if you pick a card at random from a well shuffled deck, what is the probability that you get a face card or a spade

Answer:

3√5 or ≈ 6.71

Step-by-step explanation:

The Distance Formula is d = √((x2-x1)² + (y2-y1)²)

Given Points: (-3, 2) and (0, -4)

          Points: (x1, y1) and (x2, y2)

Find the difference between coordinates:

(x2 - x1) = (0 - (-3)) = 3

(y2-y1) = (-4 - 2) = -6

Square the results and sum them up:

(3)² + (-6)² = 9 + 36 = 45

Now Find the square root and that's your result:

Exact solution: √45 = 3√5

Approximate solution: 6.7082

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The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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Answer:

-2x-8

Step-by-step explanation:

-5x + (3x-8)

-5x +3x -8

-2x - 8

Answer:

-2x-8

Step-by-step explanation:

-5x+(3x-8)

-5x+3x-8

-2x-8

Try this

Answer:

31,41,51,71

Step-by-step explanation:

Answer:

The answer is: 31,41,51,71

Answer:

There are 6 possible outcomes for die A and 6 possible outcomes for die B.

Each of the 6 outcomes of die A can be combined with each of the 6 outcomes of die B. Therefore the total number of possible outcomes for each roll is given by:

6*6=36

Using the hypergeometric distribution, there is a 0.2486 = 24.86% probability that the entire batch will be rejected.

The formula to find the hypergeometric distribution formula is

P(X=x)=P(x, N, n, K)[tex]=\frac{C_{k, x} C_{N-k, n-x} }{C_{N, n} }[/tex]

[tex]C_{n, x} =\frac{n!}{(n-x)!}[/tex]

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

For this problem, the values of the parameters are given as follows:

N = 8000, n = 7, k = 0.04 x 8000 = 320

The probability that the entire batch will be rejected is P(x≥1), given as follows: P(x≥1)=1-P(X=0)

In which,

P(X=0)=P(0, 8000, 7, 320)[tex]=\frac{C_{320, 0} C_{7680, 7} }{C_{8000, 320} }=0.7514[/tex]

Now, P(x≥1)=1-0.7514=0.2486

Therefore, 0.2486 = 24.86% probability that the entire batch will be rejected.

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Answer:

200+500

Step-by-step explanation:

its wrong i answered the wrong question

Answer:

84 mm

Step-by-step explanation:

1 cm = 10 mm

8.4 cm = 84 mm

Answer:

23.20

Step-by-step explanation:

join my stream for an explanation

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Answer:

α ≈ 23.20°

Step-by-step explanation:

given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α

tanα = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{7}[/tex] , then

α = [tex]tan^{-1}[/tex] ( [tex]\frac{3}{7}[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

sinα = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{58} }[/tex] , then

α = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

or

cosα = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{\sqrt{58} }[/tex] , then

α = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )

The formula that will help eli determine how much money he will earn in one week is a = 9h + nb

Let

a = (9 × h) + (n × b)

a = 9h + nb

Complete question:

Eli works in an electronics repair shop. he earns 9 dollars an hour plus a bonus for each item her repairs.

write a formula that will help eli determine how much money he will earn in one week

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Step-by-step explanation:

a square has the same perimeter as a 5cm by 7cm rectangle. which of the following area of the square

Answer:

At sea level, the altimeter would read 0 feet. Any positive readings on the altimeter would indicate she is above sea level. Any negative readings on the altimeter would indicate she is below sea level.

Step-by-step explanation: PLATO

Answer:

[tex] \frac{2 ln(5) }{3 ln(2) } [/tex]

Step-by-step explanation:

[tex] log_{8}(25) = \frac{ ln(25) }{ ln(8) } = \frac{ ln( {5}^{2} ) }{ ln( {2}^{3} ) } = \frac{2 ln(5) }{3 ln(2) } [/tex]

The correct options about the dilation are; Options A, B and E

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

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Answer: 13 questions

Step-by-step explanation:

52% of 25 is 13

25/x=100%/52%

x=13

The greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.

Given the numbers -5 1/2, 3. 75, -20. 8, -4, 11 1/4

a. SUM

=8 + [tex]11* \frac{1}{4}[/tex]

= [tex]8 + \frac{45}{4}[/tex]

= [tex]\frac{32 + 4}{4}[/tex]

= [tex]\frac{36}{4}[/tex]

= 9

B. Difference

= 8 - (-4)

= 8 + 4

= 12

C. Product

= [tex]8 * \frac{45}{4}[/tex]

= [tex]2 * \frac{45}{1}[/tex]

= 90

D. Quotient

= [tex]8 * 3. 25[/tex]

= 26

Thus, the greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.

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Answer:

one hundred and two years

Answer:

  42

Step-by-step explanation:

Each ages at the same rate. In 3 years, all will be 3 years older.

The sum of their ages now is ...

  A +J +D = 33

In 3 years, the sum will be ...

  (A +3) +(J +3) +(D +3) = (A +J +D) +(3 +3 +3) = 33 +9 = 42

In 3 years, the sum of their ages will be 42.

Answer:

Hello! The answer to your question is (-7, -4).

Step-by-step explanation:

To solve this problem, you have to use the midpoint formula:

[tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

Now, we can substitute our values in:

[tex](\frac{-9 + -5}{2}, \frac{1 - 9}{2} )\\= (\frac{-14}{2} , \frac{-8}{2}) \\= (-7, -4)[/tex]

Answer:

B

Step-by-step explanation:

The only x,y pair in the table is  4,2

The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)

An equation is an expression that shows the relationship between two or more numbers and variables.

The conversion from polar to rectangular coordinates is:

x = rcosФ and y = rsinФ

Hence:

x = 6cos(π/2) = 0, y = 6sin(π/2) = 6

The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)

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Using the normal distribution, it is found that there is a 0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given, respectively, by:

p = 0.4, n = 743

Hence the mean and the standard error are given, respectively, by:

The probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3% is the p-value of Z when X = 0.43 subtracted by the p-value of Z when X = 0.37, hence:

X = 0.43:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.43 - 0.4}{0.018}[/tex]

Z = 1.67

Z = 1.67 has a p-value of 0.9525.

X = 0.37:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.37 - 0.4}{0.018}[/tex]

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

0.9525 - 0.0475 = 0.905.

0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.

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1/216 is the equivalent expression for the given exponent [tex]6^{-3}[/tex].

An algebraic expression is a mathematical expression involving mathematical operations, variables, numbers, and mathematical quantities and combinations of them.

A negative exponent is the reciprocal of the same exponent with a positive value.

The reciprocal of any number is given by the fraction with the number as denominator and 1 as the numerator.

Here the given negative exponent is given by,

[tex]6^{-3}[/tex]

The exponent with positive value of the given negative exponent is given by [tex]6^3[/tex]

Reciprocal of the above exponent with positive value is given by,

[tex]\frac{1}{6^3}[/tex]

So now Calculating the negative exponent we have,

[tex]6^{-3} = \frac{1}{ {6}^{3} } = \frac{1}{216} [/tex]

Hence the equivalent expression for the given negative exponent is 1/216.

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The quantity of wheat to be transported by the company in metric tonnes is; 1.224 metric tonnes.

Since it follows that 1 metric tonne is equivalent to 2205 lb. It therefore follows that the quantity which is equivalent to 2700lb to be transported is;

= 2700/2205 = 1.224

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Answer:

Step-by-step explanation:

the triangles are similar, so same angles

the sum of the interior angles of a triangles is 180°

take away from 180° the know angles and you will have your answer

180 - 62 - 90 =

28°

The Answer Is:

4z

Hope this helped!

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{Identify the equivalent expression z + z + z + z}\downarrow[/tex]

[tex]\huge\textbf{Let's find out which one is equal to}\\\\\huge\textbf{the following expressions:}[/tex]

[tex]\large\textbf{z + z + z + z}[/tex]

[tex]\large\textbf{= 1z + 1z + 1z + 1z}[/tex]

[tex]\large\textbf{= 2z + 1z + 1z}[/tex]

[tex]\large\textbf{= 3z + 1z}[/tex]

[tex]\large\textbf{= 4z}[/tex]

[tex]\huge\textbf{Anwer:}[/tex]

[tex]\huge\boxed{\textsf{Option A. 4z}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The test statistic for the hypothesis would be 1.413.

Given that the participants in its new diet program lose, on average, more than 13 pounds and the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds.

The objective is to text the advertisement's claim that participants in new diet program lose weight, on average, more than 13 pounds.

Hypothesis:

Null hypothesis:H₀:μ=13

Alternative hypothesis:Hₐ:μ>13

Here, μ be the mean weight loss of all participants.

n=30,

Degree of freedom n-1=30-1=29

[tex]\bar{x}[/tex]=13.8 and s=3.1

To test the null hypothesis H₀, the value of test static would be calculated as follows:

[tex]\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end[/tex]

Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.

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Bricklayer Ben placed a total of 462 bricks.

Bricklayer Ben places 42 bricks per hour.

Bricklayer Bob places 36 bricks per hour.

Let

x = number of hours worked by Bricklayer Bob

y = number of hours worked  by Bricklayer Ben

Therefore,

x = 2y

42y + 36x = 1254

42y + 36(2y) = 1254

42y + 72y = 1254

114y = 1254

y = 1254 / 114

y = 11

Hence,  Bricklayer Ben placed a total of 42 × 11 = 462 bricks.

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If sin theta < 0 and tan theta > 0 as described in the task content, then, cos theta < 0 and 180<theta <270.

From the task content, it was described that sin theta < 0 and tan theta > 0.

Upon recall of angle quadrants, it follows that only the 3rd quadrant angles have positive tan values and negative sin values. Hence, it follows that the angle theta is in the 3rd quadrant and also has cos theta < 0.

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The true statements about the function are:

The table of values is given as:

x     f(x)

-3    -15

-2     0

-1      3

0      0

1      -3

2      0

3      15

From the table, the function values do not exceed 0 at the interval 0 to 2.

This means that f(x) ≤ 0 over the interval [0, 2].

Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0

This means that f(x)>0 over the interval (-2,0)

Also from the table, the function values are at least 0 at the intervals greater than 2

This means that f(x) ≥ 0 over the interval [2,∞)

Hence, the true statements are (b), (d) and (e)

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Answer:

The answers are B, C, and D

Step-by-step explanation:

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