Given a standard deck of playing cards, what is the probability of randomly selecting a card that is either red or a face card or both

The length of the hypotenuse is: [tex]\[ c = \sqrt{61} \][/tex]

To find the length of the hypotenuse of a right triangle with legs measuring 6 and 5, we use the Pythagorean theorem, which states:

[tex]\[ a^2 + b^2 = c^2 \][/tex]

where a  and b  are the lengths of the legs, and c is the length of the hypotenuse.

Given:

a = 6

b = 5

We need to find  c . Plugging the values into the Pythagorean theorem, we get:

[tex]\[ 6^2 + 5^2 = c^2 \][/tex]

Calculating the squares:

[tex]\[ 36 + 25 = c^2 \][/tex]

Adding the numbers:

[tex]\[ 61 = c^2 \][/tex]

To find c , we take the square root of both sides:

[tex]\[ c = \sqrt{61} \][/tex]

Therefore, the length of the hypotenuse is:

[tex]\[ c = \sqrt{61} \][/tex]

There were 945 girls and 1575 boys respectively.

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b or a/b

We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. The numerator is the upper quantity in the fraction and the denominator is the lower quantity in the fraction). Remember that the ratio should always be taken of quantities with the same unit of measurement. Also, the ratio is a unitless(no units) quantity.

We have been given that the ratio of the number of girls to the number of boys was 3 to 5.

The ratio girls to boys;

3 to 5

The Total = 8

The number of boys was 3 to 5 . of 2,520, Then;

3/8(2520) = 7560/8

girls = 945  

5/8(2520) = 12600/8

boys = 1575

Therefore, there were 945 girls and 1575 boys respectively.

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There are two correct answers which are not techniques used in geometric constructions with paper folding and these are:

A. Creating arcs and circles work the compass

C. Measuring lengths of line segments by folding the paper and matching the endpoints

In geometric folding, a straight line becomes a crease or a fold. This is achieved by a person by folding a piece of paper and flattening the crease rather than drawing lines to make a guide. Therefore this means that shapes like arcs, curves, circles by using the compass, and measurement of line segments are not used. However, constructions using compass have a long history in Euclidean geometry.

The following are not techniques used in geometric constructions with paper folding:

A. Creating arcs and circles with the compass.

C. Measuring lengths.

A geometric construction can be defined as a process that is used to draw angles, lines, and other geometric figures (shapes), especially through the use of only a compass and straightedge such as a ruler without measurements.

In Geometry, the techniques that should be used in geometric constructions with paper folding include the following:

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The probability of choosing both yellow hats can be obtained as 1/5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The number of yellow, green and blue hats are given as 7, 5 and 3.

Then, the total number of hats is 7 + 5 + 3 = 15.

Now, the probability for both hats to be yellow without replacement can be given as,

P(Both hats are yellow) = 7/15 × 6/14

⇒ P(Both hats are yellow) = 1/5.

Hence, the required value of probability is given as 1/5.

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Final answer:

For each kilometer increase in altitude, the temperature on the distant planet decreases by 235 degrees Celsius, according to the given equation y = -235x.

Explanation:

The question pertains to the relationship between altitude and temperature on a distant planet. Given the equation y = -235x, where y represents the temperature in degrees Celsius and x represents the height above the surface in kilometers, we are asked to determine the temperature change for each kilometer as we increase elevation from the surface.

To find the temperature change per kilometer, we examine the coefficient of x in the equation. Since the coefficient is -235, it signifies that for every kilometer increase in altitude, the temperature on this planet decreases by 235 degrees Celsius.

Final answer:

The determinant of the given 3x3 matrix [1 4 4 5 2 2 1 5 5] is calculated by expanding across the first row and is found to be -60.

Explanation:

To evaluate the determinant of a 3x3 matrix, you can use the method of expansion across any row or any column. Given the matrix [1 4 4 5 2 2 1 5 5], let's expand across the first row:

The determinant of the matrix is the sum of the products of each element in the chosen row or column and the determinant of the 2x2 matrix that remains after removing the row and column of that element.

Multiply the first element of the first row by the determinant of the remaining 2x2 matrix, then subtract the product of the second element and its associated 2x2 matrix, and add the product of the third element and its 2x2 matrix.

Calculating the values, we get: 1*(2*5 - 2*5) - 4*(5*5 - 2*1) + 4*(5*2 - 2*1) = 1*0 - 4*23 + 4*8 = 0 - 92 + 32.

Therefore, the determinant of the given matrix is -60.

The number 256,000 can be written as 2.56 x [tex]10^5[/tex]  in scientific notation

The number is written in the form [tex]a \times 10^b[/tex]

The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. We can for a time, ignore the value of 'a' for two comparable quantities and only compare their orders(this type of comparison is useful when difference is too big, like size of human to size of a star etc sort of comparisons).

Scientific notations value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.

To write 256,000 in scientific notation.

[tex]10^5[/tex] is followed by 5 zeros, so, it is 100,000.

Now Multiply 2.56 and 100,000 we get

2.56 x 100,000 = 256,000.

Therefore, First box is 100,000 and the second box is 5

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The graph of the inequality 12 - 2x < 16 is represented by an open circle at -2 on a number line, with shading to the right, indicating all values greater than -2.

To describe the graph representing the inequality 12 - 2x < 16, we first need to solve for x. Subtracting 12 from both sides of the inequality, we get -2x < 4. Dividing both sides by -2 (and remembering to flip the inequality symbol when dividing by a negative), we have x > -2.

Graphically, this is represented on a number line with an open circle at -2 and a shaded area to the right of -2, indicating that x can be any number greater than -2.

Answer:

A. x = two over three and x = -5

The equation 3x^2 + 13x = 10 can be solved using the quadratic formula. The solutions are given by:

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

Substituting the values from the equation (where a = 3, b = 13, and c = -10), we get:

[tex]$$x = \frac{-13 \pm \sqrt{13^2 - 4*3*(-10)}}{2*3}$$[/tex]

This simplifies to:

[tex]$$x = \frac{-13 \pm \sqrt{289}}{6}$$[/tex]

So, the solutions are:

[tex]$$x = \frac{-13 + \sqrt{289}}{6} = \frac{2}{3}$$[/tex]

and

[tex]$$x = \frac{-13 - \sqrt{289}}{6} = -5$$[/tex]

So, the correct answer is A. x = two over three and x = −5.

The cost of the cell phone is a function of the number of features.

The answer that best represents the situation described is option A. The cost of the cell phone is a function of the number of features.

In this case, as Kurt is buying a new cell phone, he knows that the more features the cell phone has, the more expensive it will be. This implies that the cost of the cell phone is dependent on the number of features it has.

For example, if a cell phone with basic features costs $200, a cell phone with additional features like a better camera, more storage, and waterproof capabilities may cost $400 or more.

the answer is 8.8

that is the answer

it was 1091227 on APEX

Answer:

True

Step-by-step explanation:

All work is shown and pictured

Answer:

Option 5th is correct

[tex]35x+120y = 500[/tex]

Step-by-step explanation:

Here, x represents only the clients that got a cut and y represent the clients that got a cut and color combo.

As per the statement:

Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo.

" Charges $35 for a cut" translated to 35x

"$120 for a cut and color combo" translated to 120y

It is also given that yesterday she had seven clients and earned $500.

⇒[tex]35x+120y = 500[/tex]

therefore, an  equations could be used to represent this situation is, [tex]35x+120y = 500[/tex]

Final answer:

To find when g(x) = 0 for the function g(x) = 6x² + 23x – 4, the quadratic formula is used, yielding the solutions x = 0.25 or x = −4.

Explanation:

The question asks for the values of x for which the quadratic function g(x) = 6x² + 23x – 4 equals zero. To find the values of x when g(x) = 0, one can use the quadratic formula, which is x = −(b ± √(b² ∔ 4ac)) / (2a) for a quadratic equation ax2 + bx + c = 0.

Here, a = 6, b = 23, and c = −4. Substituting these values into the quadratic formula gives:

x = −(23 ± √(23² ∔ 4 × 6 × (−4))) / (2 × 6)

After calculating the discriminant (√(b² ∔ 4ac)) and simplifying, we obtain the two solutions for x. Therefore, the correct answer is:

So, the correct answer, marked as (d) on Education 2020, corresponds to x = 0.25 or x = −4.

Answer:

C  (1, 1) is the solution to line K but not to line J..

Answer:

(0, 6)

Step-by-step explanation:

Since, when a points is reflected through the line y = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x, -(y-4))[/tex]

While, the points is reflected through the line x = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x-4, y)[/tex]

So, when (4,-2) is reflected over the line y = 2 is,

[tex](4,-2)\rightarrow (4, -(-2-4))[/tex]

Hence, the position of (4,-2) after reflection through line y = 2 is (4,6),

Now,  when (4,6) is reflected over the line x=2 is,

[tex](4,6)\rightarrow (4-4, 6)[/tex]

Hence, the position of (4,6) after reflection through line x = 2 is (0,6),

Third option is correct.

answer is 2x+3, x not equal to 6

 see attached pic for steps

Answer:

2x + 3, x ≠ 6

Step-by-step explanation: