A deck of cards contains 52 cards. These cards consist of four suits​ (hearts, spades,​ clubs, and​ diamonds) of each of the​ following: 2,​ 3, 4,​ 5, 6,​ 7, 8,​ 9, 10,​ jack, queen,​ king, and ace. If a card is chosen from a deck of​ cards, find the probability of drawing the 8 of spades.

Answer:

No, it's not a counterexample, because 48 is a multiple of 8

Step-by-step explanation:

I think like 4 x 3 + 8 x 2 = 28 is a counterexample, because 28 is not a multiple of 8.

Perl's conjecture that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8 is incorrect. In fact, the sum would definitely be a multiple of 4 but not necessarily a multiple of 8, since the sum of integers multiplied by 4 does not guarantee that it's a multiple of 8.

The subject of this question is Mathematics, specifically dealing with number theory and the properties of multiples and factorization. Perl's conjecture is that the sum of a multiple of 4 and a multiple of 8 must be a multiple of 8. We can examine this by understanding how multiples work.

A multiple of 4 can also be considered as 4n, where n is an integer. Similarly, a multiple of 8 is 8m, where m is integer. If we add both, we get 4n+8m. Now, as per distributive property of multiplication over addition, the expression becomes 4n+4(2m), which can be further simplified as 4(n+2m).

We can now see that the sum is actually 4 times the sum of some integer, so it must indeed be a multiple of 4. However, since it's not necessarily the case that 'n+2m' itself is a multiple of 2, we cannot say that the overall sum is guaranteed to be multiple of 8.

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The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Step-by-step explanation:

The function transformations are defined as:

Shifting function upwards b units

[tex]f(x) => g(x) = f(x)+b[/tex]

Shifting functions to the left b units

[tex]f(x) => g(x) = f(x+b)[/tex]

Given function is:

[tex]g(x) = \frac{1}{x}[/tex]

Shifting the function 4 units to the left will give us:

[tex]g(x) => g(x+b)\\= \frac{1}{x+4}[/tex]

Now shifting the function 4 units upwards

[tex]g(x) = \frac{1}{x+4} + 4[/tex]

Simplifying

[tex]g(x) = \frac{1+x+4}{x+4}\\= \frac{x+5}{x+4}[/tex]

The new equation will be:

[tex]g(x) =\frac{1}{x+4}+4[/tex]

OR

[tex]g(x) = \frac{x+5}{x+4}[/tex]

Keywords: function, transformations

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Answer:

410 / 23 = 17.8260869565

Lydia would need about 18 rolls of wallpaper to paper the walls of her kitchen.

Answer:

Step-by-step explanation:

bodyoddydyydydydydyyd∵㏒㏒㏒㏒㏒㏒㏒㏒㏒㏒㏒㏒⇒⇒⇒⇒⇒⇒⇒⇒≅≅≅≅≅≅≅≅≅≅≅≅≅⊂⊂⊂⊂⊂⊂⊂⊂⊂⊂⊂⊕⊕⊕∦∦∦∦∦

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Step-by-step explanation:

Given

Diameter of Cone = d = 6 cm

Radius will be:

r = d/2 = 6/2 = 3 cm

Height of cone = h = 3d = 18 cm

The volume of cone is given by:

[tex]V = \frac{1}{3}\pi r^2h[/tex]

Putting the values

[tex]V = \frac{1}{3} (3.14)(3)^2(18)[/tex]

Hence,

Option A: 1/3(3.14)(3cm)^2(18cm) is the correct answer

Keywords: Volume, cone

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Answer:

[tex]4\dfrac{1}{6}\ \text{kilometers per minute}[/tex]

Step-by-step explanation:

The graph shows a proportional relationship between the number of kilometers traveled (y) and the number of minutes spent traveling (x). This graph passes through the point (75,30). This means that in 30 minutes (x = 30), it was traveled 75 kilometers.

To find unit rate, divide the number of kilometers by the number of minutes:

[tex]\dfrac{75}{30}=\dfrac{25}{6}=4\dfrac{1}{6}\ \text{kilometers per minute}[/tex]

Answer:

x = -8

Step-by-step explanation:

-2x-16+0 = 0

Combine like terms.

-2x-16 = 0

Add 16 to both sides (to isolate the -2x from -16)

-2x = 16

Divide both sides by -2 to isolate the x from -2

x = -8

Answer:

The slope of f(x) is 1.5

Step-by-step explanation:

step 1

Find the slope of the linear function that has an x-intercept of 2/3 and a y-intercept of -1

so

we have the points

(2/3,0) and (0,-1)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{-1-0}{0-2/3}[/tex]

[tex]m=\frac{-1}{-2/3}[/tex]

[tex]m=\frac{3}{2}=1.5[/tex]

step 2

Find the slope of the function graphed

take the points

(0,-1) and (3,6)  approximately

substitute in the formula

[tex]m=\frac{6+1}{3-0}[/tex]

[tex]m=\frac{7}{3}=2.33[/tex]

step 3

we know that

f(x) represents the function with the smaller slope

The smaller slope is 1.5

therefore

The slope of f(x) is 1.5

You know that m<TSU=m<PSR because they make a vertical angle pair.

So...m<PSR=4x.

If, m<QSR=3x then m<PSQ=4x-3x=x because they are adjacent.

And, m<PQS=180-68=112 degrees (linear pair).

Now we know all the interior angles in triangle PQS so we can say that...

x+x+112=180 (sum of interior angles in triangle)

2x=68

x=34 degrees

The requried value of x is 34 in each case, as of the given conditions

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
As given in the question,

PU ∩ RT = S, Q ∈ PR

Since the sum of the remote interior angles is equal to the sum of the remote exterior angles.
∠SPQ + ∠PSQ = ∠SQR
∠PSQ = 68 - x

Now, When two lines intersect each other, their alternate angles are equal,
∠TSU = ∠PSR
4x = ∠PSQ + ∠QSR
4x = 68 - x + 3x
2x = 68
x = 34

Thus, the requried value of x is 34.

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Answer: Domain = { -3 , 6 , 5 , -6}

Range = { 7 , 2 , -1 , -6 }

Step-by-step explanation:

considering the points given

[tex]x_{1}[/tex] = -3                                [tex]y_{1}[/tex] = 7

[tex]x_{2}[/tex] = 6                                [tex]y_{2}[/tex] = 2

[tex]x_{3}[/tex] = 5                                [tex]y_{3}[/tex] = -1

[tex]x_{4}[/tex] = -9                               [tex]y_{4}[/tex] = -6

This shows that that is relationship between the values of x and the values of y.

All the values of x represent the domain and all the values of y represent the range.

Therefore :

Domain = { -3 , 6 , 5 , -6}

Range = { 7 , 2 , -1 , -6 }

Answer:

BC=16.992

Step-by-step explanation:

Answer:

16.992

Step-by-step explanation:

Answer:

y-4=-2(x+4)

Step-by-step explanation:

Perpendicular means negative reciprocal of the slope.

y-y1=m(x-x1)

y-4=-2(x-(-4))

y-4=-2(x+4)

The equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]y = -2x - 4[/tex].

To find the equation of the line that passes through the point (-4, 4) and is perpendicular to the line [tex]y = \frac{1}{2}x + 1[/tex], we need to do the following steps:

Determine the slope of the given line:
The slope of the given line [tex]y = \frac{1}{2}x + 1[/tex] is [tex]\frac{1}{2}[/tex].

Find the slope of the perpendicular line:
The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, if the slope of the given line is [tex]\frac{1}{2}[/tex], the slope of the perpendicular line will be [tex]-2[/tex] (since [tex]-1 \div \frac{1}{2} = -2[/tex]).

Use the point-slope form to find the equation:
The point-slope form of a line is [tex]y - y_1 = m(x - x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point on the line, and [tex]m[/tex] is the slope.
Here, the point is [tex](-4, 4)[/tex] and the slope [tex]m = -2[/tex].

Substituting these values into the point-slope form, we get:
[tex]y - 4 = -2(x + 4)[/tex]

Simplify the equation:
Distribute the slope on the right side:
[tex]y - 4 = -2x - 8[/tex]

Add 4 to both sides to solve for [tex]y[/tex]:
[tex]y = -2x - 4[/tex]

Answer:

It's your friend at school. 8360 is your answer.

Step-by-step explanation:

88 + 88

= 176 + 88

= 264 + 88

= 352 + 88

= 440 + 88

= 528 + 88

= 616 + 88 =

704 x 88

= 8360

Answer:

8,360

Step-by-step explanation:

88 + 88 + 88 + 88 + 88 + 88 + 88 + 88 × 88 is our problem.

Instead of adding all of these 88's together, we will just multiply 88 by 8 because there are 8 of these 88's.

That will leave us with: 704

But that is not our answer.

We still have one more step, and it is to multiply 704 by 8.

After we do that we will have: 8,360 as our answer.

I hope this helps! :>

To calculate the probability of a student scoring 75% or above, count how many scores are 75 or higher, and then divide by the total number of scores. In this case, the probability is 6 out of 15, or 0.4.

The question asks about the probability that a student picked at random scored 75% or above based on a list of exam scores.

To find this probability, one must count the number of scores that are 75% or higher and divide by the total number of scores.

Out of the provided scores (61, 74, 60, 70, 83, 90, 90, 80, 100, 102, 28, 75, 98, 21, 49), we see that there are 6 scores that are 75 or above (83, 90, 90, 80, 100, 102, 98, 75).

Since there are 15 scores in total, the probability is calculated as -

= 6/15

= 0.4.

Answer:

Percent change is −31.19%.

Step-by-step explanation:

It is given that "a price of a dirt bike dropped from $872 to $600".

Initial price = $872

New price = $600

We need to find the Percent change.

[tex]\text{Percent change}=\dfrac{\text{New price - Initial price}}{\text{Initial price}}\times 100[/tex]

[tex]\text{Percent change}=\dfrac{600-872}{872}\times 100[/tex]

[tex]\text{Percent change}=\dfrac{-272}{872}\times 100[/tex]

[tex]\text{Percent change}=-31.19266[/tex]

[tex]\text{Percent change}\approx -31.19[/tex]

Therefore, the percent change is −31.19%.

Final answer:

The chance change in the price of the dirt bike is-31.2, indicating a  drop in price from$ 872 to$ 600.

Explanation:

To calculate the chance change in the price of a dirt bike that dropped from$ 872 to$ 600, we follow this formula given in the reference  Chance change = (( change in value)/( original value)) × 100  

First, we find the change in value, which is the new price abated from the original price $ 600-$ 872 = -$ 272  also, we divide this change by the original price  -$ 272/$ 872 ≈-0.312  

Eventually, to find the chance change, we multiply this bit by 100  -0.312 × 100 = -31.2  This means the price of the dirt bike  dropped by31.2.

Let X = the number of hours the server works.

The equation for the amount Nick spends is 15x + 47

The next job pays 14x + 54

Set the equations to equal and solve for x:

15x + 47 = 14x +54

Subtract 14x from both sides:

X + 47 = 54

Subtract 47 from both sides:

X = 7

Now replace x with 7 in the second equation:

14x + 54 = 14(7) + 54 = 98 +54 = 152

The job would pay $152 and be 7 hours long.

Answer:

Tax on her normal wage is $ 6755

She can work 176 hours in a year and still remain in the same tax category

Step-by-step explanation:

Becky earns $633.81 for a 40 hour week.

Her normal monthly  wage is $ 633.81 *4 = $ 2535.24

Her annual income is $ 2535.2 *12=  $ 30,422.88

Tax on her annual income is  $30,422.88- $ 20,700= $9722.88

Tax on $ 20,700 is $ 3060

Tax on remaining $ 9722.88 is 0.38*9722.88=  $36,95

Total tax is $ 3060 + $ 3695= $ 6755

She can earn up to ( $ 36,000- $ 30, 423=) $ 5577 to remain in the same tax bracket.

She earns  $633.81/40= $ 15.84 in one hour

She gets twice the wage for the overtime  $ 31. 69

No of hours she can work = $5577/ $ 31.69 = 175.98 almost 176 hours

Answer:

[tex]\frac{2}{15}[/tex]

Step-by-step explanation:

Number of students participating in the competition = 13.

Total number of students in the school = 15.

Thus ,

the number of students who did not make to this competition =

Total number of students - number of students participated

= 15-13 = 2.

Now ,

probability of the student who do not makes it to the competition

= fraction of students who did not make to this competition from the total number of students .

=[tex]\frac{2}{15}[/tex].

Answer:

Step-by-step explanation:

buying the windows and having them installed costs $ 7699.25

installation alone costs 3325

therefore, the cost of the windows is : 7699.25 - 3325 = 4374.25

and if they are paying 230.25 per window, then there is

4374.25 / 230.25 = 18.997 windows

let me check something...

18 * 230.25 = 4144.50

19 * 230.25 = 4374.75

if ur numbers are written correctly, they can only buy 18 windows.....they would be short 50 cents from buying 19 windows

To determine the number of windows the Rayhills purchased, the total cost minus the installation cost was divided by the cost per window, leading to an estimate of approximately 19 windows.

To find out how many windows Rayhills bought, we need to subtract the installation cost from the total cost and then divide the result by the cost per window. The total cost of buying the windows and having them installed is $7,699.25, and the company charges $3,325 for the installation. If each window costs $230.25, we can calculate the number of windows as follows:

Now let's perform the division:

$4,374.25 / $230.25 ≈ 19 windows (rounded to the nearest whole number since you can't buy a fraction of a window).

Therefore, the Rayhills bought approximately 19 windows.

Answer:

45 degrees

Step-by-step explanation:

because 2 and 5 are vertical angles they are therefore congruent by definition, 5 is half of one and one is a right angle so measure angle 2 = 45 degrees

Answer:

50

Step-by-step explanation:

The total of all 6 angles make a circle, which equals 360°. Using the information below the figure,

2 * m∠5 = 90°, since 2 * m∠5 = m∠1 and ∠1 is a right angle.

Because ∠1, ∠5, and ∠6 are on one side of line L, they must equal 180°, and if ∠1 equals 90°,

m∠5 + m∠6=90°.

Since 2 * m∠5=m∠1 and m∠1=90°, m∠1 must be 45°. And by Transitive Property, m∠6 also equals 90°.

If the total measure of the angles is 360° and ∠1, ∠5, and ∠6 add up to 180°, ∠2, ∠3, and ∠4 must also add to 180°.

m∠6=m∠3 - 20°. We know that m∠6 is 45°, so we put that into an equation. I am going to use x as the measure of ∠3.

45=x-20  >>>  20+45=x-20+20  >>>  20+45=x  >>>  65=x  >>>  x=m∠3  >>>  m∠3=65

m∠3=m∠4, so m∠3+m∠4=65+65, or 130. And like I said above, ∠2, ∠3, and ∠4 must add to 180°. 180 minus 130 (the measure of ∠3 + ∠4) = 50, which has to be the measure of ∠2

Answer:

[tex]\text{Area of quadrilateral QRST}=216[/tex]

Step-by-step explanation:

Please find the attached image for the quadrilateral QRST.

We have been given that [tex]QS=18 \text{ and } RT=24[/tex]. We are asked to find the area of quadrilateral QRST.

Upon looking at the image of quadrilateral QRST, we can see that quadrilateral QRST is a kite as it has one pair of diagonally opposite equal angles (98 degrees).

We know that area of kite is equal to half the product of its diagonal.

We can see from our image that QS and RT are diagonal of kite, so the area of quadrilateral QRST would be:

[tex]\text{Area of quadrilateral QRST}=\frac{QS\cdot RT}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=\frac{18\cdot 24}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=\frac{432}{2}[/tex]

[tex]\text{Area of quadrilateral QRST}=216[/tex]

Therefore, the area of quadrilateral QRST is 216 square units.

well 4 is basically 1/5 of 20, so that would be about 20%

and since 4 x 4 is 16, my guess is that 16 is 80% of 20

Answer: 80%

Step-by-step explanation: To answer the question what percent of 20 is 16, we translate the question into an equation.

So we have "what percent" that's x, "of 20" means times 20, "is 16" = 16. So now we have the equation (x)(20) = 16.

Now to solve for x, since x is being multiplied by 20, we need to divide by 20 on both sides of the equation. On the left side of the equation the 20's cancel and we have x and on the right side of the equation we have 16 divided by 20 which is 0.8.

Now, remember that we want to write our answer as a percent so we need to convert 0.8 into a percent.

We can convert a decimal into a percent by moving the decimal point two places to the right so we can change 0.8 to a percent by simply moving the decimal point two places to the right and we have 80%.

This means that 80% of 20 is 16.

Answer:

Account C will give George at least a 4% annual yield.

Step-by-step explanation:

This problem can be solved by using simple maths formula given below

Year rate = (1+i)^n-1

where i = compounding rate and n = interval period

Now checking annual rate for each option using above formula

Account A)

Yr = 3.8% ( n= 12 and i= 3.75/12)

Account B)

Yr = 3.9 % ( n= 4 and i= 3.85/4)

Account C)

Yr = 4 % ( n= 365 and i= 3.95/365)

Answer:

the answer is 1.3

Step-by-step explanation:

12+4.3 is 16.3

16.3-15 is 1.3

Answer:

9

Step-by-step explanation:

PEMDAS stands for Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

So, the first thing you would do is Multiply:

12+4*3-15

12+12-15

Then Add:

24-15

Finally Subtract:

9

Answer:

The two integers are -47 and -48.

Step-by-step explanation:

Let the two consecutive integers be [tex]$ (n - 1) $[/tex] and [tex]$ n $[/tex].

Given that their sum is -95.

⇒ (n - 1) + n = - 95

⇒ 2n - 1 = - 95

⇒ 2n = - 94

Dividing by 2 throughout, we get:

n = - 47

⇒ n - 1 = - 47 - 1 = - 48

Therefore, the two integers should be - 47 and - 48.

Step-by-step explanation:

The answer will be 380 inches as of what I have done

Answer:

Step-by-step explanation:

[tex]1+3+9+27+81\\\\a_1=1,\ a_2=3,\ a_3=9,\ a_4=27,\ a_5=81\\\\r=\dfrac{a_{n+1}}{a_n}\Rightarrow r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=\dfrac{a_5}{a_4}\\\\r=\dfrac{3}{1}=\dfrac{9}{3}=\dfrac{27}{9}=\dfrac{81}{27}=3[/tex]

Good evening ,

Answer:

Step-by-step explanation:

Since it’s a geometric series then

a₁ = 1 ( because 1 is the first term of the series)

3/1 = 9/3 = 27/9 = 81/27 = 3 then r=3.

:)