A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of
gold in each bracelet is 7 grams and the amount of gold in each necklace is 24 grams.
The jeweler used 172 grams of gold and made 2 more necklaces than bracelets. Write
a system of equations that could be used to determine the number of bracelets made
and the number of necklaces made. Define the variables that you use to write the
system.

Answer:

8/11, 7/9, 4/5, 84% these are the answers to your question

Answer:

f(x)-g(x)

= \((x^{2} - 13x + 36) - ( x -4)\)

= \(x^{2} -13x+36-x+4\)

= \(x^{2} -14x-40\)

The quadratic function for the path of the basketball as it is thrown indicates;

The path of the basketball will not make the shot

The height reached is about 5.24 meters

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.

The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2

The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;

n(x) = The vertical height of the basketball

Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;

b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2

(-1/7)·x² + 1.36·x + 2 - 3 = 0

(-1/7)·x² + 1.36·x - 1 = 0

(1/7)·x² - 1.36·x + 1 = 0

Solving the above equation, we get;

x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717

Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.

Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)

Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76

The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters

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Step-by-step explanation:

it would be best if you snapped this question for better understanding, however

4/√5. +. 3√125

4/√5. +. 3(√25 x √5)

4/√5 + 3(5√5)

4/√5 + 15√5

Answer:

tndjxisjebducu

ejdjdnebdix

Answer:

1 3/5 boxes

Step-by-step explanation:

There are 5 1/2-3 9/10 boxes left over. We need to simplify this expression.

First, convert both fractions to improper fractions:

11/2-39/10

Now, convert both fractions to have a common denominator of 10:

11/2*5/5 (note we can only do this because any number over itself is equivalent to 1, so technically this is multiplying the number by 1)

55/10-39/10=16/10

Convert it back into a mixed fraction:

1 6/10=1 3/5 boxes

Answer:

1 3/5 boxes

Step-by-step explanation:

5 1/2=5 5/10

leftover=5 5/10-3 9/10=1 6/10=1 3/5

make sure to take 1 from 5

1=10/10

and add it to 5/10 since cant' take away 9/10

Answer:

y=√(4+x)(4−x)

Step-by-step explanation:

Answer:

Number 3 Can't find the font

Answer:

53\(x_{123}\) == 134 cf

Step-by-step explanation:

A - on the po boyds at a emase the foot, 1, of building. He. Observes an obje- et on the top, P of the building at an angle of ele- building of 66 Aviation of 66 Hemows directly backwards to new point C and observes the same object at an angle of elevation of 53° · 1P) |MT|= 50m point m Iame horizontal level I, a a​

The height of the building is approximately 78.63 meters.

The following is a step-by-step explanation of how to solve the problem. We'll need to use some trigonometric concepts and formulas to find the solution.

Therefore, the height of the building is approximately 78.63 meters.

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Answer:

28z-12y

Step-by-step explanation:

The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

Answer:

\(-15.11\)

Step-by-step explanation:

\(-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11\)

Answer:

-15.11

Step-by-step explanation:

-12.48+2.99-5.62=

-9.49 - 5.62= - (9.49+5.62)=-15.11

1. The Pythagoras theorem is (6+r)² = r²+9²

2. 36+12r+r² = r²+9²

3. The value of r is 3.75

Pythagoras theorem states that; the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

This means that, c² = a² + b²

In the triangle, 6+r is the hypotenuse, 9 and r are the other two legs.

therefore;

(6+r)² = r²+9²

= (6+r)(6+r) =r²+9²

36+6r+6r+r² = r²+9

36+12r+r² = r²+9

Collecting like terms

12r+r²-r²= 81-36

12r = 45

r = 45/12

r = 3.75

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i beilive this is unknown

The surface area of the wooden structure is approximately 1012 cm².

To calculate the surface area of the wooden structure, we need to find the surface area of the cone and the surface area of the hemispherical base, and then add them together.

Surface Area of the Cone:

The surface area of a cone is given by the formula:

A_{cone = \(\pi \times r_{cone} \times (r_{cone} + s_{cone})\), \(r_{cone\) is the radius of the base of the cone and \(s_{cone\) is the slant height of the cone.

The vertical height of the cone is 24 cm, and the base radius is 7 cm, we can calculate the slant height using the Pythagorean theorem:

\(s_{cone\) = \(\sqrt{(r_{cone}^2 + h_{cone}^2).\)

Using the given measurements:

\(s_{cone\) = √(7² + 24²) cm

\(s_{cone\) ≈ √(49 + 576) cm

\(s_{cone\) ≈ √625 cm

\(s_{cone\) ≈ 25 cm

Now, we can calculate the surface area of the cone:

\(A_{cone\) = π × 7 cm × (7 cm + 25 cm)

\(A_{cone\) = (22/7) × 7 cm × 32 cm

\(A_{cone\) = 704 cm²

Surface Area of the Hemispherical Base:

The surface area of a hemisphere is given by the formula:

\(A_{hemisphere\) = \(2 \times \pi \times r_{base}^2\), \(r_{base\) is the radius of the base of the hemisphere.

Given that the base radius is 7 cm, we can calculate the surface area of the hemispherical base:

\(A_{hemisphere\) = 2 × (22/7) × (7 cm)²

\(A_{hemisphere\) = (22/7) × 2 × 49 cm²

\(A_{hemisphere\) = 308 cm²

Total Surface Area:

To calculate the total surface area, we add the surface area of the cone and the surface area of the hemispherical base:

Total Surface Area = \(A_{cone} + A_{hemisphere}\)

Total Surface Area = 704 cm² + 308 cm²

Total Surface Area = 1012 cm²

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Answer:

x = 50

Step-by-step explanation:

2485 ÷ x = 49 R 35

We know that 2485 ÷ x = 49 R 35, or 2485 ÷ x = 49 + 35

Step 1:

Now, I want to subtract 35 from the left side of the equation:

Step 2:

Now I want to find x. We can start by multiplying both sides by x, then dividing by the coefficient.

x = 50

Check:

-Chetan K

Differentiate both sides of

\(6x f(x)^4 + 9x^3 f(x) = 78\)

with respect to x :

\(\left(6x f(x)^4 + 9x^3 f(x)\right)' = (78)' \\\\ 6\left(xf(x)^4\right)' + 9\left(x^3f(x)\right)' = 0\)

Use the product and chain rules for the left side:

\(\left(xf(x)^4\right)' = (x)'f(x)^4 + x\left(f(x)^4\right)' = f(x)^4 + 4xf(x)^3f'(x)\)

\(\left(x^3f(x)\right)' = \left(x^3\right)'f(x) + x^3f'(x) = 3x^2f(x)+x^3f'(x)\)

Solve for f '(x) :

\(6\left(f(x)^4+4xf(x)^3f'(x)\right) + 9\left(3x^2f(x)+x^3f'(x)\right) = 0 \\\\ 6f(x)^4+27x^2f(x) + \left(24xf(x)^3+9x^3\right)f'(x) = 0 \\\\ f'(x) = -\dfrac{6f(x)^4+27x^2f(x)}{24xf(x)^3+9x^3}\)

Then

\(f'(1) = \boxed{\dfrac{14}{61}}\)

Answer:

36.69%

Step-by-step explanation:

Given a standard normal distribution :

P(Z < - 0.34) :

Using the Z distribution table :

Look up the value - 0.3 down the row and 0.04 a cross the column. The value at the intersection of the two points gives the required proportion:

P(Z < - 0.34) = 0.3669

0.3669 as a percentage = 0.3669 * 100% = 36.69%

The value can also be obtained using the Z probability calculator.

Answer:

a. Z = 1.99

b. 97.67%

c. Z = 2.56

d. 0.52%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

a. If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

The heights of adult men in America are normally distributed, with a mean of 69.7 inches and a standard deviation of 2.66 inches, and thus, we have \(\mu = 69.7, \sigma = 2.66\)

6 feet 3 inches = 6*12 + 3 = 75 inches, which means that we have to find z when X = 75. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{75 - 69.7}{2.66}\)

\(Z = 1.99\)

b. What percentage of men are SHORTER than 6 feet 3 inches?

The proportion is the p-value of Z = 1.99.

Looking at the z-table, Z = 1.99 has a p-value of 0.9767.

0.9767*100% = 97.67%, which is the answer.

c. If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.54 inches, and thus, we have \(\mu = 64.5, \sigma = 2.54\). We have to find Z when X = 5*12 + 11 = 71. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{71 - 64.5}{2.54}\)

\(Z = 2.56\)

d. What percentage of women are TALLER than 5 feet 11 inches?

The proportion is 1 subtracted by the p-value of Z = 2.56.

Looking at the z-table, Z = 2.56 has a p-value of 0.9948.

1 - 0.9948 = 0.0052

0.0052*100% = 0.52%, which is the answer.

The probability (area under the curve) of picking a client who spends between $57 and $83 per month is 0.4032.

Given,

Mean, μ = $70

Standard Deviation, σ = $10

z = (x-μ) ÷ σ

P(The consumer was charged from around $70 and $83),

P(70 ≤ x ≤ 83) = P((70 - 70) ÷ 10)) ≤ z ≤ ((83-70) ÷ 10)) = P(0 ≤ z ≤ 1.3)

=P(z ≤  1.3) - P(z ≤ 0)

=0.9032 - 0.500 = 0.4032 = 40.32%

P(70 ≤ x ≤ 83) = 40.32%

Customers with Key Refining Company loans typically spend an average of $70 monthly on gasoline and servicing. With either a standard deviation of $10, the expenditure distribution is about normal. For z = 1.3, the area under the curve is 0.4032.

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The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

c

Step-by-step explanation:

the number goes to both of the numbers in the equation

Answer: There are 9 mangoes left in the basket.

Step-by-step explanation:

(2/5) * 15 = 6.

15 - 6 = 9.

Step-by-step explanation:

hope this helps. the process is shown above

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer: 10w

Step-by-step explanation:

Answer:

8.2%

Step-by-step explanation:

9,895x = 809.41

x = 0.08179 or 8.2%

Answer:

=0.5(1.1) - 0.5(2x)+2.4x-2.10

=0.55-x+2.4x-2.10

=1.4x-1.55

Ans A