how many cards from a standard deck must be drawn to guarantee atleast 3 cards of the same suit have been drawn, pidgeon hole

Answer:

7

Step-by-step explanation:

we have 1008=2×2××2×3×3×3

The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.

Now 1008×7=2×2×2×2×3×3×7×7

7056=2×2×3×7

=84

Answer : 7

Answer:

1.   7

2.  square root is 84.

Step-by-step explanation:

First find the prime factors:

1008 =2*2*2*2*3*3*7

There's an even number of 2's and 3's but only one 7, so we multiply by 7

Smallest number = 7.

The square number is 1008 * 7

= 7056.

Its square root is  2*2*3*7 = 84.

The lifetime of the batteries in a package is 14.31 hours which exceeds that value for only 5% of all packages.

Give sample mean of 13 hours and standard deviation of 1 hour and sample size is 9.

We have to apply t test in this because the value of n which is sample size is less than 30.

We have been given the p value of the required mean so we have to find the t value for this with degree of freedom (9-1)=8

t value=2.306.

We know that

t=X bar-μ/s/[tex]\sqrt{n}[/tex]

s/[tex]\sqrt{n}[/tex]=1/[tex]\sqrt{3}[/tex]=0.57

Put all the values in the above formula to calculate required mean.

2.306=X bar-13/0.57

X bar=1.31442+13

=14.31442

after rounding off we get

X bar=14.31

Hence the lifetime of the batteries is 14.31 for which  the percentage exceeds 5%.

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Answer:

[tex]b^{2} +7b+7[/tex] with remainder 1

Answer:

See my picture below for the answer.

Step-by-step explanation:

If you look at the unit circle and locate 240 degrees.  You will see an ordered pair.  The first number -1/2 is the cos of 240 and the second number is the sin.

Answer:

it’s the square root of 3, divided by 2 (sorry, can’t type any special characters at the moment)

Step-by-step explanation:

-240 = 120 because you measure negative angles clockwise starting at 0.

Using unit circle, value of sin for an angle is the 2nd number

Answer:

3x + 2 >= 0

Step-by-step explanation:

Since this is a 4th root, not a cubic root, the radical can only contain 0 or positive numbers. Therefore there is 3x + 2 >= 0.

Answer:

x=4 and y=−9

Step-by-step explanation:

Problem:

Solve 7x+4y=−8;−8x−5y=13

Steps:

I will solve your system by substitution.

(You can also solve this system by elimination.)'

7x+4y=−8;−8x−5y=13

Step: Solve 7x+4y=−8 for x:

7x+4y+−4y=−8+−4y(Add -4y to both sides)

7x=−4y−8

7x/7 =  -4y-8/7 (Divide both sides by 7)

x=-4/7y + -8/7

Step: Substitute -4/7y + -8/7 for x in −8x−5y=13:

−8x−5y=13

-8(-4/7y + -8/7) −5y=13

-3/7y + 64/7 =13(Simplify both sides of the equation)

-3/7y + 64/7 + -64/7 = 13 + -64/7 (Add (-64)/7 to both sides)

-3/7y = 27/7

-3/7y/-3/7 = 27/7/-3/7 (Divide both sides by (-3)/7)

y=−9

Step: Substitute −9 for y in x= -4/7y + -8/7:

x = -4/7y + -8/7

x = -4/7 (-9) + -8/7

x=4(Simplify both sides of the equation)

Answer:

x=4 and y=−9

Answer:

c = 10

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)

Here given: a = 8 cm, b = 6 cm, c = ?

Substituting values:

8² + 6² = c²

c² = 64 + 36

c² = 100

c = √100

c = 10

Answer:

10 cm

Step-by-step explanation:

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

[tex]a^2=6^2+8^2[/tex]

[tex]a^2=100[/tex]

[tex]\sqrt{a^2}=\sqrt{100[/tex]

a=10

Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.

According to this question, a 2-column table with 5 rows is given.

If y varies directly with x, the mathematical representation is as follows:

y = kx

Since y = 3, when x = 1

3 = k × 1

k = 3

The relationship between x and y is as follows: y = 3x

Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.

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Answer:

5×3=15

15×3=45

therefore the largest value is 45

The largest possible value in the set is 92. The set has an equal mean and median. So, the set is {29, 29, 50, 50, 92}.

Mean:

For a set of data, the average of all the data values is said to be its mean.

Median:

When the set is arranged in ascending order, the middle term is said to be its median (if there are an odd number of data values in the set) or the average value of the two middle terms is the median (if there are an even number of data values in the set).

It is given that,

there are 5 numbers in the set

Mean = 50 and Median = Mean

So, Median = 50

Since there are 5 numbers in the set (odd number), the median is the third(middle) number.

Consider the first or smallest number as 's'.

Then the largest number = 3s + 5

By minimizing each term we get,

first term = s

second term = s

third term = 50

fourth term = 50

fifth term = 3s+5

If the mean is 50, then the sum of all the terms = 50 × 5 = 250

So,

s + s + 50 + 50 + 3s + 5 = 250

⇒ 5s + 105 = 250

⇒ 5s = 145

∴ s = 29

Thus, the smallest number is 29

Then, the largest number = 3s + 5 = 3 × 29 + 5 = 92

Therefore, the largest number in the given set is 92.

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The country is 3250 miles in distance from east to west, and 3400 miles from north to south.

Given Information

It is given that,

The distance of the country on map from east to west, l = 65 inches

The distance of the country on map from north to south, b = 68 inches

As per the given scaling of map, 1 inch = 50 miles

How large is the actual country?

Thus, the actual distance from east to west, L = l × 50 miles

L = 65 × 50 miles

L = 3250 miles

The actual distance from north to south, B = b × 50 miles

B = 68 × 50 miles

B = 3400 miles

Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.

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The value of angle C in the triangle is 50°.

From the information given, the angle A = 60° while B is given as 70° and we are told to calculate the value of C.

It should be noted that the sum of angles on a triangle is 180°. Therefore, the value of C will be:

= 180° - (60° + 70°)

= 180° - 130°

= 50°

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Total number of five letter strings formed by A,B,C and D with repetitions allowed

={4x4x4x4x4 = 4 power 5 = 1024

Now, fix BAD in a string at one place then we have 2 more places to be filled with 4 letters, total number of such strings

=4x4=16

Here, BAD can be at any of the 3 positions,

Hence the total number of strings with BAD in it

= 3 x 16=48

Now, The total number of strings not containing BAD

=1024-48

=976

Using 26 letters, the number of 5-letter words that can be formed when the letters are different is determined as follows: 26P5 = 26 × 25 × 24 × 23 × 22 = 7883600 different words.

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The compound inequality represents the situation is r > 4 and r ≤ 4.1

r > 4

r ≤ 4.1

Therefore, r > 4 and r ≤ 4.1 is the compound inequality which represent the situation.

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Its A: r > 4 and r ≤ 4.1

Answer:

9cm

Step-by-step explanation:

If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm

This gives us a ratio of 1:3

PQ = LM*3 = 3cm*3 = 9cm

Answer:

1161 confirmed cases

Step-by-step explanation:

In 2000 the number of cases was 86

Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.

So, we must multiply 13.5 and 86 to get the amount of cases in 2019.

13.5*86 = 1161 confirmed cases in 2019

#6

Yes

Direct variation because Time increases cupcakes increases and vice versa

#B

Constant of proportionality represents the amount of time required per cupcakes

#7

Yes we can find it

We have to check the x and y values of the ordered pairs (x,y)

If y is decreasing with respect to increase in x then it's inverse variation

Answer:

C

Step-by-step explanation:

You have a total of 6 outcomes (1,2,3,4,5,6).  That is your numerator.  Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3

The length of the hypotenuse of the triangle as given is; √58 cm.

It follows from the task content that the triangle described in the task content is a right triangle with two other side lengths; 7cm and 5cm.

Hence, it follows from Pythagoras theorem that the length of the hypotenuse side of the triangle is;

Hypotenuse = √(5² + 7²)

Hypotenuse = √58 cm.

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A ratio measure can be used to show this.

Therefore, a ratio measure can be used to show the given situation.

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ANSWER :          -7x + 14

EXPLANATION, to reverse division multiply

17.49 is the magnitude of the resultant vector. This can be obtained by adding the vectors and finding magnitude.

Resultant vector: vector that gives the combined effect of all the vectors. When we add two or more vectors, the outcome is the resultant vector.

For example,

(3,4) + (5,7) = (3+5,4+7) = (8,11)

(8,11) is the resultant vector of vector (3,4) and vector (5,7)

Magnitude of a vector: the length of the vector. The magnitude of the vector a is denoted as ∥a∥.

Magnitude of a = (a₁, a₂)

∥a∥=[tex]\sqrt{a_{1}^{2} +a_{2}^{2} }[/tex]

In the given question,

v (8,10) and w (7, -1)

Adding the vectors,

resultant vector = (8,10) + (7, -1) = (15, 9)

Magnitude of a vector (a,b) = √a²+b²

Here, magnitude = √15²+9² = √225+81 = √306 ≈ 17.49

Hence 17.49 is the magnitude of the resultant vector.

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The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Formation of the linear equation for the drinks bought by Maria:

The total number of drinks bought by the Maria is 13.

Lets say 'm' represents the number of medium drink.

's' represents the number of small drink.

Total drinks comprises of medium drinks and small drinks.

Thus,

s + m = 13, is the first linear equation.

Now medium drinks cost $3.

Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)

Total price for medium drinks = 3×m

Similarly,

Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)

Total price for small drinks = 2×s

Total cost = total cost of medium drink + total cost of small drink

          32  = 3×m + 2×s, is second linear equation.

From equation first substitute the value of 'm' in second equation to fine the total number of drink.

32 = 3×(13 - s) + 2×s

32 = 39 - 3s + 22

s = 7

Put s = 7 in first equation and calculate 'm'.

m = 13 -7

m = 6

Therefore, The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

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Using translation concepts, the equation of F(x) is:

A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is:

[tex]G(x) = x^4[/tex]

For function F(x), we have that:

Then the equation is:

A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]

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Answer:

  Tuesday

Step-by-step explanation:

Days of the week repeat every seven days, so Saturday is day (1+7n) for some integer n.

The value of n that makes the day number just under 10,000 is ...

  1 +7n ≤ 10000

  7n ≤ 9999

  n ≤ 1428 3/7

So, Day 1 +1428·7 = 9997 is Saturday. Day 10,000 is 3 days later. That makes Day 10,000 a Tuesday.

__

Additional comment

1428 weeks is about 27.5 years. You got married at age 27.

The number of pounds of 60% protein and 20% protein supplement used is 700 and 700 pounds respectively.

let

x + y = 1400

0.60x + 0.20y = 1400×0.40

0.60x + 0.20y = 560

From (1)

x + y = 1400

x = 1400 - y

Substitute into (2)

0.60x + 0.20y = 560

0.60(1400 - y) + 0.20y = 560

840 - 0.60y + 0.20y = 560

- 0.60y + 0.20y = 560 - 840

-0.40y = -280

y = -280/-0.40

y = 700 pounds

Recall,

x + y = 1400

x + 700 = 1400

x = 1400 - 700

x = 700 pounds

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Answer:

  (a)  see attached

Step-by-step explanation:

A table will represent a function if no input (x) values are repeated.

The offered tables can be evaluated as follows:

  (a) x-values {-4, -1, 1, 4}, no repeats. Is a function.

  (b) x-values {2, 2, 3, 3}, both values repeated

  (c) x-values {-5, -5, 5, 5}, both values repeated

  (d) x-values {2, 2, 7, 7}, both values repeated

The mean of the distribution given is 0.569.

Given some distribution like under:

     x                           p(x)

     0                            0.650

     1                             0.216

     2                             0.087

     3                             0.026

     4                             0.014

      5                            0.009

We have to find the mean of the distribution.

Mean is the sum of numbers divided by the numbers which are taken into consideration. It is also known as average.

Mean=sum/n

To find the mean of distribution we have to find sum of x*p(x)

∑xp(x)=0*0.650+1*0.216+2*0.0087+3*0.026+4*0.014+5*0.009

=0+0.216+0.174+0.078+0.056+0.045

=0.569

Hence the mean of the distribution given in the question is 0.569.

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Distribution in the given question is wrong and the right question is as the right distribution is as under:

 x                           p(x)

     0                            0.650

     1                             0.216

     2                             0.087

     3                             0.026

     4                             0.014

     5                            0.009

Answer:

1. Translate 5 units up (Fixed after a comment from subtomex0 - Thanks again!)

2. Vertical Compression by a scale factor of 3/8

3. Reflect across the y-axis, and shift 2 units to the left

4. Vertical stretch by a scale factor of 6, and shifting 1 unit up

5. Shifting 11 units to the left

6. Vertical stretch by a scale factor of 8

7. Vertical compression by a scale factor of 1/2, and reflection across the y-axis.

Answer:

W(2) = 5

Step-by-step explanation:

Because when you look at the graph, the y value is 5 when the x value is 2.

Answer:

w(2) = 5

Step-by-step explanation:

by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept

to calculate w(2):

w(2) = 4(2) - 3

w(2) = 8 - 3

w(2) = 5

or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)