In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither.

Find probability that a student chosen at random has a cat or a dog.

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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The probability that at least 5 will do their homework on time in a class of 50 students is 0.1

Probability

Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes. Probability and odds are different concepts. Odds are the probability that something happens divided by the probability that it doesn't happen.

the probability that a randomly chosen student in a statistics class submits his/her homework on time is 0.06.

Each student does homework independently.

In a statistics class of 50 students, what is the probability that at least 5 will do their homework on time.

Probability = event occur/ total number of outcomes

                  = 5/50= 1/10=0.1

Thus the probability becomes 0.1

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Answer:

1. 45*4 = 180
2. 65*5= 325
3. 77*6=462
4. 89*7= 623

5. 52*3= 156

Answer:

5.8

13.25

22.62

34.23

16.56

Step-by-step explanation:

The radius of the circular garden is 14.3 meters

Any line connecting a circle's center and circumference is said to be the circle's radius. Within a circle, a diameter is equal to the sum of two radii. The area and circumference of a circle are determined using the radius of the circle.

The perimeter of a circle with a radius of r is given by

Here we have

George walks around one-quarter of a quarter of a circular garden.  

He walks a total of 30 meters.

Let x be the Perimeter or circumference of the circular garden

Given that George walks around one-quarter of a quarter of a circular garden.

=> The length of the path that George walked = x/3

Given that He walks a total of 30 meters

=>  x/3 = 30 meters

=>  x = 90 meters

So we can conclude that circumference of the circular garden = 90 m

As we know Perimeter of the circle = 2πr  

=> 2πr = 90

=>  πr = 45

=> 22/7(r) = 45

=> 22(r) = 315

=> r = 14.318181818181 ≅ 14.3

Therefore,

The radius of the circular garden is 14.3 meters

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The algebraic expression for "9 less than the quotient of z and 8" exists 9 - z / 8.

Using variables, constants, and algebraic operations, an expression can be described as an algebraic expression in mathematics (addition, subtraction, etc.). Terms are used to construct expressions.

Similar to this, when we describe an algebraic expression in English and it has a variable, we are doing so (an expression with a variable).

A mathematical expression made composed of integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Let the given expression be "9 less than the quotient of z and 8".

simplifying the expression, we get

= 9 - z / 8

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In order to maximize the number of bags with 9 balls he needs at least 32 bags.

9x + 11y = 304

To begin, solve for y so that you may graph it:

y = -9x/11 +304/11

Then look for the place where x has the largest possible value and x and y are both positive integers (keeping in mind that y1).

This is an important point (24,8). There are 24 bags of nine marbles and eight bags of eleven marbles.

Anand should put 9 marbles in 24 bags and 11 marbles in 8 bags, for a total of 32 bags.

Marble is a metamorphic rock made up of recrystallized carbonate minerals, the most common of which being calcite or dolomite. There are certain exceptions to the rule that marble is not foliated (layered).

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Answer:

w = [tex]\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3}{5}[/tex] w = 4 ( multiply both sides by 5 to clear the fraction )

3w = 20 ( divide both sides by 3 )

w = [tex]\frac{20}{3}[/tex]

The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

Expression 10x – x²

The expression can be written as

10x – x² = p – (x – q)²

10x – x² = p - x² - q² + 2xq

10x – x² = - x² + 2xq + p - q²

Compare the quantities on both sides,

10x = 2xq and 0 = p - q², p = q²

q = 10x / 2x = 5

p = 5² = 25

Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

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The value after double integration is 45.73

We can evaluate rectangle integrals in any order we like in Cartesian coordinates. We treat the other integral as a constant regardless of which integral we assess first; this is something to keep in mind while choosing the order of integration.

We want that x to be constant; we can easily integrate with respect to y. So we will evaluate y first. We get:

[tex]\int\limits^ \int\limits^ \frac{6x}{1+xy} dA=6\int\limits^6_0 \int\limits^1_0 {\frac{x}{1+xy} } \, dydx[/tex]

[tex]or, 6\int\limits^6_0 {[In(1+xy)}_{0} ^{1} ]} \, dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, -In 1dx[/tex]

[tex]or, 6\int\limits^6_0 {In(1+x)} } \, dx[/tex]

[tex]or,[(1+x)In(1+x)-(1-x)]^{6} _{0}[/tex]

[tex]or,[7In7-In1-7+1]\\or,6(7In7-6)\\or,45.73[/tex]

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Do not reject H(0). There is not sufficient evidence to a manufacturer of transistors claims that its transistors will last an average of different than 1000 hours. at 0.01 significance level.

In the given question, a manufacturer of transistors claims that its transistors will last an average of 1000 hours.

To maintain this average, 25 resistors are tested each month.

We may assume that the distribution of the lifetime of a transistor is normal.

We have to calculate a sample that has a mean of 1010 and a standard deviation of 60.

So let us consider

X : Life time of a transistor

So we have

N=25

x=1010

s=60

Since sample size n(25≤30) is small and population standard is unknown so we use t statistic for hypothesis testing.

Now our null and alternate hypotheses are given as:

H(0): μ=1000

H(1): μ≠1000 (two tailed test)

Under Null hypothesis our test statistic is;

t=(x-μ)/(s/√n)

t=(1010-1000)/(60/√25)

t=0.83

Critical Value:

t(α,(n-1))=t(0.01, 24)

t(α,(n-1))=2.80

We have given level of significance α=0.01 and also we find the t-score 0.83 and degree of freedom=24

p value

The Excel formula is used to calculate the p value is:

P value =2×(1- (t(24) > 0.83))

P value =2×(1-0.7926)

P value =2×0.2074

P value =0.4147

Since p value=0.42 greater than α=0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected and we claims that its transistors will last an average of 1000 hours.

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Answer:

Step-by-step explanation:

52%

Answer:

x = -3

Step-by-step explanation:

Welcome to Brainly! :]

3/4(x-13)=-2(9+x)

0.75x - 9.75 = -18 - 2x

2.75x = -8.25

x = -3

:]

The angle between the ladder and the ground is - 0.075 rad/s.

Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative  facets.

cosθ = x/10

On differentiating the above equation,

- sinθdθ/dt = (1/10)dx/dt

dθ/dt = -(1/10)dx/dt/sinθ

sinθ = y/10

= √(100 - 36)/10

= 0.8; dθ/dt

= -(1/10)·0.6 ft/s/0.8

= - 0.075 rad/s

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Answer:

96 dollars

Step-by-step explanation:

The ratio of Miguel's savings to his earnings is 8: 10 = 40: 50 = 120: 150 is equal to ratio 4:5

If Miguel earns $120, then he will save 4/5 of his earnings.

This can be expressed as a ratio as follows:

Savings: Earnings = 4 : 5

This means that for every 4 units of savings, there are 5 units of earnings. In other words, the ratio of savings to earnings is 4 to 5.

In order to calculate the amount of money that Miguel will save; we can multiply the ratio by the amount of earnings.

In this case, the amount of earnings is $120, so the amount of money that Miguel will save is:

[tex]\textsf{Savings} =\dfrac{ 4}{5 }* 120 = 96[/tex] dollars

Therefore, He will save 96 dollars if he earns 120 dollars.

The current population density  is 125 people / square kilometers.

Given :

plumeria island is an island in the indian ocean. the island is 4,000 square kilometers in size. currently, 500,000 people live there. last year, 150,000 children were born and 50,000 people immigrated. 100,000 people died and 10,000 emigrated. it is believed that the island could support up to 350 people per square kilometer.

Total people =  500000

Area = 4000 square kilometers

we know that ,

Population density = total people / area

= 500000 / 4000

= 500 / 4

= 125

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The possible value of 3rd side is x ≤  35.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that the length of two sides of a triangle are 20 and 15.

Triangle inequality theorem:

The sum of two sides of a triangle is always greater than the third side.

The of two sides of the triangle is (20 + 15) = 35.

According to triangle inequality theorem,

The third side of the triangle must be less than 35.

Assume that the length of the third side is x.

Therefore, x ≤  35.

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The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Jane bought 3 shirts and returned 2 pairs of pants

Laura bought 4 shirt and 3 pairs of pants.

Let, s = cost of shirt

and, p = cost of a pair of pants

The equation for Jane is

3s - 2p = $5

Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.

Now, the equation for Laura is

4s + 3p = $120

Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.

So, the system of equation we get

3s - 2p = $5

4s + 3p = $120

After solving  simultaneously we get the values s = 15 and p = 20.

Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,

for 1st equation,

3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)

for 2nd equation,

4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)

Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.

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0.0076 is  the probability that the first 30 igniters tested do not fail .

What is probability in math?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences.

a)if the failure rate for the super igniters is 15% then the probability that each igniter fails is 0.15,and the probability that it does not fail is 0.85.Therefore the probability that the first 30 igniters tested do not fail is       (0.85)30= 0.0076.

b)given that there are no failures in the first 30 tries,the probabilities occurs on 31st try is 0.15 and the probability that it does not occur on 31st but occurs on 32nd try is (0.85)(0.15)=0.1275.therefore the probability of one or the other is 0.15+0.1275=0.2775.

c)the result of the probability calculation in part(a) provides reason to believ the failure rate of the super igniters is less than 15%.The calculated proability of 0.0076 shows that there is less than a 1% chance that 30 or more igniters in a row would not fail if the failured rate was 15%.This probability is smaller than conventional significance levels such as alpha=0.05 and 0.01 and thus is small enough to make it reasonable to believe that the failure rate of the super igniters is less than 15%.

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Using equation of motion to calculate the distance covered during acceleration is 540m

Distance is the total length between two points, while displacement is the length between two points, but it also takes into account the direction of the motion. Distance is a scalar quantity, while displacement is a vector quantity.

In this problem, we can either draw a velocity - time graph or proceed to solve using equations of motions.

We are required to calculate the distance covered during the period of acceleration.

Data;

a = v - u / t

a = acceleration

a = (60 - 30) / 12

a = 30 / 12

a = 2.5 m/s²

But we have another equation as

v² = u² + 2as

s = distance

60² = 30² + 2*2.5*s

x = 540

The distance covered is 540m

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Answer:

217

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

A= -5

B= -10

c= 4

Step-by-step explanation:

hope this helps

Answer:

a) -5

b)-10

c) 4

Hope this helps!

As per the given confidence interval, the interval notation is 2.576

Confidence interval:

Is statistics, an estimate of an interval in statistics that may contain a population parameter is known as confidence interval.

Given,

Here we have to calculate a 99% confidence interval for the difference in the proportions of those older than 30 and those 30 or younger that believe alcoholic beverage commercials targeted teenagers and young adults. let the 30 or younger age group be population 1 and let the older than 30 age group be population.

And we need to find the write your answer using interval notation and round the interval endpoints to three decimal places.

While we looking into the given question,

We have identified the following things,

Confidence interval = 99%

When we convert this into decimal, then we get the value as 0.99

Then the z score of the given data is calculated as

=> 2.576

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Answer: below

Step-by-step explanation:

A. x=20+2n n= number of months

y=10(1+0.15)^n

B.

x 20,22,24,26,28,30....40

y 12.5,13.225,15.2,....40.5

C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.

D.

From the given information in question, we can sat that, The  regular polyhedron have 30 edges.

A polygon that is based on the solid in the three dimensions is known as  a polyhedron. It has flat faces, straight edges and corners. A polyhedron is something like a cube, prism, or pyramid. Cones, spheres, and cylinders do not have polygonal sides, hence they are not polyhedra. Polyhedron is also the name of the polyhedron's plural form. They are classified as prisms, pyramids, and regular polyhedra. Polyhedra include, for instance, cubes (regular polyhedrons), square prisms, triangular prisms, square pyramids, and square pyramids. Consider the diagram below displaying different sorts of polyhedra.

chris discovered that the centers of the faces of a regular icosahedron are also the vertices of another regular polyhedron and he  regular polyhedron have 30 edges.

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The dinner party needs 400 pieces of silverware for 10 tables and 8 seats at each table. By evaluating the given expression, we get the required value.

The given expression is,

A dinner party with tables t' and seats at each table 's' needs "5ts" pieces of silverware.

I.e., number of pieces of silverware = 5ts

Thus, the given expression gives the required value.

If Aaron is planning for a dinner party with t = 10 tables and s = 8 seats at each table, then the number of pieces of silverware required for the dinner party is

5ts = 5 × 10 × 8 = 40 × 10 = 400

Therefore, it needs 400 piece of silverware.

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The HA Theorem is a special case of proving that two triangles are congruent. The HA theorem is a special case of the AAS theorem.

The HA congruence theorem for right triangles says that if the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle then the two triangles are congruent.

It states that if both hypotenuses and a pair of acute angles of two right triangles are congruent, then the triangles are congruent.

The HA Theorem is a special case of proving that two triangles are congruent.

AAS theorem says that if two angles and any side of a triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent.

Hence, the HA theorem is a special case of the AAS theorem.

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The value of a is 42.

Simply use cross multiplication :

The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.

Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.

[tex](15-a)/3=-9[/tex]

or, [tex]15-a=-9*3[/tex]

or,[tex]-a=-27-15[/tex]

or, [tex]a=42[/tex]

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Answer:

(a) y=x             YES

(b) y=-9            YES

(c) y=4x²¹ +8    NO

(d) y=-4x+7       YES

Step-by-step explanation:

See attached worksheet.

The value of x = 50

Exterior angle:

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.

In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

given that

m∠6 = x

m∠7 = x-20

m∠11 = 80

we solve this by using exterior angles

sum of 2 interior angles is equal to one  exterior angle

m∠6 + m ∠7 = m∠11

x + x - 20 = 80

2x = 80 + 20

2x = 100

x = 100/2

the value of x = 50

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The equation of the line that passes through the point (-1,2) and has a slope of -1, in point-slope form is: y - 2 = -1(x + 1).

If we know one point (a, b), that a line passes through and its slope (m), we can write the equation of that line in point-slope form as y - b = m(x - a).

Given the following:

A point (a, b) = (-1, 2)

The slope of the line (m) = -1

To write the equation of the line, substitute m = -1, a = -1, and b = 2 into y - b = m(x - a):

y - 2 = -1(x - (-1))

y - 2 = -1(x + 1).

The answer is: y - 2 = -1(x + 1).

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