"4 times the difference of 3 and y"

A: 1-y

B:4(3-y)

C:3(4-y)

D:4x(3-y)

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

D.

Step-by-step explanation:

the slope is going up 1 over 2 and the 1 is the y....hope this helps.

Answer:

The return on stockholders' equity is 11.3% and the return on common stockholders' equity is 20.1%.

Step-by-step explanation:

To calculate the return on stockholders' equity and the return on common stockholders' equity, we can use the following formulas:

Return on Stockholders' Equity = Net Income / Average Stockholders' Equity

Return on Common Stockholders' Equity = Net Income - Preferred Dividends / Average Common Stockholders' Equity

Using the given values, we can calculate:

a. Return on Stockholders' Equity:

Return on Stockholders' Equity = $135,000 / $1,194,690

Return on Stockholders' Equity = 0.113 or 11.3%

b. Return on Common Stockholders' Equity:

Return on Common Stockholders' Equity = ($135,000 - $5,400) / $644,776

Return on Common Stockholders' Equity = $129,600 / $644,776

Return on Common Stockholders' Equity = 0.201 or 20.1%

Therefore, the return on stockholders' equity is 11.3% and the return on common stockholders' equity is 20.1%.

Answer:

Step-by-step explanation:

      Population of the state will reach 40,000,000 in 21 years from year 2005.

      Option (3) will be the correct option.

          F = I(1 + r)ⁿ

          Here, F = Final population

                    I = Initial population

                    r = Growth rate

                    n = Number of years for population growth

Given in the question,

To find the number of years for population growth, substitute the values,

F = I(1 + r)ⁿ

40000000 = 31006000(1 + 0.012)ⁿ

40000 = 31006(1.012)ⁿ

\((1.012)^n=\frac{40000}{31006}\)

\(\text{log}(1.012)^n=\text{log}(1.29)\)

nlog(1.012) = log(1.29)

0.00518n = 0.11059

n = \(\frac{0.11059}{0.00518}\)

n = 21.34

n ≈ 21 years

     Therefore, population of the state will reach 40,000,000 in 21 years from 2005. Option (3) will be the answer.

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The function A(x) = x(400 - x) gives the area (in square feet) of the fenced-in region as a function of the length of the side of the rectangle perpendicular to the building (x).

The area of a rectangular field enclosed by 400 feet of fence can be calculated using the formula Area = Length x Width. Since one side of the field is against a building, fencing is not required on that side. Thus, the length of the rectangle perpendicular to the building (x) is one of the sides of the rectangle. The other side is calculated by subtracting x from 400 feet. The area (in square feet) of the fenced-in region is then given by the function A(x) = x(400 - x).

To illustrate, if the length of the rectangle perpendicular to the building (x) is 200 feet, then the width is calculated by subtracting 200 from 400, giving a width of 200 feet. The area of the fenced-in region is then given by A(x) = 200 x (400 - 200) = 200 x 200 = 40,000 square feet.

Therefore, the function A(x) = x(400 - x) gives the area (in square feet) of the fenced-in region as a function of the length of the side of the rectangle perpendicular to the building (x).

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Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16

Answer:

6

Step-by-step explanation:

First you subract 7 on both sides then you divide by 3 which gives you 6. 6 should be you answer.

7+3*x=25

-7         -7

3*x     = 18

/3         /3

     x=6

Answer:

4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The absolute value of any number is just its distance from 0.

-4 is 4 away from 0, so its absolute value is 4.

-5 is 5 away from 0, so its absolute value is 5.

Therefore, the equation is basically just asking what is 4 + 5, which is 9 :D.

Answer:

9

Step-by-step explanation:

The bars around the two numbers imply that it wants you to find the absolute value. Absolute value is the distance a number is from zero since distance is always positive to find the answer just make the number positive. Following this rule l-4l=4 and l-5l=5. Then add them together 4+5=9.

Answer:

  -1

Step-by-step explanation:

The slope is the ratio of "rise" to "run" for the line.

Here, the line passes through points (-2, 0) and (0, -2). For a "run" of 2 units, the line decreases by 2 units, so the slope is ...

  m = rise/run = -2/2 = -1

The slope of the line is -1.

Answer:

a) £320

b) £720

c) 2 days

Step-by-step explanation:

The question is all about inputting values and finding a result or rearranging and finding a result.

a) d = 6. C = 50(6)+20      = 320

b) d = 2x7 (7 days a week)  C = 50(2x7) + 20     = 720

c) C = 120 ... 120 = 50d+20

100 =50d      d = 100/50      = 2

Answer:

210

Step-by-step explanation:

(52-10)

42÷5

8.4×25=210

Answer:

BEODMASS

( 52 - 10 ) ÷ 5 × 23

42÷5 ×23

8.4 x 23

193.2

Answer:

(A) The value of t test statistics is 2.767 and P-value is 0.0042.

(B) We conclude that the mean of first group is greater than the mean of second group.

Step-by-step explanation:

We are given the following hypothesis below;

Null Hypothesis, \(H_0\) : \(\mu_1=\mu_2\)      {means that the mean of first group is equal to the mean of second group}

Alternate Hypothesis, \(H_A\) : \(\mu_1>\mu_2\)      {means that the mean of first group is greater than the mean of second group}

The test statistics that would be used here Two-sample t-test statistics as we don't know about population standard deviation;

                            T.S. =  \(\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }\)  ~ \(t__n__1-_n__2-2\)

where, \(\bar X_1\) = sample mean of first group = 56

\(\bar X_2\) = sample mean of second group = 51

\(s_1\) = sample standard deviation of first group = 8.2

\(s_2\) = sample standard deviation of second group = 6.9

\(n_1\) = sample of first group = 30

\(n_2\) = sample of second group = 40

Also, \(s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} }\) = \(\sqrt{\frac{(30-1)\times 8.2^{2} +(40-1)\times 6.9^{2} }{30+40-2} }\)  = 7.482

So, the test statistics  =  \(\frac{(56-51)-(0)}{7.482 \times \sqrt{\frac{1}{30} +\frac{1}{40} } }\)  ~ \(t_6_8\)

                                     =  2.767

(A) The value of t test statistics is 2.767.

Also, P-value of the test statistics is given by;

              P-value = P( \(t_6_8\) > 2.767) = 0.0042

(B) Now, at 10% significance level the t table gives critical value of 1.295 at 68 degree of freedom for right-tailed test.

Since our test statistic is more than the critical values of t as 2.767 > 1.295, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean of first group is greater than the mean of second group.

The mathematical function that models Autumn's situation of saving $500 that she keeps at home and does not add to the savings is G(x) = 500 + 0x.

A mathematical function is an equation, expression, rule, or law defining the relationship between the independent variable and the dependent variable.

There are many types of mathematical function, including:

The amount that Autumn saved = $500

The amount that Autumn adds to the savings = $0

Let the number of periods that Autumn saves the above amount = x

G(x) = 500 + 0x

Thus, based on the linear function above, the amount that Autumn saved would remain $500 after many periods.

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Answer:

Step-by-step explanation:

total interest paid is given as $4,643.46.

total payments = $429.95 x 36 months = $15,478.20

total lease payments = total payments - total interest

total lease payments = $15,478.20 - $4,643.46 = $10,834.74

Remaining balance = Total cost of the lease - Total lease payments

$23,495 - $10,834.74 = $12,660.26

If the Bitcoin economy had a yearly growth rate of 7% from 2017 to 2019, then the value in 2019 would be $1.07^3 = $1.225. If the economy had a negative growth rate of 5% in 2020, then the value in 2020 would be $1.225 x 0.95 = $1.1638. If the negative growth rate doubled in the next year, then the value in the next year would be $1.1638 x 0.9 = $1.04742.

To calculate the percentage change from 2018 to the next year, we can compare the values of the Bitcoin economy in those two years. The value in 2018 would be $1.07^2 = $1.1449. The percentage change would be ((value in next year - value in 2018) / value in 2018) x 100%. Substituting the values, we get ((1.04742 - 1.1449) / 1.1449) x 100% = -8.5%.

Therefore, the approximate percentage decrease of the Bitcoin economy in the next year, compared to 2018, is approximately 9%. The closest option is "Approximately 9% decrease".

Answer:

3.999 millimeters.

Step-by-step explanation:

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the radius (r) of the cylinder is 4 millimeters and the volume (V) is 200.96 cubic millimeters, we can substitute these values into the formula and solve for the height (h).

200.96 = π(4²)h

200.96 = 16πh

To solve for h, we can divide both sides of the equation by 16π:

200.96 / (16π) = h

Using a calculator, we can calculate the approximate value of h:

h ≈ 200.96 / (16 × 3.14159)

h ≈ 3.999

Therefore, the height of the cylinder is approximately 3.999 millimeters.

These triangles can be proven congruent by using ASA RULE.

What is congruent triangles and its rules ?

When two triangles are congruent, their three sides and their three angles match precisely.

If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.

ASA rule stands for Angle-Side-Angle rule which means two angles and a side of both triangles are equal.

Main Body:

In ΔTUV and ΔTWV

VT =VT                 ----(1)

∠VTU=∠TVW      -----(2)

As TUVW is a parallelogram

so, ∠T = ∠U

hence, ∠TVU =∠VTW    ----(3)

taking equation 1, 2,3

therefore, ΔTUV ≅ ΔTWV by ASA rule which means by Angle- Side- Angle rule.

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50

Step-by-step explanation:

plot it on the number line

Answer:

8/3

Step-by-step explanation:

i put equations as this:

x+40 = y

where x is galllons of pure mixture and y is the gallons of the new mixture

the other equation i id was:

x+0.2(40) = 0.25y

x+8 = 0.25y

y = 4x+32

solve using substitution

(x+40) = 4x+32

x = 4x-8

-3x = -8

x = 8/3

The resulting matrix after the row operation is given as follows:

\(\left[\begin{array}{ccc}-6&1&-8\\2&9&7\\-7&5&2\\2&8&-8\end{array}\right]\)

The matrix in the context of this problem is defined as follows:

\(\left[\begin{array}{ccc}-6&1&-8\\-7&5&2\\2&9&7\\2&8&-8\end{array}\right]\)

The row operation is given as follows:

R2 <-> R3.

Meaning that we must exchange the elements on the rows 2 and 3.

The rows of the matrix are given as follows:

Exchanging the rows, the resulting matrix is given as follows:

\(\left[\begin{array}{ccc}-6&1&-8\\2&9&7\\-7&5&2\\2&8&-8\end{array}\right]\)

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The value of x in the secant intersection is 4.

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.

Therefore, let's find the value of x using the secant intersection theorem as follows;

4(4+x + 2) = 5(5 + x - 1)

4(6 + x) = 5(4 + x)

24 + 4x = 20 + 5x

24 - 20 = 5x - 4x

x = 4

Therefore,

x = 4

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Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

2.83333333333

Step-by-step explanation:

(3 2/5) / (1 1/5) = 2.83333333333

Answer:

85/30 or 2.833333333

Step-by-step explanation:

When dividing fractions, you must find the reciprocal of the second number and multiply it as usual.

It is also much easier to solve after you convert these numbers to improper fractions.

In this case,

3 2/5 = 17/5

1 1/5 = 6/5

17/5 ÷ 6/5

17/5 x 5/6

85/30 (17/6 reduced)

or

2.83333333333333333333

Thus, the translation rule which represents the translation of pre-image, ΔABC, into the image, ΔA'B'C is of : (x, y) → (x + 7, y – 6)

In geometry, a function that shifts an object a specific distance is referred to as translation. Nothing else is done to change the object. It is not scaled, reflected, rotated, or refracted.

Every point of such object must be translated by the same amount and in the same direction.

Given data:

coordinates of pre-image ΔABC:

A(-3,4), B(-2, 1) C(-4,1)

coordinates of image ΔABC:

A'(4,-2), B'(3, -5) C'(5,-5)

A(-3 + 7,4 – 6) - > A'(4,-2)

B(-2 + 7, 1 – 6) - > B'(3, -5)

C(-4 + 7,1 – 6) -> C'(5,-5)

Thus, the translation rule which represents the translation of pre-image, ΔABC, into the image, ΔA'B'C is of : (x, y) → (x + 7, y – 6)

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So

And

sin47=0.73

cos47=0.68

So meanwhile sin is greater so 6sin is also greater

Answer:

Ship 2

Step-by-step explanation:

From inspection of the diagram, the problem has been modeled as a right triangle.  Therefore, to find \(x\) and \(y\), use trigonometric ratios then compare to determine which distance is the smallest.

Trigonometric ratios

\(\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}\)

where:

To find \(x\) use the sine trig ratio:

\(\implies \sf \sin(\theta)=\dfrac{O}{H}\)

\(\implies \sin(47^{\circ})=\dfrac{x}{6}\)

\(\implies x=6 \sin(47^{\circ})\)

\(\implies x=4.39 \: \sf miles \:(2\:dp)\)

To find \(y\) use the cosine trig ratio:

\(\implies \sf \cos(\theta)=\dfrac{A}{H}\)

\(\implies \cos(47^{\circ})=\dfrac{y}{6}\)

\(\implies y=6 \cos(47^{\circ})\)

\(\implies y=4.09 \: \sf miles \: (2 \: dp)\)

As 4.09 < 4.39, ship 2 is currently closer to the coast guard.

Answer: -3

Explanation:

Follow PEMDAS for Order of Operations

Calculate within the parentheses

then Add and subtract

Answer:

-3

Step-by-step explanation:

(10-7)-14+8=3-14+8

11-14= -3

Greetings from Brasil...

It is possible to answer this question through Determinant

| X     Y     1 |

| X₁    Y₁    1 |  = 0

| X₂    Y₂   1 |

We have:

(X₁; Y₁) = (-9; 8)

(X₂; Y₂) = (-3; -1)

then

| X   Y   1 |

| -9  8   1 |  = 0

| -3  -1   1 |