In a regular deck of cards, there are 52 total cards, 26 red, 26 black, and 13 of each of the four suits (hearts, clubs, spades, and diamonds). What is the probability, if you draw a card randomly, that the card will be a heart?

Answer:

Equation x(6+6)=3(10+x)

x=3.33

Step-by-step explanation:

Form an equation:

x(6+6) The result of 6+6 is multiplied by x, so you would put 6+6 in a bracket (you do what's inside the bracket first in BODMAS) and the x on the outside so you times the result by x.

3(10+x) The number x is added to 10 and the result is multiplied by 3, so the 10+x would go in a bracket with 3 on the outside.

These equal each other, so you would put an equals sign between it to make:

x(6+6)=3(10+x)

Solve to find x:

12x=30+3x You expand the brackets to make this.

9x=30 You would move 3x to the other side by doing the inverse and taking away 3x from 12x.

x=3.33 To get x you would have to do 30 divided by 9 which is 3.33.

Hope this helps :)

The number asked is 8

The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, When six is added to six times a number, the result obtained is the same as when the number is added to 10 and the result multiplied by 3.

Let the number be x,

Establishing, the equation,

6x+6 = 3(x+10)

6(x+1) = 3(x+10)

6/3(x+1) = x+10

2(x+1) = x+10

2x+2 = x+10

x = 8

Hence, the required number is 8.

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Answer:

slope=0

Step-by-step explanation:

Slope (m) = ΔY /ΔX =0  

ΔX = -3 – 6 = -9

ΔY = 8 – 8 = 0

Distance (d) = √ΔX2 + ΔY2 = √81 = 9

Equation of the line:

y = 0x + 8

When x=0, y = 8

We found that x = 5 is the value that makes the equation true.The solution to the equation 2x + 4 = 14 is x = 5.

The guess-and-check method involves making an initial guess for the solution of the equation and then systematically checking whether the guess satisfies the equation. By manipulating the equation and trying different values for x, we can determine the solution. In this case, the equation is 2x + 4 = 14, and we can use the guess-and-check method to find the value of x that satisfies the equation.

We start with the equation 2x + 4 = 14 and want to find the value of x that satisfies this equation. We can use the guess-and-check method to systematically determine the solution.

Step 1: Make an initial guess.

Lets start with x = 5 as an initial guess.

Step 2: Check the guess.

Substituting x = 5 into the equation:

2(5) + 4 = 14

10 + 4 = 14

14 = 14

Since the left side of the equation equals the right side, the guess is correct, and x = 5 is a solution to the equation.

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Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

\(\bold{\huge{\underline{ Solution }}}\)

Here,

\(\sf{ x + 2y = 13 ...eq(1)}\)

\(\sf{ x + 5y = 28 ...eq(2)}\)

By solving eq(1) :-

\(\sf{ x + 2y = 13 }\)

\(\sf{ x = 13 - 2y ...eq(3)}\)

Subsitute eq(3) in eq(2) :-

\(\sf{ (13 - 2y) + 5y = 28 }\)

\(\sf{ 13 - 2y + 5y = 28 }\)

\(\sf{ 13 + 3y = 28 }\)

\(\sf{ 3y = 28 - 13 }\)

\(\sf{ 3y = 28 - 13 }\)

\(\sf{ 3y = 15 }\)

\(\sf{ y = }{\sf{\dfrac{ 15}{3}}}\)

\(\sf{ y = }{\sf{\cancel{\dfrac{ 15}{3}}}}\)

\(\bold{ y = 5 }\)

Thus, The value of y is 5

Subsitute the value of y in eq(1) :-

\(\sf{ x + 2(5) = 13 }\)

\(\sf{ x + 10 = 13 }\)

\(\sf{ x = 13 - 10 }\)

\(\bold{ x = 3 }\)

Hence, The value of x and y are 5 and 3 .

\(\bold{\huge{\underline{ Let's \: Verify }}}\)

\(\sf{ x + 2y = 13 }\)

\(\sf{ 3 + 2(5) = 13 }\)

\(\sf{ 3 + 10 = 13 }\)

\(\sf{ 13 = 13 }\)

\(\bold{ LHS = RHS }\)

\(\sf{ x + 5y = 28 }\)

\(\sf{ 3 + 5(5) = 28 }\)

\(\sf{ 3 + 25 = 28 }\)

\(\sf{ 28 = 28 }\)

\(\bold{ LHS = RHS }\)

Let's use elimination method

We get

\(\\ \rm\Rrightarrow 2y-5y=13-28\)

\(\\ \rm\Rrightarrow -3y=-15\)

\(\\ \rm\Rrightarrow y=\dfrac{-15}{-3}\)

\(\\ \rm\Rrightarrow y=5\)

Putting on eq(1)

\(\\ \rm\Rrightarrow x+2y=13\)

\(\\ \rm\Rrightarrow x+2(5)=13\)

\(\\ \rm\Rrightarrow x+10=13\)

\(\\ \rm\Rrightarrow x=13-10\)

\(\\ \rm\Rrightarrow x=3\)

\(\LARGE{\underbrace{\underline{\rm{Verification:-}}}}\)

\(\\ \rm\Rrightarrow x+2y=13\)

\(\\ \rm\Rrightarrow 3+2(5)=13\)

\(\\ \rm\Rrightarrow 3+10=13\)

\(\\ \rm\Rrightarrow 13=13\)

And

\(\\ \rm\Rrightarrow x+5y=28\)

\(\\ \rm\Rrightarrow 3+5(5)=28\)

\(\\ \rm\Rrightarrow 3+25=28\)

\(\\ \rm\Rrightarrow 28=28\)

Hence verified!

Answer:

Step-by-step explanation:

m

Answer: 2

Step-by-step explanation:

The graph is a downward-opening parabola opening downward with its vertex at (2,0). Therefore, the correct option is C.

The equation y = -16t^2 + 64t + 16 represents the path of a projectile launched from a 16-ft-tall tower. To determine the correct graph, we can analyze the equation. The coefficient of t^2 (-16) is negative, indicating a downward-opening parabola. The coefficient of t (64) determines the horizontal shift of the graph, and in this case, t = 4 represents the maximum height of the projectile. The constant term (16) represents the initial height of the tower.

Considering these factors, we find that the correct graph of the equation is option C. It depicts a downward-opening parabola with its vertex at (2,0). The parabola starts at an initial height of 16 ft (the tower's height) and descends symmetrically from its vertex.

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This will give us a single value that is the best-predicted test score for a person who studies 4.5 years.

Based on the significant linear correlation between years of study and test scores, we can use regression analysis to find the best predicted test score for a person who studies 4.5 years. The regression equation can be represented as:

predicted test score = a + bx

where "a" is the y-intercept (the predicted test score when years of study is 0), "b" is the slope (the change in predicted test score for every additional year of study), and "x" is the number of years of study.

Assuming we have the necessary data and calculations for the regression equation, we can substitute x = 4.5 into the equation to find the predicted test score:

predicted test score = a + b(4.5)

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In the above case, the possible point system will be:

1st choice vote: 4 points

2nd choice vote: 2 points

In arranging for the turtle to win in this point framework, the point values relegated for 1st choice and 2nd choice votes have to be meet the taking after criteria:

Lets say:

1st choice vote: 4 points

2nd choice vote: 2 points

Thus by the use of these point values, the turtle would have the next chance of winning since 1st choice votes would be worth more point (4 point ) compared to 2nd choice votes (3 point ). This would push individuals to select the turtle as their 1st choice, because it would allow the turtle a better add up to point gains and increase its chances of winning.

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To obtain a sense of predictability, Kelly suggests engaging in hypothesis testing (d).

Kelly's suggestion aligns with the scientific method, which involves formulating hypotheses and testing them to make predictions and gain a sense of predictability. Hypothesis testing is a systematic approach that allows us to evaluate the validity of a proposed explanation or theory.

Template matching (a) refers to a process where incoming information is compared to stored templates or patterns to identify similarities. While it may be useful in certain contexts, it does not directly address the concept of predictability or the systematic evaluation of hypotheses.

Theory construction (b) involves the development of explanatory frameworks that describe and explain phenomena. While theory construction can contribute to predictability by providing overarching explanations, it is typically preceded by hypothesis testing to validate or refine the proposed theories.

Scientific discovery (c) refers to the process of making new observations, uncovering new phenomena, or formulating novel theories. While scientific discovery plays a crucial role in expanding knowledge and understanding, it is often followed by hypothesis testing to validate or refine the newly discovered information.

Therefore, Kelly's suggestion of engaging in hypothesis testing (d) is aimed at obtaining a sense of predictability by systematically evaluating and testing hypotheses to make reliable predictions about future outcomes or observations.

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Probability that the number drawn is less than 4 is given by 0.3

The likelihood of an event happening is gauged by probability.

The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

The overall chance of every event in a sample space is 1.

Let random variable X represent the number of the drawn tag.

Since the simple space consists of 10 equally likely events

S = {1,2,3,4,5,6,7,8,9,10}

The formula for probability distribution is given by:

f(x) = { (1/10) for x = 1,2....10,    else 0 elsewhere

since, each number can equally likely occur, therefore

P(x) = 1/10 = 0.1

Probability that the number drawn is less than 4 is given by:

P(x<4) = P(1) + P(2) + P(3)

           = 0.1 + 0.1 + 0.1

           = 0.3

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Answer:32.05

Step-by-step explanation:

SO after tax the total would be  $37.71.With original price $37.71 and 15% discount,

Price after discount: $32.05

You saved: $5.66

Answer:

Option A.

Step-by-step explanation

Divide 52 by 4 and get 13. Since Y is the amount of money you get from four hours, try finding the unit rate of one hour. Then, you can multiply the thirteen by 4, 8, 12, and 15, and you will get the answer in the chart.

70% of the days in San Diego are sunny.

In San Diego, the ratio of cloudy days to sunny days is 3:7.

To find the percentage of sunny days, we need to determine the proportion of sunny days out of the total number of days.

Let's assume that there are a total of 10 days.

Based on the ratio, we can say that 3 out of 10 days are cloudy, and 7 out of 10 days are sunny.

To calculate the percentage of sunny days, we divide the number of sunny days (7) by the total number of days (10) and multiply by 100.

So, \((\frac{7}{10} )\times 100= 70\%\).

Therefore, approximately 70% of the days in San Diego are sunny.

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But where are the equations?

Answer:

You need to give us the answers

Step-by-step explanation:

Given the points on the line:

(x1, y1) ==> (-2, 5)

(x2, y2) ==> (2, -3)

Let's find the equations that represent the line.

Apply the point-slope form:

y - y1 = m(x - x1)

Where m represents the slope, x1 and y1 represents the values of one point on the line.

To find the slope of the line apply the slope formula:

Substitute values into the formula and solve for m:

Substitute -2 for m in the point-slope equation:

y - y1 = -2(x - x1)

Substitute the coordinates of each point for x1 and y1

At (-2, 5):

y - 5 = -2(x - (-2)) ==> y - 5 = -2(x + 2)

At (2, -3):

y - (-3) = -2(x - 2) ==> y + 3 = -2(x - 2)

The possible equations for line are:

• y - 5 = -2(x + 2)

• y + 3 = -2(x - 2)

ANSWER:

• A. y + 3= -2(x - 2)

• B. y - 5 = -2(x + 2)

Answer:

I

Step-by-step explanation:

We have to added up the like therms

like therms are therms with the same literal parts

3a - 7a = -4a

6b-3b= 3b

-4a + 3b+ 9c

Answer:

$797.30 or B on egunty :

)

Answer:

The answer is B.$797.30 on Edge 2021

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Answer:

velocity = displacement/change in time

Step-by-step explanation:

Answer:

v = delta s/ delta t

Step-by-step explanation:

velocity = change in displacement / change in time

Answer: 6

Step-by-step explanation: 288

=

3

(

4

)

×

w

×

4

w

=

288

3

(

4

)

⋅

4

=

72

12

=

6

I think <3

Answer:

The width is  

6  cm. You can find it by taking the formula for the volume of a cube and rearranging it to find the width.

Step-by-step explanation:

Answer:

24496

Step-by-step explanation:

40912 * (1-5%) ^10 = 24495.5

becuase they are humans, so round up to 24496

Answer:

The next statements are are;

Statement                                                  \({}\)        Reason

Segment \(\overline {DC}\) ≅ Segment \(\overline {AB}\)                        \({}\)   CPCTC

\(\overline {AD}\) ≅ \(\overline {BC}\) and \(\overline {DC}\) ≅ \(\overline {AB}\), therefore;

ABCD is a parallelogram                    \({}\)               Parallelogram side theorem

Step-by-step explanation:

Statement                                                  \({}\)        Reason

Segment \(\overline {DC}\) ≅ Segment \(\overline {AB}\)  by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

Given that \(\overline {AD}\) ≅ \(\overline {BC}\) and we have that \(\overline {DC}\) ≅ \(\overline {AB}\), we get;

ABCD is a parallelogram                    \({}\)               Parallelogram side theorem

The parallelogram side theorem states that a quadrilateral is a parallelogram if it has two pairs or sets of congruent opposite sides.

The quadratic equation from the graph is ax²+8=0.

From the given figure, the vertex (h, k)=(0, 0) and the point is (x, y)=(4, -8).

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

Now, f(x) = a(x - 0)² + 0

f(x) = ax²

Here, f(4)=-8

So, -8=ax²

⇒ ax²+8=0

Therefore, the quadratic equation from the graph is ax²+8=0.

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There are 7 degrees of freedom.

In performing the pooled-variance t test, the degrees of freedom can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)

Substituting the given values:
df = (4 - 1) + (5 - 1)
df = 3 + 4
df = 7

Therefore, there are 7 degrees of  freedom.

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There are 7 degrees of freedom for the pooled-variance t-test.

To perform a pooled-variance t-test, we need to calculate the degrees of freedom. The formula for degrees of freedom in a pooled-variance t-test is:

\(\[\text{{df}} = n_1 + n_2 - 2\]\)

where \(\(n_1\)\) and \(\(n_2\)\) are the sample sizes of the two independent samples.

In this case, \(\(n_1 = 4\)\) and \(\(n_2 = 5\)\). Substituting these values into the formula, we get:

\(\[\text{{df}} = 4 + 5 - 2 = 7\]\)

In a pooled-variance t-test, we combine the sample variances from two independent samples to estimate the population variance. The degrees of freedom for this test are calculated using the formula \(df = n1 + n2 - 2\), where \(n_1\)and \(n_2\) are the sample sizes of the two independent samples.

To understand why the formula is \(df = n1 + n2 - 2\), we need to consider the concept of degrees of freedom. Degrees of freedom represent the number of independent pieces of information available to estimate a parameter. In the case of a pooled-variance t-test, we subtract 2 from the total sample sizes because we use two sample means to estimate the population means, thereby reducing the degrees of freedom by 2.

In this specific case, the sample sizes are \(n1 = 4\) and \(n2 = 5\). Plugging these values into the formula gives us \(df = 4 + 5 - 2 = 7\). Hence, there are 7 degrees of freedom for the pooled-variance t-test.

Therefore, there are 7 degrees of freedom for the pooled-variance t-test.

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The area of the wafer is 1590.43 cm² and the number of dies the same wafer can contain if each die has a side of 4 cm is 63

If a wafer can contain 500 dies with 2 cm diagonal, then the wafer's diagonal length would be

√(2 * 2 * 500)

= sqrt(2000)

= 45 cm

Therefore, diagonal length would be 45 cm.

Area of wafer is given by,

= πr²

= π(45/2)²

= 1590.43 cm²

Therefore, the area of the Wafer is 1590.43 cm².

The number of dies that can be fixed if die has a side of 4 cm,

√4√2 x 4√2 x X = 45

32X = 2025

x = 63

Therefore, the number of dices that can be contained by the wafer if side is 4cm is 63

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Answer:

AB = 10

Step-by-step explanation:

ΔABC ≈ ΔDEC

AB/5 = AC/DC

12AB = 120

AB = 120/12 or 10