if b<0 and |b| = 4b+15 what is the value of b

Answer:

Step-by-step explanation:

[tex]a \: apples = 1 \: hours\\x \: apples = 5 \: hours\\x = 5a\\Total \:no \:of \:apples \:picked\\\:by \:david \:= 5a\\\\\\b \:apples = 1 \:hour\\x \:apples = 8 hours\\x = 8b\\Total \:no \:of \:apples \:picked\\ \:by \:elanor = 8b\\\\Total \:no \:of \:Apples =5a+8b[/tex]

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

Answer:

This list of all the outcome of  [tex]E^c[/tex] is  [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

 [tex]P(E^c ) = 0.5[/tex]

Step-by-step explanation:

From the question we are told that

      The sample sample space is  [tex]S = \{ 1,2,3,4,5,6,7,8,9,10,11,12 \}[/tex]

       The number of elements in the sample space is [tex]n = 12[/tex]

        The event is  [tex]E = \{ 3,4,5,6,7,8 \}[/tex]

        The  number of outcomes in the Event is  [tex]n_e = 6[/tex]

The objective in to obtain [tex]P(E^c)[/tex]

 Now  [tex]E^c[/tex]  is the compliment of  E  and number of elements in [tex]E^c[/tex] ican be mathematically evaluated as

            [tex]nE^c = n - n_e[/tex]

substituting values

            [tex]E^c = 12-6[/tex]

             [tex]E^c = 6[/tex]

This list of all the outcomes of [tex]E^c[/tex] is

        [tex]E^c = \{ 1,2,9,10,11,12,\}[/tex]

Generally  [tex]P(E^c )[/tex]  which is the probability of  [tex]E^c[/tex] is mathematically evaluated  as

      [tex]P(E^c ) = \frac{nE^c}{n}[/tex]

substituting values

         [tex]P(E^c ) = \frac{6}{12}[/tex]

         [tex]P(E^c ) = 0.5[/tex]

Answer:

a). BLUE color

b). 20%

Step-by-step explanation:

a). "Which color was chosen by approximately one fourth of the students?"

  Since one fourth of the students will be represented by one fourth area of the circle given.

That means color of choice represented by the quarter of the circle will be the color liked by one fourth students.

In the figure attached, BLUE color is the choice of one fourth students in the class.

b). Area represented by purple, green and other colors is a quarter of the circle.

If we divide this quarter into five equal sections, then the total of purple and green will be  [tex]4\times \frac{1}{5}[/tex] of the the quarter of the circle.

Measure of the angle defined by purple or green sections = [tex]\frac{4}{5}\times 90[/tex]

                                                                                                     = 72°

Percentage of the students who preferred purple or green = [tex]\frac{72}{360}\times 100[/tex]

                                                                                                     = 20%

Answer:

blue

20%

Step-by-step explanation:

Answer:

The answer is 1/14w-8

Step-by-step explanation:

The limit of a function is the value it approaches.

In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1.  As x approaches negative infinity (far to the left), the curve f(x) approaches -1.

lim(x→∞) f(x) = 1

lim(x→-∞) f(x) = -1

In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2.  As x approaches negative infinity (far to the left), the curve f(x) approaches -3.

lim(x→∞) f(x) = 2

lim(x→-∞) f(x) = -3

Answer:

3 1/4

Step-by-step explanation:

Hey there!

Well if Cedarburg to Westford is 8 3/4 miles and Oxford to Westford is 5 1/2 miles, we can make the following,

CO = CW - OW

CO = 8 3/4 - 5 1/2

Make the denominators the same,

5 1/2

improper

11/2

*2

22/4

Proper

5 2/4

8 3/4 - 5 2/4

3 1/4 miles

Hope this helps :)

Answer:

[tex]\huge\boxed{n = 108\ nickels}[/tex]

Step-by-step explanation:

Let the nickels with Katy be n

So, the condition is

n = 6 (Shaun nickels)

While Nickels of Shaun = 18 , So

n = 6 (18)

n = 108 nickels

Answer:

0.033316

Step-by-step explanation:

We use the z score formula to solve for this question.

Since we are given the number of samples in the question, our z score formula is given as:

z = (x-μ)/ S.E

where x is the raw score

μ is the sample mean

S.E is the Standard error.

x is the raw score = 900

μ is the sample mean = Population mean = 947

Standard error =

This is calculated as Population standard deviation/ √No of samples

= 205/√64.

= 205/8

= 25.625

We proceed to calculate the z score

z = (x-μ)/ S.E

z = 900 - 947/25.625

= -1.83415

Using the z score table for normal distribution,

P(x≤ z) = P(z ≤ -1.83) = P(x ≤ 900)

P(x<900) = 0.033316

Therefore, the probability the mean of the sample is below 900 is 0.033316

Answer:

160 liters of 25%, 20 liters of 40%, 60 liters of 60%

Step-by-step explanation:

x + y + z = 240

0.25x + 0.4y + 0.6z = 0.35*240 = 84

z = 3y

x = 160

y = 20

z = 60

Answer:

x≥4

Step-by-step explanation:

The required solution for the inequality 5 - 2x ≤ -3 is x ≥ 4 or x ∈ [4, ∞).

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

5 - 2x ≤ -3.

Solve the inequality,

Add 3 to both the sides,

5 - 2x + 3 ≤ -3 + 3

8 - 2x ≤ 0

-2x  ≤ -8

Multiply -1 both the sides,

2x ≥ 8

x ≥ 4

The solution for the inequality is x ≥ 4 or x ∈ [4, ∞).

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Answer:

1 hour

Step-by-step explanation:

Hello, let's say that her departure trip takes t in minutes, as her return speed is 3 times her departure speed, she took t/3 for the return and we know that this 40 minutes less, so we can write.

t/3=t-40

We can multiply by 3

t = 3t -40*3 = 3t - 120

This is equivalent to

3t -120 = t

We subtract t

2t-120 = 0

2t = 120

We divide by 2

t = 120/2 = 60

So this is 60 minutes = 1 hour.

Thank you.

Answer:

a.0.375

b.0.125

c.0.375

1.0.375

2.0.125

3.0.375

Step-by-step explanation:

a.

The total events in a sample space are n(S)=8

The events that contains exactly two boys

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy.

Let A be the event that there are exactly two boys. Thus, n(A)=3.

So, probability of exactly 2 boys is P(A)=n(A)/n(S)=3/8=0.375.

b.

The event that contains exactly 0 girls.

Boy Boy Boy

Let B be the event that contains exactly 0 girls. Thus, n(B)=1.

So, probability of exactly 0 girls is

P(B)=n(B)/n(S)=1/8=0.125.

c.

The events that contains exactly 1 girl.

Boy Boy Girl,Boy Girl Boy,Girl Boy Boy

Let C be the event that contains exactly 1 girl. Thus, n(C)=3.

So, probability of exactly 1 girl is

P(C)=n(C)/n(S)=3/8=0.375.

Q1 is same as part a.

Q2 is same as part b.

Q3. is same as part c

Answer:

4b + .60a

Step-by-step explanation:

b represents the number of bunches of bananas

a represents the number of apple

Multiply the cost by the number purchased of each item and add them together

4b + .60a

Answer:

[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]

Step-by-step explanation:

Bananas represented by b

1 banana costs $4 so b bananas will cost $ 4 b

Apples represented  by a

1 apples costs 0.60 $ so a apples will cost $ 0.60 a

Totally, they will cost:

=> $ (4 b + 0.60 a)

Answer:

126°

Step-by-step explanation:

If that angle is 27, so is angle a.

180-27-27=126

Answer:

x≤−8

Step-by-step explanation:

2x+3≤x−5

Subtract x from each side

2x-x+3≤x-x−5

x+3≤−5

Subtract 3 from each side

x+3-3≤−5-3

x≤−8

Answer:

[tex]\huge \boxed{x \leq -8}[/tex]

Step-by-step explanation:

[tex]2x+3 \leq x-5[/tex]

[tex]\sf Subtract \ x \ from \ both \ parts.[/tex]

[tex]2x+3 -x\leq x-5-x[/tex]

[tex]\sf Simplify \ the \ inequality.[/tex]

[tex]x+3 \leq -5[/tex]

[tex]\sf Subtract \ 3 \ from \ both \ parts.[/tex]

[tex]x+3-3 \leq -5-3[/tex]

[tex]\sf Simplify \ the \ inequality.[/tex]

[tex]x \leq -8[/tex]

Answer:

D question,somewhat confusing, itsit's like simultaneous equation,but values are different

Answer:

x = 4 + 2y/3

Step-by-step explanation:

Answer:

His earnings for the period= $123

Step-by-step explanation:

Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.

If 30% of his earnings = $369

His earnings = x

30/100 * x= 369

X= 369*100/30

X= 123*10

X=$ 1230

His earnings for the period= $123

Answer/Step-by-step explanation:

The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.

Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.

The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].

Using the model, we can solve 0.34 + 0.49.

Add both fractions together.

[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]

[tex] \frac{83}{100} = 0.83 [/tex]

Answer:

The number of ways is  [tex]\left n} \atop {}} \right. P_r = 336[/tex]

Step-by-step explanation:

From the question we are told that

   The number of tickets are   [tex]n = 8[/tex]

    The number of finalist are [tex]r =3[/tex]

Generally the number of way by which this winners can be drawn and arrange in the order of   [tex]1^{st} , \ 2nd , \ 3rd[/tex]    is mathematically represented as

             [tex]\left n} \atop {}} \right. P_r = \frac{n\ !}{(n-r) !}[/tex]

substituting values

             [tex]\left n} \atop {}} \right. P_r = \frac{ 8!}{(8-3) !}[/tex]

           [tex]\left n} \atop {}} \right. P_r = \frac{ 8* 7*6*5*4*3*2*1}{ 5*4*3*2*1}[/tex]

           [tex]\left n} \atop {}} \right. P_r = 336[/tex]

Answer:

Step-by-step explanation:

50 : 10 = 5 speaks French only

50 -5= 45 the remainder

4/5 * 45= 36 speaks French and English

45 - 36= 9 speaks English only

The number of students who speak:

i) French only = 5 students,

ii) both French and English = 36 students,

iii) English only = 9 students.

Step 1: Find the number of students who speak French only.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Step 3: Find the number of students who speak both French and English.

Step 4: Find the number of students who speak English only.

Let's calculate it step by step:

Step 1: Find the number of students who speak French only.

1/10 of 50 pupils speak French only:

French-only speakers = (1/10) * 50 = 5 students.

Step 2: Find the remainder (students who speak both French and English) after subtracting the French-only speakers.

Remaining students = Total students - French-only speakers

Remaining students = 50 - 5 = 45 students.

Step 3: Find the number of students who speak both French and English.

4/5 of the remaining students speak both French and English:

Both French and English speakers = (4/5) * 45 = 36 students.

Step 4: Find the number of students who speak English only.

To find the English-only speakers, subtract the total number of French-only speakers and both French and English speakers from the total number of students:

English-only speakers = Total students - (French-only speakers + Both French and English speakers)

English-only speakers = 50 - (5 + 36) = 50 - 41 = 9 students.

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Complete question is:

There are 50 pupils in a class. Out of this number, 1/10 speak French only and 4/5 of the remainder speak both French and English. If the rest speak English only, find the number of students who speak​

i) French only,

ii) both French and English,

iii) English only,

Answer:

21

Step-by-step explanation:

√1500 = 38.7

Round to nearest whole number

≈39

39²-1500

= 1521 - 1500

= 21

Answer:

The answer is D)90

Hope I helped

Answer:

[tex]71,100[/tex]

Step-by-step explanation:

If you are trying to find a number that is written in word form, we can just use place values to find what goes where.

A number is broken down into this:

Ten thousands, thousands, hundreds, tens, ones.

If they have 7 ten thousands, the first digit will be a 7.

If they have 1 thousand, the second digit will be a 1.

If they have 1 hundred, the third digit will be a 1.

Since nothing is stated about tens, we assume it's value is 0.

And since there are no ones, it's value is 0.

So:

71,100.

Hope this helped!

=========================================================

Explanation:

The original line has a given slope of -6/13. The opposite reciprocal is 13/6. We flip the fraction and the sign from negative to positive.

With any two perpendicular slopes, they always multiply to -1

(-6/13)*(13/6) = (-6*13)/(13*6) = -78/78 = -1

--------------------

Since the perpendicular slope is 13/6, we need to see which of the four answer choices produces a slope of 13/6. Use the slope formula.

This is something you do through trial and error. You could start with A and work your way to D, or just pick at random. I'll go through each one by one starting at choice A.

---------------------

Let's try choice A

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 13)

m = (2 + 4)/(-7 - 13)

m = 6/(-20)

m = -3/10, we can see that choice A is not the answer, since we want m = 13/6 instead.

-----------------------

Let's try choice B

m = (y2 - y1)/(x2 - x1)

m = (2 - (-4))/(-7 - 6)

m = (2 + 4)/(-7 - 6)

m = 6/(-13)

m = -6/13, that doesn't work either

------------------------

Let's try choice C

m = (y2 - y1)/(x2 - x1)

m = (-7 - 6)/(-4 - 2)

m = -13/(-6)

m = 13/6, we found the answer

------------------------

For the sake of completeness, here is what choice D would look like

m = (y2 - y1)/(x2 - x1)

m = (-4 - 9)/(-4 - 6)

m = -13/(-10)

m = 13/10, which isn't the slope we want

Answer:

y = 15°

Step-by-step explanation:

Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:

5y + 5y + 2y = 180

12y = 180

y = 15°

Answer: c = 4.97 and c = -1.97

Step-by-step explanation: Mean Value Theorem states if a function f(x) is continuous on interval [a,b] and differentiable on (a,b), there is at least one value c in the interval (a<c<b) such that:

[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex]

So, for the function f(x) = [tex]2x^{3}-9x^{2}-60x+1[/tex] on interval [-4,9]

[tex]f'(x) = 6x^{2}-18x-60[/tex]

f(-4) = [tex]2.(-4)^{3}-9.(-4)^{2}-60.(-4)+1[/tex]

f(-4) = 113

f(9) = [tex]2.(9)^{3}-9.(9)^{2}-60.(9)+1[/tex]

f(9) = 100

Calculating average:

[tex]6c^{2}-18c-60 = \frac{100-113}{9-(-4)}[/tex]

[tex]6c^{2}-18c-60 = -1[/tex]

[tex]6c^{2}-18c-59 = 0[/tex]

Resolving through Bhaskara:

c = [tex]\frac{18+\sqrt{1740} }{12}[/tex]

c = [tex]\frac{18+41.71 }{12}[/tex] = 4.97

c = [tex]\frac{18-41.71 }{12}[/tex] = -1.97

Both values of c exist inside the interval [-4,9], so both values are mean slope: c = 4.97 and c = -1.97

Answer:

0.70319018

Step-by-step explanation:

Given the following:

Number of students surveyed (n) = 15

Probability of attending tet festival (p) = 24% =0.24

Therefore,

Probability of not attending (1 - p) = (1 - 0.24) = 0.76.

The probability that at most 4 students will attend can be obtained using the binomial probability relation:

p(x) = nCx * p^x * (1 - p)^(n-x)

At most 4 students means:

p(x=0) + p(x=1) + p(x=2) + p(x=3) + p(x=4)

p(x=0) = 15C0 * 0.24^0 * 0.76^(15 - 0)

p(x=0) = 1 * 1 * 0.0004701 = 0.00047018

p(x=1) = 15C1 * 0.24^1 * 0.76^(14)

p(x=1) = 15 * 0.24 * 0.021448 = 0.07721

p(x=2) = 15C2 * 0.24^2 * 0.76^(13) =

p(x=2) = 105 * 0.0576 * 0.02822 = 0.17068

p(x=3) = 15C3 * 0.24^3 * 0.76^(12)

p(x=3) = 455 * 0.013824 * 0.037133 = 0.23356

p(x=4) = 15C4 * 0.24^4 * 0.76^(11) =

p(x=4) = 1365 * 0.0033177 * 0.048859 = 0.22127

0.00047018 + 0.07721 + 0.17068 + 0.23356 + 0.22127 = 0.70319018

Answer:

the events of using Brand Z computers and quitting your job are independent.

Step-by-step explanation:

Let A be the event that the population used Brand Z computers and let B be the event that the population quit their jobs.

We are told that 50% of the population used Brand Z computers last year. Thus, the probability of event A is;

P(A) = 50% = 0.5

Also, we are told that 4% of the population quit their jobs last year. Thus the probability of event B is;

P(B) = 4% = 0.04

Since 2% of the population used Brand Z computers and then quit their jobs. Then the probability of the population used Brand Z computers and then quit their jobs is;

P(A ∩ B) = 2% = 0.02

From the law of independent events, if A and B are to be independent events, then;

P(A ∩ B) = P(A) × P(B)

Thus;

P(A ∩ B) = 0.5 × 0.04 = 0.02

This is same value as what was given in the question, thus the events of using Brand Z computers and quitting your job are independent.