customers of a hardware shop make a payment either in cash or with credit/debit card with probabilities 0.3 and 0.7, respectively. assume these probabilities apply to all customers independently. if 20 customers pay at the hardware shop, what is the probability that exactly 5 customers pay in cash?

Answer: Least 1/2

Step-by-step explanation: Middle 2/3

Greatest 5/6

Answer:

Least 1/2

Middle 2/3

Greatest 5/6

Step-by-step explanation:

First,5 divided by 6,is 0.83(in to 1 decimal point)

Then 2 divided by 3 is 0.67(in to 1 decimal point)

Last 1 divided by 2 is 0.5(in to 1 decimal point)

So is 5/6 is greatest and 2/3 is in the middle and the least is 1/2.

Answer:

$3.02

Step-by-step explanation:

You just subtract 97.98-94.96.

Answer:

3.02

Step-by-step explanation:

you subtract 94.96 from 97.98

Answer: 1

Step-by-step explanation: look at the image attached to show which quadrant is what.

when the x coord is +, it's on the right half of the graph, so by this, quadrants 1 and 4 are possible answers.

when the y coord is +, it's on the top half of the graph, this makes quadrants 1 and 2 possible answers.

look for the consistency, in this case since 1 is the only possible answer between both, the answer is 1

When 12 / (y -x) is a denominator of x - y the numerator will be

The problem involves division of fractions

The fractions is a number type that has two major divisions,

the numerator : the number at the top

the denominator: the number below or at the bottom

The division of the fraction: In this case the denominator is the divisor

= (x - y) ÷ 12 / (y -x)

inverting the divisor of the fraction

= (x - y) *  (y -x)/12

= { (x - y) * (y -x) } / 12

the numerator is (x - y)(y -x)

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Answer:

Step-by-step explanation:

Step-by-step explanation:

length = 3x

breadth= 7x

area = 1029m2

area = length × breadth

(3x) × (7x)= 1029

now,

3×7=21

7×7=49

(verification 21×49=1029)

so length = 21

breadth = 49

now perimeter = 2(l+b)

=2(21+49)

=2(70)

= 140

so perimeter = 140m

Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.

Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.

To explain the concept behind this question we first need to know about the principle of correlation.

Correlation - It is a measure of comparison of two quantities by which we compute that which two quantities are linearly equal means that if we change one quantity the other will also change at a constant rate.

This principle simply makes a relationship without causing any effect on the quantities.

Now according to the question, we can see that,

Therefore, from the data that scientists predicted, we can conclude that,

Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.

Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.

Option 4 is correct.

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A group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". When this interesting creature dies, it explodes itself into a number of baby piknits called gogles. The scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. After the piknits died they counted the number of gogles that each piknit produced. They wanted to know if the weight of the piknits can be used to predict the number of gogles.

What are the appropriate null and alternative hypotheses?

Group of answer choices

H0: There is no linear relationship between the weight of piknits and the number of gogles

Ha: There is a negative linear relationship between the weight of piknits and the number of gogles

H0: Weight of piknits is a useful predictor for the number of gogles

Ha: Weight of piknits is not a useful predictor for the number of gogles H0: There is a linear relationship between the weight of piknits and the number of gogles

Ha: There is no linear relationship between the weight of piknits and the number of gogles

H0: There is no linear relationship between the weight of piknits and the number of gogles

Ha: There is a linear relationship between the weight of piknits and the number of gogles

Answer:

The numbers that when multiplied give 15 and when added give -12 are -3 and 5. Multiplying -3 by 5 gives -15, and adding -3 and 5 gives -8.

Explanation:

To find the numbers that when multiplied give 15 and when added give -12, we need to find two numbers that multiply to give -15 and add to give -12. One pair of numbers that satisfy these conditions is -3 and 5. When multiplied, -3 and 5 give -15, and when added, -3 and 5 give -8.

Answer: 52,000

Step-by-step explanation: Because we are rounding to the nearest hundred, we only need to focus on the #'s 4, 3, and 7 in 52,437. So, 3 is less than 5, so we have to round down to 3 (stays the same) and 4 is less than 5 so, we round down to 4 (also stays the same), and since 7 is greater than 5, we can round up to 440. But, 440 is still less than 500, so your final answer should be 52,000.

Answer:

0.5

Step-by-step explanation:

A coefficient is a number that multiplies an unknown

Answer:

X = add 25  Y =add 3 see 3 ,3+3=6  so i think y is 3

Step-by-step explanation:

Answer:

There are 78 plums and 42 peaches.

Step-by-step explanation:

Let p = number of plums.

Let e = number of peaches.

The value of the plums is 2p.

The value of the peaches is 3e.

"total cost of plims was 30$ more than the cost of peaches"

2p = 3e + 30

"there are 120 fruits some are plums [...] others are peaches"

p + e = 120

We have a system of simultaneous equations.

2p = 3e + 30

p + e = 120

2p = 3e + 30

p = -e + 120

     2p = 3e + 30

+   3p = -3e + 360

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

     5p =         390

p = 78

p + e = 120

78 + e = 120

e = 42

Answer: There are 78 plums and 42 peaches.

Check:

78 plums cost 78 × $2 = $156

42 peaches cost 42 × $3 = 126

$156 - $126 = $30

The plums do cost $30 more than the peaches.

78 + 42 = 120

The total is indeed 120.

The answer above is correct.

Triangle A and Triangle B are right triangle. Triangle A ha a height of 8 meter and a bae of 6 meter. then The length of one of the legs of the triangle is 10 units.

An isosceles triangle has a base length of 126 units and a height of 16 units. We need to find out the length of one of the legs of the triangle.

First of all, we will consider a perpendicular bisector of the triangle. This divides the given triangle into two equal right-angled triangles. Now, in the smaller triangle, we will use the Pythagorean theorem.

Let the length of the leg be represented by the variable "x". The length of the base of the right-angled triangle is half the length of the base of the original triangle.

x² = (6)² + (8)²

x = sqrt ( 36+64)

x = √100

x = 10

Hence, the length of one of the legs of the triangle is 10 units.

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Answer:

Step-by-step explanation:

81.64

The charge on the 150 nF capacitor is 3200 nF, the charge on the 120 nF capacitor is 3200 nF, the total energy stored in the network is [tex]76.8 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 150 nF capacitor is [tex]34.1 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 120 nF capacitor is [tex]42.67 \times 10^{-6} \mathrm{~J}[/tex], the potential difference across the 120 nF and 150 nF capacitor is 21.33V, 26.67 V.

The equivalent capacitance when the capacitors are connected in series is,

[tex]$$C_{\text {eq }}=\left(\frac{1}{C_1}+\frac{1}{C_2}\right)^{-1}=\left(\frac{1}{150 \mathrm{nF}}+\frac{1}{120 \mathrm{nF}}\right)^{-1}=66.67 \mathrm{nF}$$[/tex]

the charge on each capacitor remains the same because they connected in series. Hence, the charge on each capacitor is,

Q=C V=(66.67 nF) (48 V)=3200 nC

the charge on the 150 nF capacitor is  [tex]Q_{150}[/tex]=3200 nC

the charge on the 120 nF capacitor is [tex]Q_{120}[/tex]=3200 nC

the total energy stored in the network is,

[tex]$$$U=\frac{Q^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(66.67 \times 10^{-9} \mathrm{~F}\right)}=76.8 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 150 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(150 \times 10^{-9} \mathrm{~F}\right)}=34.1 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 120 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 \mathrm{C}}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(120 \times 10^{-9} \mathrm{~F}\right)}=42.67 \times 10^{-6} \mathrm{~J}$$[/tex]

the potential difference across the 150 nF capacitor is,

[tex]$$V_{150}=\frac{Q_{150}}{C_{150}}=\frac{3200 \times 10^{-9} \mathrm{C}}{150 \times 10^{-9} \mathrm{~F}}=21.33 \mathrm{~V}$$[/tex]

the potential difference across the 120 nF capacitor is,

[tex]$$V_{120}=\frac{Q_{100}}{C_{120}}=\frac{3200 \times 10^{-9} \mathrm{C}}{120 \times 10^{-9} \mathrm{~F}}=26.67 \mathrm{~V}$$[/tex]

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QN:-- For the capacitor network shown in (Figure 1) , the potential difference across ab is 48 V .

Find the charge on the 150 nF capacitor.

Find the charge on the 120 nF capacitor.

Find the total energy stored in the network.

Find the energy stored in the 150nF capacitor.

Find the energy stored in the 120nF capacitor.

Find the potential difference across the 150 nF capacitor.

Find the potential difference across the 120 nF capacitor.

The tip of man's shadow moving with speed of 25/3 ft/sec, when he is 40 feet from the pole.

We have, height of street light on pole,

AB = 15ft.

Height of man , BC = 6 ft.

Speed of man walks away from the pole.

= 5 ft/sec

This problem is look like a time rate problem , Let us consider x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole, i.e,

length of Shadow, CE =( y -x) ft

We assume the man and pole are standing straight up, which means the 2 triangles are similar. By similarity of triangles, (y − x)/y = 6/15

=> 15(y-x) = 6y

=> 15y - 15x = 6y

=> 15y - 6y = 15x

=> 9y = 15x

=> y = (15/9)x = (5/3)x

differentiate the above equation with respect to t or time.

dy/dt = (5/3)dx/dt

We know that, dx/dt = 5 ft/sec because the man is walking that speed away from the pole. We want to calculate dy/dt, how fast the tip of the shadow is moving when y = 40 feet

dy/dt = (5/3) (5) = 25/3 ft/sec.

We see actually, the man's distance from the pole doesn't matter since only his speed affects how fast his shadow moves. Hence, the tip of the shadow is moving with speed of 25/3 ft/sec.

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Parameters are values that describe the entire population, while statistics are values that describe only a sample of the population. Since there is no way to know the exact values of the parameters, they cannot be calculated from a sample of data.

Parameters are values that describe the characteristics of the entire population. They are used to make inferences about the population and provide a basis for making decisions. On the other hand, statistics are values that describe only a sample of the population. They are used to estimate the parameters of the population. Since it is not possible to know the exact values of the parameters, they cannot be calculated from a sample of data. Instead, we use statistics to estimate the parameters. This is why it is important to use a representative sample when collecting data, as it provides a better estimate for the population parameters

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18 inches is not a possible length for the third side of a triangle

What is the triangle inequality theorem?

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the remaining side.

By triangle inequality theorem:

This theorem states that the sum of any two sides of a triangle must be greater than the third side.

As per the statement:

A triangle has two sides of lengths 8 inches and 10 inches.

Let the third side be x.

The Sum of the two sides is:

8 + 10 = 18

By triangle inequality theorem:

18 > x

or

x < 18

⇒ the length of the third side must be less than 18

From the given options:

Length of third sides 12, 16, and 17 which are less than 18.

the value which could the length of the third side be are: 12, 16, and 17.

Hence, 18 inches is not a possible length for the third side of a triangle

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Answer:

  40%

Step-by-step explanation:

You want to know what percent of $70 is $28.

The question can be written as an equation, using a variable for the unknown percentage:

  x% · $70 = $28

The percent sign can be considered to be fully equivalent to "/100". Dividing by dollars on both sides, we can rewrite the equation as ...

  x/100 · 70 = 28

Dividing by the coefficient of x gives ...

  x = 28/0.70

  x = 40

The complete statement is ...

  40% of $70 = $28

__

Additional comment

If you're comfortable with writing decimal fractions as percentages, and vice versa, you can do without the %, and simply write ...

  x · 70 = 28

  x = 28/70 = 0.40 = 40%

This tells you 40% of $70 is $28, which is what you want to know.

A triangle is closed, with a 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The labels of the vertices of the triangle, which are generally used in capital letters, are used to name a triangle and we can call the triangle ABC since A, B, and C are vertices of the triangle.

Parts of a Triangle:

A triangle has 3 sides, which consist of ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠.

A triangle has three angles, whose angles of triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A.

The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.

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The number of different ways of distributing the scholarships is 32,760.


consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship  is to be a position In which a student assigned.
This is a permutation problem as:
   

A) each student selected from the same set.  
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.  

Four students  are assigned in 4 activities For scholarships.

Activity A1: select a student from the set of 15 students for giving away the first scholarship.

Activity A2: select a student from remaining 14 students for giving away the second scholarship.

Activity A3: select a  student from remaining 13 students for giving away the third scholarship.

Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.

According to multiplication rule of accounting the number of different arrangements is  A1 X A2 X A3 X A4  
15 X 14 X 13 X 12=32760  

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The solution of the three variable system will be (- 8, 4, - 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ - 5x + y - 4z = 60

⇒ 2x + 4y + 3z = - 12

⇒ 6x - 3y - 2z = - 52

Now,

Since, The system of equation are,

⇒ - 5x + y - 4z = 60

⇒ 2x + 4y + 3z = - 12

⇒ 6x - 3y - 2z = - 52

From option c;

⇒ (x, y, z) = (- 8, 4, - 4)

So, Put x = - 8, y = 4 and z = - 4

We get;

⇒ - 5x + y - 4z = 60

⇒ - 5 × - 8 + 4 - 4 × - 4 = 60

⇒ 40 + 4 + 16 = 60

⇒ 60 = 60

And, ⇒ 2x + 4y + 3z = - 12

⇒ 2 × - 8 + 4 × 4 + 3 × - 4 = - 12

⇒ - 16 + 16 - 12 = - 12

⇒ - 12 = - 12

⇒ 6x - 3y - 2z = - 52

⇒ 6 × - 8 - 3 × 4 - 2 × -4 = - 52

⇒ - 48 - 12 + 8 = - 52

⇒ - 52 = - 52

Thus, The solution of the three variable system = (- 8, 4, - 4).

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The complete table is

Length of fencing(feet)   1             3          6            9            10

cost($)                               9         27         54          81           90

What is fencing of a wall?

A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets. In contrast to a wall, a fence lacks a firm basis over its whole length.

The cost of fencing 3 feet is $27.

Applying unitary method:

The cost of fencing 1 feet is $27/3 = $9.

The  cost of fencing 6 feet is $(6×9) = $54

The  cost of fencing 10 feet is $(10×9) = $90.

$27 needs to make a fencing with length 3 feet.

$1 needs to make a fencing with length 3/27 feet = 1/9

$9 needs to make a fencing with length (1/9)× 9 = 1 feet.

$81 needs to make a fencing with length (1/9)× 81 = 9 feet.

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Answer:

Read Below:

12 or 40/9

Unclear, please comment to clarify.

Step-by-step explanation:

Quotient: x, when: [tex]\frac{a}{b} = x[/tex], answer to a division problem.

This could be interpreted 2 ways:

[tex]\frac{(\frac{3}{1/3} )}{3/4}[/tex]

[tex]\frac{9}{3/4}[/tex]

12

or

3 1/3 = 10/3

[tex]\frac{10/3}{3/4}[/tex]

10/3 * 4/3

40/9

Answer:

Slope is (6/7)

Step-by-step explanation:

6-0= -6

7-0= -7

-6/-7= 6/7

Answer:

There are several measurements that a professional engineer would need to make in order to design and construct a bridge over a stream for a farmer's sheep to graze. These measurements may include:

Width and depth of the stream: The engineer will need to determine the width and depth of the stream in order to determine the size and type of bridge that is needed.

Soil composition and stability: The engineer will need to assess the soil composition and stability of the area surrounding the stream in order to determine the foundation and support structure needed for the bridge.

Water flow: The engineer will need to measure the water flow in the stream in order to determine the load-bearing capacity of the bridge and to ensure that it is able to withstand the forces of the water.

Distance between the two banks: The engineer will need to measure the distance between the two banks of the stream in order to determine the length of the bridge and ensure that it is long enough to span the stream.

Height of the banks: The engineer will need to measure the height of the banks of the stream in order to determine the height of the bridge and ensure that it is tall enough to allow the sheep to pass under it.

Answer:

y = -1

Step-by-step explanation:

y = 4 · -2 + 7

y = -8 + 7

y = -1

Answer:

second option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

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

Red line

using (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 8) ← 2 points on the line

m = [tex]\frac{8-0}{2-0}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then

y = 4x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 ) then

0 = 4(0) + c

0 = 0 + c

0 = c

y = 4x + 0 , that is y = 4x ← equation of red line

Black line

using (x₁, y₁ ) = (0, 10) and (x₂, y₂ ) = (2, 8) ← 2 points on the line

m = [tex]\frac{8-10}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = - x + 10 ← equation of black line

The probability that the hotel receives at least one of the defective sets is 0.571 or 57.1%.

The probability of receiving at least one of the defective sets is calculated using the formula for the binomial distribution. The formula has 3 variables: the number of trials (n) being 8, the probability of success (p) being 0.286 (4 defective sets divided by 14 total sets) and the number of successes (k) being 1. We calculate the probability by plugging the variables into the formula and summing the probabilities of all the k values from 1 to 8. This gives us a probability of 0.571 or 57.1%.

P(k≥1) = Σ P(X=k)

       = P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)

       = 0.286^1.0 x 0.714^7.0 + 0.286^2.0 x 0.714^6.0 + 0.286^3.0 x 0.714^5.0 + 0.286^4.0 x 0.714^4.0 + 0.286^5.0 x 0.714^3.0 + 0.286^6.0 x 0.714^2.0 + 0.286^7.0 x 0.714^1.0 + 0.286^8.0 x 0.714^0.0

       = 0.571 or 57.1%

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