The odds that you will pick a heart from a standard deck of 52 cards is 13:39. TRUE or FALSE

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Questions like these are really simple to answer, for one, all you have to know is Rise over Run (or Rise/Run)...

This being:
Rise: the distance from one y value to the other...
Run: the distance from one x value to the other...

Naturally graph points are represented as (x, y).
So, all we need to is do the math....

For Rise: the distance from 5 to -12 is 17...
For Run: the distance from 3.5 (or 3 1/2) to 3.5 is 0, but because the denominator of ANY fraction can never be 0, we will change it to 1...

So, our equation looks like: 17/1 (or 17 over 1)...
And our answer is: The 2 points are EXACTLY 17 units apart...

The given expression is [tex]4(a^2 + 2b) - 2b[/tex]. when a = 2 and b = –2 then the answer would be 4.

Usually, simplification involves proceeding with the pending operations in the expression.

Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]4(a^2 + 2b) - 2b[/tex]

when a = 2 and b = –2.

[tex]4(2^2 + 2(-2)) - 2(-2) \\\\ =4(4-4) + 4 \\\\= 4\times 0 + 4 = 4[/tex]

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The value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).

To evaluate the expression 8x-2y over 10xy when x=4 and y=-7, we substitute these values into the expression:

8(4)-2(-7) over 10(4)(-7)

Simplifying further,

32+14 over -280

46 over -280

Therefore, the value of the expression 8x-2y over 10xy when x=4 and y=-7 is -0.1643 (rounded to four decimal places).

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To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).

To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.

Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:

Using the sine function, we can find the length of side MJ:

sin(angle MLJ) = length of side MJ / length of side LJ

sin(-29ᵒ) = MJ / rM

Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:

sin(29ᵒ) = MJ / rM

Now, we can rearrange the equation to solve for MJ:

MJ = rM * sin(29ᵒ)

Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.

Remember to round the answer to the nearest hundredth as specified in the question.

Answer:

(2 2/7, 5 1/3)

Step-by-step explanation:

The coordinates of point Q, lies along R(-2,4) and S(18,-6)

thus, QR and RS, that is in ratio of QR : RS = 3 : 7

Let point Q = (x,y)

Hence, QR = -2 - x; RS =  -6 - 4

Thus, QR/RS = 3/7, which is: (-2 - x)/(-6 - 4) = 3/7

7(-2 - x) = -30

-14 - 7x = -30

7x = 16

∴ x = 16/7 = 2 2/7

If x : y = 3 : 7 ( where x = 2 2/7)

Hence, (2 2/7)/y = 3/7

3y = 16

∴ y = 16/3 = 5 1/3

The coordinates  of point Q = (2 2/7, 5 1/3)

The number of cylindrical candles of 15cm height and 10cm diameter to be made from 4500[tex]cm^{3}[/tex] of wax is : 3.81 approximately 4

A cylinder is a solid geometrical shape with two parallel sides and two oval or circular cross-sections.

Analysis:

Given data:

Volume of wax = 4500[tex]cm^{3}[/tex]

Diameter of candle = 10cm

Radius of candle = diameter/2 = 10/2 = 5cm

Height of candle = 15cm

Volume of each cylindrical candle = π[tex]r^{2}[/tex]h

Volume of each cylindrical candle = [tex]\frac{22}{7}[/tex] x [tex](5)^{2}[/tex] x 15 = [tex]\frac{8250}{7}[/tex][tex]cm^{3}[/tex]

Volume of wax = n x volume of each cylindrical candle

n = number of candles

n = [tex]\frac{volume of wax}{volume of each cylindrical candle}[/tex]

n = [tex]\frac{4500}{\frac{8250}{7} }[/tex] = 3.81 approximately 4

In conclusion, the number of cylindrical candles to be made from 4500 cubic centimeters wax is 4.

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Final answer:

To find the number of cylindrical candles that can be made from a given volume of wax, one needs to calculate the volume of one candle with the formula for the volume of a cylinder and then divide the total wax volume by a single candle's volume.

Approximately 3 candles can be made from 4500 cm^3 of wax if each candle is 15 cm tall with a 10 cm diameter.

Explanation:

To calculate the number of cylindrical candles that can be made from 4500 cubic centimeters of wax, with each candle being 15 centimeters tall and with a diameter of 10 centimeters, we use the formula for the volume of a cylinder, V = πr^2h.

First, we need to calculate the radius of the cylinder by dividing the diameter by 2. The diameter is 10 cm, so the radius is 5 cm. Next, we apply the formula to find the volume V of one candle:

V = (π)(5 cm)^2(15 cm) = 3.14159 × 25 cm^2 × 15 cm = 1177.5 cm^3 approximately

To find out how many candles we can make, we divide the total volume of wax by the volume of one candle:

{4500 cm^3/}{1177.5 cm^3} approx 3.82

As it is not possible to make a fraction of a candle, you can make 3 complete candles with the given amount of wax.

Answer:

Option 1st is correct

[tex]f(-3) = -5[/tex]

Step-by-step explanation:

If any point [tex](x, y)[/tex] is on the graph then we can write the function as:

[tex]y= f(x)[/tex]

where

x is the independent variable and

y is the dependent variable.

As per the statement:

The point (–3, –5) is on the graph of a function.

⇒x = -3 and y = -5

By above definition we have;

[tex]f(-3) = -5[/tex]

Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]

We state restrictions for rational expressions to ensure that the denominator does not equal zero, as division by zero is undefined in mathematics. The restrictions are the values of the variable that make the denominator equal to zero. We state the restrictions whenever we are simplifying, performing operations with, or solving rational expressions.

A rational expression is an expression that can be written in the form of a fraction, where the numerator and the denominator are polynomials. The denominator of a rational expression cannot be zero because division by zero is not defined in mathematics. Therefore, when working with rational expressions, it is crucial to identify the values of the variable that would make the denominator equal to zero. These values are the restrictions, or domain restrictions, for the rational expression.

For example, consider the rational expression [tex]\(\frac{1}{x-3}\)[/tex]. The denominator is[tex]\(x-3\)[/tex]. To find the restriction, we set the denominator equal to zero and solve for [tex]\(x\)[/tex]:

[tex]\[x - 3 = 0\][/tex]

[tex]\[x = 3\][/tex]

Therefore, the restriction for this rational expression is [tex]\(x \neq 3\)[/tex], meaning that [tex]\(x\)[/tex] can be any real number except 3.

We must state these restrictions whenever we perform operations such as simplifying, adding, subtracting, multiplying, or dividing rational expressions, as well as when we are solving rational equations. This ensures that the operations are valid and that the solutions to the equations do not include any undefined expressions.

In summary, stating restrictions for rational expressions is a critical step in avoiding mathematical errors and ensuring that the expressions and equations we work with are well-defined.

GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.

GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9

2/3 + 4/9

= 2(3) + 4 (1) / 9

Now 2 is the common factor, so it allow us to use the distributive property.

= 2 (3 + 2) / 9

= 2(5) /9

=10 / 9 is the answer.

The confidence interval for a given sample value can be calculated using the following formula:

Confidence interval = Average value ± Margin of error

Which in this case the values are:

Average value = 85%

Margin of error = 12%

Therefore substituting the given values into the equation will give us:

Confidence interval = 85 ± 12

Confidence interval = 73, 97

Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.

Based from the given choices, only letter B 79% is within this range:

Answer:

B. 79%

Answer:

B. 79%

Step-by-step explanation:

yes

In order to transform (5 square root x^7)^3 into an expression with a rational exponent, first transform square root x^7 into x^(7/2), then raise entire expression to the power of 3. So, final expression is 125x^(21/2).

To transform (5 square root x^7)^3 into an expression with a rational exponent, firstly simplify the expression inside the bracket, then apply the exponent of 3 to the simplified expression.

So, the transformed expression with a rational exponent is 125x^(21/2).

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The question asks for the dimensions of a rectangular container with given volume and specific proportional relationships between its dimensions. Setting up and solving the equation 2500 = d × (4d) × (4d + 5) leads us to find the distinct depth, width, and height of the container.

The subject matter of the student's question pertains to the mathematics concepts of volume and dimensional relationships of rectangular prisms. Let's represent the depth of the shipping container as d, the width as 4d (since it is four times the depth), and the height as 4d + 5 (since it is 5cm taller than the width). The volume of a rectangular prism (such as our shipping container) is given by the formula Volume = length × width × height. Given the volume is 2500 cubic cm, or 2500 cm³, we can set up the equation 2500 = d × (4d) × (4d + 5).

Solving this equation leads us to find the dimensions of the container, wherein the depth, width, and height are represented by the variables d, 4d, and 4d + 5

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Approximately 1978 ft a passenger travel during a 5-minute ride and this can be determined by using the formula of the perimeter of a circle.

Given :

A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute.

The following steps can be used in order to determine the total distance travel by the passenger during a 5 minutes ride:

Step 1 - First determine the perimeter of the circle. The formula of the perimeter of the circle is given by:

[tex]\rm C = 2\pi r[/tex]

Step 2 - Now, substitute the value of known terms in the above formula.

[tex]\rm C=2\pi\times(21)[/tex]

[tex]\rm C= 131.94\;ft[/tex]

Step 3 - In one minute passenger travels:

[tex]\rm =131.94\times 3=395.82\; ft[/tex]

Step 4 - So, in three minutes passenger travels:

[tex]=395.82\times5[/tex]

= 1978 ft

So, approximately 1978 ft a passenger travel during a 5-minute ride.

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The equation for the student's question is 25 - (1/5)x = 18. Solving for x involves simple algebraic manipulation, resulting in x being equal to 35.

The student's question '25 decreased by 1/5 of a number is 18' is a basic algebra problem. We could represent the unknown number as x. So the equation would be 25 - (1/5)x = 18.

To solve the equation 25 decreased by 1/5 of a number is equal to 18, we can set up the equation as 25 - (1/5)x = 18, where x is the unknown number.

To isolate x, we first subtract 25 from both sides of the equation:

- (1/5)x = -7.

Next, we can multiply both sides of the equation by -5 to eliminate the fraction:

x = (-7) * (-5) = 35.

To solve for x, first, add (1/5)x to both sides to get 25 = 18 + (1/5)x.

Then, subtract 18 from both sides to obtain 7 = (1/5)x. Finally, multiply both sides by 5 to find the value of x. Thus, x equals 35.

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Answer:

The answer is B!!!!

Answer:

 [tex]\text{Probability}=4.3\%[/tex]

Step-by-step explanation:

Given : In a batch of 280 water purifiers, 12 were found to be defective.

To find : What is the probability that a water purifier chosen at random will be defective?  Write the probability as a percent.

Solution :

Total number of batch of purifiers = 280

Number of defective purifiers = 12

The probability that a water purifier chosen at random will be defective is given by,

[tex]\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total outcome}}[/tex]

 [tex]\text{Probability}=\frac{12}{280}[/tex]

 [tex]\text{Probability}=\frac{3}{70}[/tex]

Converting into percentage,

 [tex]\text{Probability}=\frac{3}{70}\times 100[/tex]

 [tex]\text{Probability}=4.28\%[/tex]

Round to nearest tenths,

 [tex]\text{Probability}=4.3\%[/tex]

The x-intercepts of the parabola with vertex (1,-9) and y-intercept of (0,-6) are of [tex]x = 1 \pm \sqrt{3}[/tex].

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the parabola has vertex (1,-9), hence h = 1, k = -9, and:

y = a(x - 1)^2 - 9.

The y-intercept is of (0,-6), hence when x = 0, y = -6, and this is used to find a.

-6 = a - 9

a = 3.

So the equation is:

y = 3(x - 1)^2 - 9.

y = 3x² - 6x - 6.

The x-intercepts are the values of x for which:

3x² - 6x - 6 = 0.

Then:

x² - 2x - 2 = 0.

Which has coefficients a = 1, b = -2, c = -2, hence:

[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(1)(-2) = 12[/tex]

[tex]x_1 = \frac{2 + \sqrt{12}}{2} = 1 + \sqrt{3}[/tex]

[tex]x_2 = \frac{2 - \sqrt{12}}{2} = 1 - \sqrt{3}[/tex]

The x-intercepts of the parabola are [tex]x = 1 \pm \sqrt{3}[/tex].

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The minimum cost of producing this product is:

                                13

The function which is used to represent the cost to produce x elements is given by:

          [tex]f(x)=5x^2-70x+258[/tex]

Now, on simplifying this term we have:

[tex]f(x)=5(x^2-14x)+258\\\\i.e.\\\\f(x)=5(x^2+49-49-14x)+258\\\\i.e.\\\\f(x)=5((x-7)^2-49)+258\\\\i.e.\\\\f(x)=5(x-7)^2-5\times 49+258\\\\i.e.\\\\f(x)=5(x-7)^2-245+258\\\\i.e.\\\\f(x)=5(x-7)^2+13[/tex]

We know that:

[tex](x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2+13\geq 13[/tex]

This means that:

[tex]f(x)\geq 13[/tex]

This means that the minimum cost of producing this product is: 13

assuming it is based on a 40 hour work week, working 52 weeks per year:

35485/52 = 682.40 per week

682.40/40 = 17.06 per hour

50606/52 = 973.19 per week

973.19/40 = 24.33 per hour

 so between 17.06 & 24.33 per hour