Devika buys 30 notebooks and 15 pens. Each book costs Rs40 and that of each pen is Rs15. Find out the total amount she spent.

The ratio of all the corresponding sides of the triangle are equal to each other.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two triangles are said to be similar if they have the same shape and the same corresponding angles.

Also, the ratio of all the corresponding sides of the triangle are equal to each other.

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Answer:

Step-by-step explanation:

Comment

The radius is 33 feet. The height is really a radius. The diameter consists of 2*r

r = diameter / 2

diameter = 66 feet

r = 66 /2 = 33

So you have 2 ways of finding the radius.

Solution

Area of a full circle = pi r^2

Area of a full circle = pi * 33^2

Area of a full circle = 1089 pi    

Area of a semicircle = area of a full circle / 2

Area of a semicircle = 1089 * pi /2

Area of a semicircle = 544.5 * pi

Answer

Exact answer in terms of pi is 544.5 * pi

Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73

Answer:

Area=

πr2

2

Step-by-step explanation:

3.14159⋅(33)2

2

=1710.5958

Answer:

The field is 1 and 4/10 mile long.

Step-by-step explanation:

If I understand the question:

(1/2) + (9/10) =

(5/10) + (9/10) = (14/10)

(14/10) is 1 and 4/10

The field is 1 and 4/10 mile long.

The required system of equations that can be used to determine the total number of ounces in the jug of water (x), and the total number of ounces in the bottles of juice (y) is

[tex]x - y = 192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

To write an equation,

It is given that,

The difference between the jug of water and the bottle of juice that Kira is drinking is 192 ounces

Kira has consumed a total of 42 ounces, which is 3/32 of the bottle of juice and 9/64 of the jug of water.

Consider,

The total number of ounces in the jug of water = x

The total number of ounces in the bottle of juice = y

Applying these variables in the above sentences,

[tex]x-y=192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

Therefore, these two equations are used to determine the total number of ounces in the jug of water and the bottle of juice.

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If fish are sold at [tex]10[/tex] for $[tex]864[/tex].  the cost to the nearest dollar of [tex]16[/tex]fish is $ [tex]1382[/tex]

How can we find the cost of the [tex]16[/tex] fish ?

The cost of the selling [tex]10[/tex] fish = $[tex]864[/tex]

So the cost of the [tex]1[/tex] fish is

[tex]= \frac{864}{10} \\=86.4[/tex]

So the cost of the selling [tex]16[/tex] fish

[tex]= 16* 86.4\\=1382 $[/tex]

$[tex]1382[/tex] is the selling cost of [tex]16[/tex] fish.

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The probability in all given conditions is 1/4.

According to the statement

Number of coin tossed = 3

Total outcomes = 8

Now, we have to find the probabilities on different conditions.

Probability = A head on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

Probability = alternating tale and head / total outcomes

Probability = 2/8

Probability = 1/4.

Probability = A No tails on each of the last two tosses/ total outcomes

Probability = 2/8

Probability = 1/4.

So, The probability in all given conditions is 1/4.

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1) If the discriminant is greater than 0, the quadratic equation has 2 real solutions. Here D is grater than 0 . the quadratic equation has two real, distinct (different) roots.

2) If the discriminant of a quadratic equation is 4, then there are two real roots.

3) A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

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By definition of a binomial random variable,  the probability that the machine will be working is 0.82045.

First of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

On the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.

A random variable is discrete if the numbers it gives rise to are integers.

Finally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.

The expression to calculate the binomial distribution is:

P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ

Where:

Remember that:

([tex]n\\ x[/tex])=[tex]\frac{n!}{x!(n-x)!}[/tex]

where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.

A machine has 28 identical components which function independently. The probability that a component will fail is 0.19.

The following random variable is defined:

x= the number of components will stop working.

Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:

P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ

P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ

Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:

P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)

Then:

P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³

Solving:

P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹

P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹

P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹

P(X≤3)= 0.82045

Finally, the probability that the machine will be working is 0.82045.

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For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

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Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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Answer:

160 ft

Step-by-step explanation:

We have

2(length + width)= perimeter

than,

let, width =x

now,

2(x+60+x) = 520

or, 2x+60 = 260

or, 2x = 200

or, x = 100

so length is 100+60 = 160

Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.

Definition of Skew Lines

Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.

Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.

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Answer:

Step-by-step explanation:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

The interior angle of a regular octagon is 135 degrees.

An octagon is a polygon that has 8 sides. Therefore, a regular octagon is a octagon with all it sides and angles equal to each other.

Therefore, the sum of angles in an octagon is each interior angle multiply by the number of sides.

Therefore,

n = number of sides = 8

Hence,

interior angle = (n - 2)180 / n

interior angle = (8 - 2)180 / 8

interior angle = 6 × 180 / 8

interior angle = 1080 / 8 = 135°

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Considering it's asymptotes, the rational function shown in the graph is:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:

(x + 2)(x - 1).

The horizontal asymptote is of y = 0, hence the function can be given by:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

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Answer:

Vertex - (2, -1)

Axis of Symmetry - x = 2

X intercept - (3,0) (1, 0)

Y intercept (0, 3)

Domain - (negative infinity, positive infinity)

Range - [-1, infinity)

Step-by-step explanation:

I graphed with desmos and found it.

Chantelle can use the following equation,

n = (Number of stickers) / (Number of friends)

or n = 56/8

Given Information

Chantelle has 56 stickers

⇒ Number of stickers = 56

She will distribute all of the stickers to 8 friends

⇒ Number of friends = 8

The number of stickers each friend will get = n

We have to form an equation for n.

Forming the Equation

Equation for  the number of stickers to be given to each friend is as follows,

n = (Number of stickers) / (Number of friends)

n = 56/8

n = 7

Therefore, Chantelle needs to give 7 stickers to each of her 8 friends. And, the equation used to find this count, n is n = (Number of stickers) / (Number of friends) or n =56/8

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The number of gallons of the 35% acid solution eli should add is; 0.125 gallons

From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

where g is number of gallons

Now,  for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

⇒ 0.05 + 0.35g = 0.15g + 0.075

⇒ 0.35g - 0.15g = 0.075 - 0.005

⇒ 0.2g = 0.025

g = 0.025/0.2

g = 0.125 g

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The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

According to the statement

Number of blue suit = 1

Number of black suit = 2

Number of brown suit = 1

Number of blue ties = 2

Number of red ties = 3

Number of pink ties = 3

Now we find the probability by its formula

Probability that picked suit is blue = blue suits/ total number of suits

Probability = 1/4

Now,

Probability that picked tie is pink = Pink tie / total number of ties

Probability = 3/8

So, The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

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1/3 portion of the mixture, costing $\$6$ contains chocolate.

Assume that, in a mixture:

chocolate = x pound

nuts = y pound

mixture= x+y

The desired value is found by dividing the weight of the chocolate by the overall weight, or x/(x+y).

From the given data,

cost of x pound chocolate at $\$10$per pound = 10x

cost of y pound nuts at $\$4$ per pound = 4y

cost of x+y pound mixture at $\$6$ = 6(x+y)

As per condition,

⇒10x + 4y = 6(x+y)

⇒10x + 4y = 6x+ 6y

⇒4x = 2y

⇒y = 2x

The fraction of the chocolate in the mixture is

[tex]x/(x+y)[/tex] = [tex]x/(x+2x)[/tex] = [tex]x/3x[/tex] = 1/3

Therefore, chocolate makes  1/3 of the mixture's weight.

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Answer:

1/3

Step-by-step explanation:

The mean calculated shows that the Chemistry score will be 87.

From the information given, the total scores will be:

= 84 × 4

= 336

The addition of the scores given will be:

= 72 + 85 + 92

= 249

The Chemistry score will be:

= 336 - 249

= 87

Complete question:

If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.

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Answer:

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

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

Explanation:

Triangle ABC is similar to triangle DEF. The order of the lettering is important because it tells us how the letters pair up.

Based on that, we can determine how the segments pair up

We want to find how long EF is, which means we'll involve BC = 17 since it is paired with it.

The diagram shows that AC = 14 and DF = 3, which is another pair we'll use

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

The key takeaway is that

Those two facts lead to the steps below

[tex]\frac{AC}{DF} = \frac{BC}{EF}\\\\\frac{14}{3} = \frac{17}{EF}\\\\14*EF = 3*17\\\\14*EF = 51\\\\EF = \frac{51}{14}\\\\EF \approx 3.642857\\\\EF \approx 3.6\\\\[/tex]

The proportion in step 1 is valid due to the similar triangles, and because of the corresponding side pairs mentioned. In step 3, I cross multiplied.

Answer:

3.6 cm

Step-by-step explanation:

Similar Triangle Theorem

If two triangles are similar, the ratio of their corresponding sides is equal.

Given triangles:

Therefore the corresponding sides are:

To find the measure of side EF, use the Similar Triangle Theorem:

[tex]\implies \sf AC:DF=BC:EF[/tex]

[tex]\implies \sf \dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]

[tex]\implies \sf \dfrac{14}{3}=\dfrac{17}{EF}[/tex]

[tex]\implies \sf EF=17 \cdot \dfrac{3}{14}[/tex]

[tex]\implies \sf EF=\dfrac{51}{14}[/tex]

[tex]\implies \sf EF=3.642857...[/tex]

[tex]\implies \sf EF=3.6\:cm\:\:(nearest\:tenth)[/tex]

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If Eli ate  one third of a pie on friday ,one fourth proportion of the pie on saturday and 50 ounces of the pie on sunday then it is found that she ate 30 ounces of pie.

Given that Eli ate one third of a pie on friday, one fourth of the pie on saturday, and final 50 ounces of the pie on sunday which is left out.

We have to find the amount of pie that she ate one saturday.

We are given fraction and we know that sum of all fractions of something is equal to 1.

Let the proportion that she ate on sunday be x.

1/3+1/4+x=1

Taking LCM.

(4+3+12x)/12=1

7+12x=12

12x=12-7

12x=5

x=5/12

So the left out out portion that she ate on sunday is 5/12 of the pie.

We are given that she ate 50 ounces on sunday so the total pie will be 12/5*50=120 ounces.

Portion eaten by Eli on saturday =1/4

Pie that she ate on saturday=1/4*120

=30 ounces.

Hence Eli ate 30 ounces of pie on saturday.

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Here,

y=mx+c

the slope of the line 6x+4y= -16 is -20.

if the two lines are perpendicular, the slope of 1st line * slope of second line=-1

the slope of the 2nd line is -1/2

y-y1=m(x-x1)

y-13=-1/2(x- -18)

when you solve, you get the equation of the line as 2y+x=50

In basic geometry, if two geometry objects intersect at right angles (90 degrees or π / 2 radians), they are vertical.

If two lines intersect at right angles, the line is perpendicular to another line. Explicitly (1) if two lines intersect, the first line is perpendicular to the second line. (2) At the intersection, the straight line angle on one side of the first line is cut by the second line into two congruent angles. Verticality can be shown as symmetric. That is, if the first line is perpendicular to the second line, then the second line is also perpendicular to the first line. Therefore, two straight lines can be said to be perpendicular (to each other) without specifying the order.

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The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]

[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]

[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]

[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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Answer:

(x-4)=0 or (x+2)=0 is correct

Step-by-step explanation:

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

x^2 -3x +x -3=5

x^2-2x-8=0

x^24x+2x-8=0

(x+2)(x-4)=0

so,

(x-4)=0 or (x+2)=0

The solutions to the expression are:

x - 4 = 0 or x + 2 = 0.

Option C is the correct answer.

We have,

To determine which of the following statements is true:

(x + 1) = 0 or (x - 3) = 0

(x + 1) = 5 or (x - 3) = 5

(x - 4) = 0 or (x + 2) = 0

We can solve the given equation (x + 1)(x - 3) = 5 by expanding the equation and setting it equal to 0:

(x + 1)(x - 3) - 5 = 0

Expanding the equation:

x² - 3x + x - 3 - 5 = 0

x² - 2x - 8 = 0

Now we can factor the quadratic equation:

(x - 4)(x + 2) = 0

From this factorization, we find two possible solutions:

x - 4 = 0 --> x = 4

x + 2 = 0 --> x = -2

Therefore,

The correct statement is:

(x - 4) = 0 or (x + 2) = 0

i.e

x - 4 = 0 or x + 2 = 0.

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Answer:

H. 15 ft by 15 ft

Step-by-step explanation:

area of square = side²

225 ft² = side²

side = √(225 ft²)

side = 15 ft

Answer: H. 15 ft by 15 ft

Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).

This is defined as the force per unit area of a body and the S. I unit is in Pascal.

Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.

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In the graph, the constant of proportionality is 40

From the question, we are to determine the constant of proportionality

The constant of proportionality = [tex]\frac{y}{x}[/tex]

From the graph, a point on the line is (1, 40)

That is,

When x = 1 and y = 40

Thus,

The constant of proportionality = [tex]\frac{40}{1}[/tex]

Constant of proportionality = 40

Hence, the constant of proportionality is 40

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Answer:

40

Step-by-step explanation:

The constant of proportionality is 40/1 which equals 40.