26 In a bag there are only red counters, blue counters, green counters and pink counters.
A counter is going to be taken at random from the bag.
The table shows the probabilities of taking a red counter or a blue counter.
Colour
Probability
red
0.05
blue
1 -0.15 -0.05
0.8
0.15
green
There are 18 blue counters in the bag.
(b) Work out the total number of counters in the bag

Answer:

d = 0.0625 m

Step-by-step explanation:

The velocity of an object dropped from a tall building is given by :

\(v=\sqrt{64d}\)

Where

d is the distance in feet

We need to find the distance when the velocity is 32 ft/s

Rearranging for d,

\(v^2=64d\\\\d=\dfrac{64}{v^2}\)

Put v = 32 ft/s

\(d=\dfrac{64}{32^2}\\\\d=0.0625\ m\)

So, the required distance is 0.0625 m.

American adults believes in alien for the  given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).

As given in the question,

Sample of American adults surveyed 'n' = 200

Percent of people believes in aliens are success  'p'= 72%

                                                                                      = 0.72

Percent of people who don't believes (failure) in aliens ' 1 - p'  = 1 - 0.72

                                                                                          = 0.28                                                                                    

95% Confidence interval that represents Americans adults who believes in aliens

value of z - score for 95% confidence interval = ± 1.96

Margin of error 'MOE'= (z-score)√p ( 1- p) /n

                                   = ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200

                                   = 1.96 ( √0.2016 / 200)

                                   = 1.96 ×√0.001008

                                   = 0.063

Lower limit = p - MOE

                 = 0.72 - 0.063

                 = 0.66

Upper limit =  p + Margin of error

                 = 0.72 + 0.063

                 = 0.78

Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).

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Answer:

10,305.99 cm^3

Step-by-step explanation:

V=4/3πr^3=4/3·π·13.5^3≈10305.9947

Answer:

523.5988in³

Step-by-step explanation:

input Data :

Length = 5 in

Objective :

Find what is volume of the sphere for given input data?

Formula :

Volume =

4πr3

3

Solution :

Volume =

4 x 3.1416 x 53

3

=

4 x 3.1416 x 125

3

=

1570.7963

3

Volume = 523.5988 in³

For the given expression √3, its index form is written as ( 3 )¹/² .

As given in the question,

Given expression is equal to :

√3

Standard form of writing expression in index form is given by:

√  ( square root ) will express the value in index form as 1 / 2 in the exponent.

√x = ( x ) ¹/²

Here x = 3 substitute the value of x in the standard way of index form we have:

Index form of the given expression is written as :

√3

= ( 3 )¹/²

Therefore, for the given expression √3, its index  form is written as ( 3 )¹/² .

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Answer:

x ≥ 10

Step-by-step explanation:

So put a filled-in dot on 10 and an arrow going to the right

Answer: x ≥ 10

Step-by-step explanation: i took the test

Answer:

27318 dollars

Step-by-step explanation:

add 24,789 to 2529 to get 27,318

Answer:

25 black and 11 white

Step-by-step explanation:

lets say black marbles are x and white marbles are y

x+y=36

y+14=x

So: y+14+y=36

2y=22

y=11

Hence, x=25

Hope that helps!

Okay, here we have this:

Considering the provided sentences, we are going to apply the law of syllogism, so we obtain the following:

Let us remember that the law of Syllogism says that:

(1) If p , then q . And (2) If q , then r .

Then we can derive that: (3) If p , then r .

Applying:

(1) If the dog jumps in the lake, then it gets wet. (R->S)

(2) If the dog gets wet, then it can't come in the house. (S->T)

We can derive that:

(3) If the dog jumps in the lake, then it can't come in the house. (R -> T)

Answer: 6/5 and -3/4

Step-by-step explanation:

(2x-3)/9=(3x-4)/6

18*(2x-3)/9=18*(3x-4)/6

2(2x-3)=3*(3x-4)

4x-6=9x-12

-5x=-6

x=6/5

(8x+2)/4=4x/3

12*(8x+2)/4=12*4x/3

3(8x+2)=4*4x

24x+6=16x

8x=-6

x=-3/4

The graph for the system of linear equation is attached

An equation is said to be linear if the variables are of power not greater than one. This is to say the power of the variables should be one. It is a norm in math not to write the power when the power is one

For the equation given the the powers of both y and x are all 1. Linear equations also have a straight line graph hence have the equation of straight line represented as

y = mx + c

where:

m is the slope

c is the y intercept

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Based on the vacation days that Lisa got when she first started her current job, the equation that models the relationship between the number of years worked and paid vacation days is y = 3x + 2

The number of paid vacation days to Lisa increases by 3 days every year. This is in addition to the 2 days that Lisa got when she first started the job.

The relationship between the vacation days and the number of years worked is therefore:

Number of paid vacation days = Number of years x Increase in paid vacation days annually + Number of paid vacation days when job started

y = 3x + 2

Full question is:

When Lisa started at her current job, her employer gave her two days of paid vacation time with a promise of three additional paid vacation days for each year she remains with the company to a maximum of four work weeks of paid vacation time.

Let x represent the number of years she has worked for this employer and y represent the number of paid vacation days she has earned. Write an equation that models the relationship between these two variables.

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Answer:

59.49

Step-by-step explanation:

total number of students who don like mountain+don like beach =56+38+94=188

total number of students=92+66+158=316

probability percentage =(total no. of favorable events/total number of events) x 100

=188/316 x 100

=59.49 ~ 59.5%

Answer:

B

Step-by-step explanation:

I- are you on a test? If yes then i rlly cant help you.

JK I LIED IGHT SO ITS

Answer:

I think it is 55 mph but I'm not 100% sure.

Step-by-step explanation:

Answer:

688 cm²

Explanation:

Area of triangular prism = Base × Height + Length × (perimeter of base)

Here given:

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

Surface Area = 6 × 12 + 20 × (30.8) = 688 cm²

The range of value of x in the inequality x/7 ≥ -6 is x≥ -42

Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.

greater than has the sign >

greater than or equal to has the sign ≥

less than has the sign < and

less than or equal to has ≤

solving the range of value of x in the inequality x/7 ≥- 6

multiply both sides by 7

x ≥ -42

Therefore the range of value of x is x ≥ -42

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Answer:

x+5

Step-by-step explanation:

15+x-10=x+5

The given statement is true.

The limit of a function as x approaches a certain value is the value that the function approaches as x gets arbitrarily close to that value. In this case, we are given the function f(x) and asked to evaluate the limit as x approaches 1.

To determine the limit, we need to examine the behavior of the function as x approaches 1 from both sides (-1 and 1). If the function approaches the same value from both sides, the limit exists and is equal to that value.

In this case, the given function f(x) does not depend on x, and it is simply $(₂) - ₁. Regardless of the value of x, the function will always evaluate to 1. Therefore, as x approaches 1, the function approaches 1 from both sides.

Hence, the statement "lim fx $(₂) - ₁ 1 x-1- True" is true.

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The number of star wars that Amy has is 255 and Carly has is 85

Linear equation:

The linear equation is a combination of algebraic terms that are used to find unknown quantities in a word problem. To solve the given problem represent the unknown value with a variable and form a linear equation according to the given condition. Now solve the equation for the value of the variable.

Here we have

Amy has three times as many star wars toys as Carly.  

Let Amy have 'x' star wars and Carly have 'y' star wars

From the given data, x = 3y  

It is also given that both have 340-star wars toys in total

=> y + 3y = 340

=> 4y = 340

=>  y = 85

Hence, the number of star wars that Carly has = 85

Number of star wars that Amy has = 3(85) = 255

Therefore,

The number of star wars that Amy has is 255 and Carly has is 85

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Answer:

C

∠L and∠Q

Step-by-step explanation:

in the congruence statementit shows

A. JL and PR

JKL≅PQR

THEY MATCH-not this one

B. ∠K and ∠Q

JKL≅ PQR

THEY MATCH-not this one

C.∠L and ∠Q

JKL≅PQR

THEY DO NOT MATCH

D. ∠J and ∠P

JKL≅PQR

THEY MATCH-not this one

Answer:71

Step-by-step explanation:

Answer:

x = 73.8

Step-by-step explanation:

to find the blue line:

tan(50) = 41/a

a = 41/tan(50)

a = 34.4 to 1 decimal place

to find x:

tan(65) = x/34.4

x = 34.4tan(65)

x = 73.8 to 1 decimal place

Answer:

x <3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

Distribute

-10 +8x < 6x-4

Subtract 6x from each side

-10+8x-6x < 6x-6x-4

-10 +2x < -4

Add 10 to each side

-10+2x+10 < -4+10

2x< 6

Divide by 2

2x/2 < 6/2

x <3

Answer:

Y = 4

Step-by-step explanation:

Answer:

As an improper fraction: \(15/11\)

As a mixed number: \(1 \frac{4}{11}\)

As a decimal: 1.36

Step-by-step explanation:

\(3/5x - 1/3x = x - 1\)

Find a common denominator between 5 and 3 (15)

\((3 * 3) / 15x - (1 * 5) / 15 = x - 1\)

\(9/15x - 5/15 = x - 1\)

Subtract the fractions

\(4/15x = x - 1\)

Subtract x from both sides of the equation

\(-11/15x = -1\)

Multiply both sides of the equation by 15/-11 to simplify

x = 15/11

Hope this helps :)

Answer:

Exact Form:

x  =  15/11

Decimal Form:

x  =  1.36

Mixed Number Form:

x  =   1(4)/(11)

Step-by-step explanation:

(3)/(5)x-(1)/(3)=x-1

Simplify  (3)/(5)x-(1)/(3)x

(4x)/(15)=x-1

Move all terms containing  x  to the left side of the equation.

-(11x)/(15)=-1

Multiply both sides of the equation by    -(15)/(11)

-(15)/(11)(-(11)/(15))= -(15)/(11) . -1

Simplify both sides of the equation.

(15)/(11)

The result can be shown in multiple forms.

Exact Form:

x  =  15/11

Decimal Form:

x  =  1.36

Mixed Number Form:

x  =   1(4)/(11)

The Inverse of given function F(x) = 1 / 4x is F⁻¹(x) = 1 / 4 x

F(x) = 1 / 4x is a function of x.

Changing F(x) to the variable y

This means that F(x) = 1/4x becomes y = 1/4x.

Changing the variables x and y in the previously obtained equation

This means that we can deduce x = 1 / 4y from the equation y = 1 / 4x.

Solving the newly discovered equation for y

This means that we must simplify the equation by rearranging the terms in order to obtain the equation in terms of the variable x.

x =  1 / 4y

=> 4 y = 1 / x

=> y = 1 / 4 x

As a result, we obtain the required equation.

Switching the variable y with F⁻¹(x)

This assumes, y = 1 / 4 x becomes F⁻¹(x) = 1 / 4 x

Hence, the value of the given function F⁻¹(x) = 1 / 4 x

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The area of the region that lies inside the first curve and outside the second curve. r = 3 − 3 sin(), r = 3 is 9π/2.

The two polar curves given are:

r1 = 3 - 3sin(θ)

r2 = 3

The region that lies inside the first curve and outside the second curve is the region bounded by these two curves. To find the area of this region, we need to integrate the area element over the region.

The area element in polar coordinates is given by dA = r dr dθ. Therefore, the area of the region can be computed as:

A = ∫θ1^θ2 ∫r2^r1 r dr dθ

where θ1 and θ2 are the angles at which the two curves intersect.

To find the intersection points, we set the two equations equal to each other:

3 - 3sin(θ) = 3

Simplifying, we get:

sin(θ) = 0

which implies that θ = 0 or θ = π.

Therefore, the integral becomes:

A = ∫0^π ∫3-3sin(θ)^3 r dr dθ

= ∫0^π [(1/2)r^2]_3-3sin(θ) dθ

= (1/2) ∫0^π (9 - 18sin(θ) + 9sin(θ)^2) dθ

= (1/2) [9θ + 6cos(θ) - 9sin(θ)]_0^π

= 9π/2

Therefore, the area of the region that lies inside the first curve and outside the second curve is 9π/2.

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Answer:

1. 144 2. 21

Step-by-step explanation:

1. 12(9 + 3)

Distributive Property is at its finest here. You'll have to multiply 12 with both numbers in the Parthentheses.

1. 12 × 9 = 144

2. 12 × 3 = 36

2. 9 + 12

1. Count up 1 9 times starting at 12 or the opposite.

The statement "There is a strong positive correlation between studying and grades" best describes the meaning of a correlation coefficient of 0.93. The correct answer is A.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, a correlation coefficient of 0.93 indicates a strong positive correlation between studying and grades.

A positive correlation means that as the value of one variable (study time) increases, the value of the other variable (grades) also tends to increase. A correlation coefficient close to +1 indicates a strong positive relationship, suggesting that an increase in study time is associated with higher grades. e correct answer is A.

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\(12=\frac{k}{-4} \\k = -48\)

Therefore: \(y=\frac{-48}{x}\)