy the phone and

her grandfather gives her $40  so she need 300 - 40

and she earns $65 tutoring after school each week so until she will not have 260 she not able to buy.

40 + 65*x >= 300

65x >= 260

x >= 260/65

x >= 4

4 week needed.

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Answer:

lol

Step-by-step explanation:

that sucks

The plane's true bearing is $27.9°N of W, and its estimated ground speed is 473.3 mph.

Math is made more fascinating and enjoyable using Speed Maths (Vedic Maths). by assisting the child in quickly performing some improbable computations. By combining the correct amount of enjoyment, memory, skills, memory recall, and formula application, your child will become a superstar performer.

Let's start with the airplane's speed.

A bearing of N25°W corresponds to a anticlockwise angle of 65° when measured from the westward direction (W).

As a result, the airplane's velocity vector can be divided into its north-south and east-west components as shown below:

V_A,north = 480 cos(65°) ≈ 200.5 mph (northward)

V_A,west = 480 sin(65°) ≈ 447.3 mph (westward)

V_W,north = 45 sin(75°) ≈ 43.5 mph (northward)

V_W,west = 45 cos(75°) ≈ 11.3 mph (westward)

To find the net velocity of the airplane, we can add the north-south and east-west components of the airplane velocity and wind velocity separately:

V_net,north = V_A,north + V_W,north ≈ 200.5 + 43.5 ≈ 244.0 mph (northward)

V_net,west = V_A,west + V_W,west ≈ 447.3 + 11.3 ≈ 458.6 mph (westward)

Now we can use the Pythagorean theorem to find the magnitude of the net velocity:

|V_net| = sqrt(V_net,north² + V_net,west²) ≈ 473.3 mph

To find the actual bearing of the airplane, we can use the inverse tangent function:

tan⁻¹(V_net,north / V_net,west) ≈ 27.9°

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Answer: Check down below!!!

Step-by-step explanation:

   8x² = 6x² + 5x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

8x² = 6x² + 5x²

8x² = 11x²

Now, we can isolate x² by subtracting 11x² from both sides of the equation:

8x² - 11x² = 11x² - 11x²

-3x² = 0

Finally, we can divide both sides of the equation by -3 to get:

(-3x²)/(-3) = 0/(-3)

x² = 0

So the solution is x = 0.

   -7x² + 6 = x² - 7x²

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

-7x² + 6 = x² - 7x²

-7x² + x² = -7x² + 6

-6x² = 6

Now, we can isolate x² by dividing both sides of the equation by -6:

(-6x²)/(-6) = 6/(-6)

x² = -1

So the solution is x = ±√(-1), which is an imaginary number.

   7x² + 9x² = -6x² - 7x

   This problem can be solved by combining like terms. To do this, we add up the coefficients of the x² terms:

7x² + 9x² = -6x² - 7x

16x² = -6x² - 7x

Now, we can isolate x² by adding 6x² to both sides of the equation:

16x² + 6x² = -6x² + 6x² - 7x

22x² = -7x

Finally, we can divide both sides of the equation by 22 to get:

22x²/22 = -7x/22

x² = -7x/22

So the solution is x = ±√(-7/22), which is a complex number.

Answer:

2.73 meters away from the building.

Step-by-step explanation:

To find the distance from the building to the flagpole, we can use the tangent function. Let's call the distance from the building to the flagpole "d".

The tangent of the angle of elevation is equal to the height of the flagpole (h) divided by the distance from the building to the flagpole (d):

tan 48° = h / d

The tangent of the angle of depression is equal to the distance from the building to the flagpole (d) divided by the height of the observer (3.5 m):

tan 35° = d / 3.5

We can use these two equations to find the value of d. Solving the first equation for h:

h = tan 48° * d

And substituting that into the second equation:

tan 35° = d / (tan 48° * d / 3.5)

Solving for d:

d = 3.5 * tan 35° / tan 48°

Using a calculator, we can find that:

d = 3.5 * tan 35° / tan 48° = 3.5 * 1.3602668 / 1.7415198 = 2.73 m

So the flagpole is 2.73 meters away from the building.

Answer:

Step-by-step explanation:

To determine whether a value is greater than or less than a specific result from an equation, you would need to substitute the value into the equation and solve for the result. For example, if you want to determine if the value "a" is greater than or less than the result of the equation -2x^2 + 16x - 36, you would substitute "a" for the variable x and solve for the result:

-2x^2 + 16x - 36 = -2a^2 + 16a - 36

Then you can compare the value of the result to "a" to determine whether it is greater than or less than.

If the result is greater than "a", you would write:

-2a^2 + 16a - 36 > a

If the result is less than "a", you would write:

-2a^2 + 16a - 36 < a

And if the result is equal to "a", you would write:

-2a^2 + 16a - 36 = a

It's important to note that the comparison only holds for a specific value of "a". The equation -2x^2 + 16x - 36 could have many solutions where the result is greater than, less than, or equal to "a".

Factor the polynomial by factoring out the greatest common factor, 7x2 + 5 - x = 6x2 + 10

x = -5

Soultion:

→ 7 × 2 + 5 - x = 6 × 2 + 10

Multiply.

→ 14 + 5 - x = 12 + 10.

Combine like terms.

→ 19 - x = 24

Isolate x (I'm going to add x and subtract 24 from both sides to avoid changing signs)

Answer

→ = x = -5

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

10.00 & 0.05

Step-by-step explanation:

[tex]10.00 - 0.05 = 9.95[/tex]

The amount of money as change is $ 0.05 and the amount of money given is $ 10.00

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the cost of the item = $ 9.95

The amount of money given = $ 10.00

So , the amount of money received as change = amount of money given - cost of the item

On simplifying the equation , we get

The amount of money received as change = 10.00 - 9.95

The amount of money received as change = $ 0.05

Hence , the amount of change is $ 0.05

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Answer:

3/8

Step-by-step explanation:

If 5/8 of the staff are male, then the remaining staff must be female, which is 1 - 5/8 = 3/8 of the staff.

So, the fraction of the staff that is female is 3/8.

ALLEN

The probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.

To find the probability of a defect, we need to determine the range of weights that would be considered as defects. The process control limit is set at plus or minus 2.4 standard deviations, which means that any weight outside the range of mean ± 2.4× standard deviation would be considered a defect. Let's calculate the mean weight (μ): μ = 0

And the control limit (LCL and UCL):

LCL = μ - (2.4 × standard deviation)

= 0 - (2.4 × 0.15) = -0.36 UCL

= μ + (2.4 × standard deviation)

= 0 + (2.4 × 0.15) = 0.36.

Since the standard deviation is 0.15 ounces and the normal distribution is symmetrical, the probability of a weight being less than -0.36 ounces or greater than 0.36 ounces is equal. To calculate the probability, we can use the cumulative distribution function (CDF) of a standard normal distribution. Using a standard normal table or a calculator with statistical functions, we can find that the probability of a standard normal distribution being less than -0.36 or greater than 0.36 is about 0.0521 or 5.21%. So, the probability of a defect (weights less than -0.36 ounces or greater than 0.36 ounces) is approximately 0.0521 × 2 = 0.1042 or 10.42% to four decimal places.

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Explanation:

2/3 of 150 = (2/3)*150 = 100 employees are male and 150-100 = 50 employees are female. This is before the resignations.

After the resignations happen, we would have:

The chances of picking a female employee at random would be 40/120 = 1/3 which is the final answer.

Notice how the chances haven't changed from earlier (male = 2/3 chance, so 1-2/3 = 1/3 are the chances of picking a woman). Why is this? Well notice the ratio of 20 men to 10 women resigning. This ratio is 2:1, meaning twice as many men resigned. Furthermore, notice how 2/3 is twice that of 1/3.

This keeps the same proportion of men to women. Therefore, the odds haven't changed.

Total 21 teams completed the escape room this week.

An employee records the number of minutes it takes each team to complete the escape room this week the dot plot shows the data.

To determine how many teams completed the escape room this week we use the dot plot.

From the dot plot we can see that at 41 min have one found one employee escape from room.

At 44 min have one found 3 employee escape from room.

At 45 min have one found 2 employee escape from room.

At 46 min have one found 4 employee escape from room.

At 47 min have one found 5 employee escape from room.

At 48 min have one found 3 employee escape from room.

At 49 min have one found 2 employee escape from room.

At 50 min have one found one employee escape from room.

Team completed the escape room this week = 1 + 3 + 2 + 4 + 5 + 3 + 2 + 1

Team completed the escape room this week = 21

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Answer:21 i got it correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

The gardener used 5/8 of the soil, which is equal to 10 * 5/8 = 10 * 0.625 = 6.25 pounds.

So, he used 6.25 pounds of soil in the garden.

The gardener had 10 - 6.25 = 3.75 pounds of soil left.

The obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

What are the different quadrants of trigonometric identities?

The first quadrant has angles between 0 and 90 degrees. The second quadrant has angles between 90 and 180 degrees. The third quadrant contains angles between 180 and 270 degrees. The fourth quadrant contains angles between 270 and 360 degrees. All six trigonometric functions have positive values in the first quadrant.  The only positive values in the second quadrant are sine and cosecant. The only positive values are tangents and cotangents in the third quadrant. The only positive values in the fourth quadrant are cosine and secant.

We are asked to find an obtuse angle θ such that 0 ≤ θ ≤ 2π and has the same sine as -275°.

The value of sin(-275°) = 0.996

Since the value of sin(-275°) is positive, the angle θ should be in the first or second quadrant, because the sine of angles in the first and second quadrants is positive.

But the θ should be an obtuse angle.

So θ should be in the second quadrant.

sin(-275) = sin(360-275) = sin 85° = 0.996

sin(180 - 85) = sin(95)  = 0.996

Therefore the obtuse angle θ which has the same value of sin(-275) is 95°, which is in the second quadrant.

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If you multiply the left side of an equation by 4, what must you multiply the right side of the equation by 4

Here you you multiply the left side of an equation by 4.

According to the solving for unknow rule you must perform same function to both side of the equation. If you multiply the left side of an equation by any integer then you must multiply the same integer on right hand side of the equation

To maintain equality, you must multiply the right side of the equation by 4 as well.

This is because the left side of the equation represents the same quantity as the right side, so any operation that is performed on one side must also be performed on the other side to preserve the equality.

Therefore, you must multiply the right side of the equation by 4

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The Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This can be expressed as:

The Mean Value Theorem (MVT) of differential calculus states that for any differentiable function f(x) on the closed interval [a,b], there exists a point c between a and b such that the slope of the tangent at c is equal to the average rate of change of f(x) over [a,b]. Mathematically, this can be expressed as:

f'(c) = [f(b) - f(a)] / (b - a)

In the given function f(x) = x^3 - 3x^2, we need to find all values of c that satisfy the conclusion of the MVT on the closed interval [0,3].

First, we need to find the derivative of f(x):

f'(x) = 3x^2 - 6x

Then, we need to evaluate the average rate of change of f(x) over [0,3]:

[f(3) - f(0)] / (3 - 0) = (27 - 0) / 3 = 9

Therefore, we need to find all values of c between 0 and 3 such that f'(c) = 9.

Setting f'(c) = 9, we get:

3c^2 - 6c = 9

c^2 - 2c - 3 = 0

(c - 3)(c + 1) = 0

Thus, the two possible values of c that satisfy the conclusion of the MVT are c = 3 and c = -1. However, we need to check if these values actually lie in the closed interval [0,3]. Since -1 is not in [0,3], the only value of c that satisfies the conclusion of the MVT on [0,3] is c = 3.

Therefore, the conclusion of the Mean Value Theorem is satisfied for c = 3 on the closed interval [0,3]. This means that there exists a point c between 0 and 3 where the slope of the tangent to the graph of f(x) is equal to the average rate of change of f(x) over [0,3].

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A large tank hold 1. 9 time 10 to the 7th power gallons of oil. The amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

To find the amount of oil that can be stored in 9 tanks that each hold 1.9 x 10^7 gallons of oil, we can use the following steps:

Write down the number of gallons that one tank can hold: 1.9 x 10^7 gallons. Multiply this value by the number of tanks: 1.9 x 10^7 gallons/tank x 9 tanks.

To multiply the two numbers, we can simply multiply the coefficients (1.9 and 9) and add the exponents (7 in this case): (1.9 x 9) x 10^(7+0) gallons.

Simplifying the coefficient gives us 17.1, so the amount of oil that can be stored in 9 tanks is 17.1 x 10^7 gallons.

Finally, we can express this result in scientific notation by writing it as 1.71 x 10^8 gallons, since 17.1 is equivalent to 1.71 x 10.

Therefore, the amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

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Answer:

Number is -10

Step-by-step explanation:

Let Number be x

so, 5x= 30+8x

Take 30 other side and 5x other side

so, 8x-5x=-30

3x=-30

x=-10

HOPE THIS HELPS... THANK YOU

Answer:

You are correct it is 12.

Step-by-step explanation:

Answer: Square root of 288, or estimated 16.97

Step-by-step explanation:

Conveniently, the points form a diagonal line as you show, so we can use the Pythagorean Theorem to find the distance.

The x-component of this is the distance between -6 and 6, which is 12, and the y-component is again the distance between -6 and 6, which is also 12.

Therefore, the distance is the square root of 12^2 + 12^2, or the squareroot of 288.

Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

Answer: We know that the volume of a cuboid is given by the product of its length, width and height, or V = l * w * h. In this case, the length is 250 cm and the height and width are both x cm. So, the volume can be written as:

V = 250 * x * x

Substituting the given value of V = 4840 cm³, we get:

4840 = 250 * x * x

Dividing both sides by 250, we get:

19.36 = x * x

Taking the square root of both sides, we get:

x = ±√19.36

Since the side length of a square must be positive, we use the positive square root:

x = ±4.4 cm

Therefore, the side length of the square cross-section is 4.4 cm.

Step-by-step explanation: