10. Your little brother borrows
$5.50 from you. You now have
$20. Which equation shows how
much money you had before you
let your brother borrow money?

Answer:

8x

Step-by-step explanation:

The values of x, y, and z are 25,15 and, 7 respectively.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. 

Given that,

x=y+10................(i)

y=z+8..................(ii)

x+y+z=47............(iii)

Solving these equations to find the values of x,y, and z.

Putting The value of x from the first equation in the third equation:

we get,

y+10+y+z=47

Solving this equation further, we get,

=>2y+z=47 -10=37

=>2(z+8)+z=37

=>2z+16+z=37

=>3z=37-16=21

=>z=21/3=7

=>y=z+8=7+8=15

=>x=y+10=15+10=25

Thus, The values of x, y, and z are 25,15 and, 7 respectively.

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Bori will run 10.5 miles in 75 minutes, using the concepts of unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method. We typically utilise this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Let us use the unitary method to solve this sum as well.

Bori can run 7 miles in 50 minutes.

This implies that, in 50 mins, Bori will run 7 miles.

Therefore, in 1 minute, Bori will run [tex]\frac{7}{50}[/tex] miles.

We have to find the number of miles Bori will run in 75 minutes.

Thus, in 75 mins, Bori will run [tex]\frac{7}{50} * 75[/tex] miles.

= 10.5 miles

Therefore, Bori will run 10.5 miles in 75 minutes.

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Answer:

1/2 = 3/6 and 1/3 = 2/6

Step-by-step explanation:

we need to make the denominators the same to be able to compare

if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

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

Given that D is the incenter of ABC, DF=6, and DB=10

We need to find EB

As D is the incenter then DF=DG=DE

so DE is 6

We know DB and DE

DBE is a right triangle and we can find EB by pythagoras theorem

EB²+DE²=DB²

EB²+36=100

EB²=100-36

EB²=64

Take square root on both sides

EB=8

Hence, if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

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The formula for the border's total area is [tex]4x^2+100x.[/tex]

A rhombus is indeed a four-sided form with equal-length sides (marked "s"). In addition, opposing sides and angles are parallel and equal. The diagonals' (dashed lines') right angle intersection in the centre is another intriguing feature.

An item with a cuboid form is a box. The angles on its six flat sides are all right angles. And rectangles make up each of its faces. Because it possesses the same bridge over a length, it is also a prism.

The garden's overall size, including the pine bark border, is provided by:

[tex]A=(30+2x)\ast(20+2x)=600+60x+40x+4x^2[/tex]

Without the boundary, the garden's total area is:

[tex]A_G=30\ast20=600[/tex]

The border's area may be calculated by deducting the entire area from the garden's area:

[tex]\begin{matrix}&A_B=A-A_G\\&A_B=600+100x+4x^2-600\\&A_B=4x^2+100x\\\end{matrix}[/tex]

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Considering the information about trees, The value of a is 5500

The value of r is calculated to be 0.92

In 1 October 2030 the number is 2022

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  N = ar^t

the starting, a = 5500

the base, r =

the exponents = t

Solving for the base

N = ar^t

5500 = ar^t in 2018 t = 0

a = 5500

in 2019, t = 1

N = ar^t

5060 = 5500 * r

r = 5060/5500

r = 0.92

From 2018 to 2030 = 12 years, hence t = 12

N = 5500 * 0.92^12

N = 2,022.165132

N = 2022

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2.21 × 10^20 is expressed in scientific notation.

What does scientific notation consist of?

Writing extremely large or extremely small numbers is done using scientific notation. When a number in the range of 1 to 10 is multiplied by a power of 10, the result is represented in scientific notation.

                         For instance, 650,000,000 can be expressed using scientific notation as 6.5 108. In scientific notation, a number is expressed in the form n10ab, where an is an integer such that 1|a|10 and b is also an integer.

The decimal point has to go 20 places to the left to give the number 2.21; that means the exponent on the 10 is 20.

= 2.21E20

= 2.21 × 10^20

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Answer: 5 chairs and 2 extra chairs

Step-by-step explanation:

Note that [tex]\frac{27}{5}=5.4[/tex]. This means we can place up to 5 chairs at each table.

However, this means that there will be [tex]27-5(5)=2[/tex] chairs left over.

Answer:

x = 8

BR = 28

Step-by-step explanation:

BF bisects WR, therefore WB = BR  

WR/2 = BW = BR

WR = 7x

BW = 5x - 12

7x/2 = 5x - 12

7x = 2(5x - 12) = 10x - 24

-3x = -24

x = -24/-3 = 8

BR = 5(8) - 12 = 28

Step-by-step explanation:

these are projections from V and W to the same projection "screen" (SU and YX).

since the angles are equal, the ratio between projection beam length and screen length must be the same.

so,

6.

24/14 = 48/x

48/28 = 48/x

x = 28

7.

besides the projection principle, we have a basic triangle situation :

the bisector of the angle W is also bisecting the opposing side YX. that means that this is an isoceles triangle (both legs are equally long).

therefore,

y = 4×sqrt(2)

Answer:

[tex]\textsf{6.} \quad x = 28[/tex]

[tex]\textsf{7.} \quad y = 4\sqrt{2}[/tex]

Step-by-step explanation:

An angle bisector is a line that divides an angle into two equal parts.

An angle bisector in a triangle divides the opposite side into two segments which are in the same proportion as the other two sides of the triangle.

Applying the Angle Bisector Theorem:

[tex]\implies \dfrac{UT}{TS}=\dfrac{VU}{VS}[/tex]

[tex]\implies \dfrac{x}{14}=\dfrac{48}{24}[/tex]

Cross multiply:

[tex]\implies 24 \cdot x=48 \cdot 14[/tex]

[tex]\implies 24x=672[/tex]

Divide both sides by 24:

[tex]\implies \dfrac{24x}{24}=\dfrac{672}{24}[/tex]

[tex]\implies x=28[/tex]

Applying the Angle Bisector Theorem:

[tex]\implies \dfrac{XZ}{ZY}=\dfrac{WX}{WY}[/tex]

[tex]\implies \dfrac{4}{4}=\dfrac{y}{4\sqrt{2}}[/tex]

Carry out the division on the left side:

[tex]\implies 1=\dfrac{y}{4\sqrt{2}}[/tex]

Multiply both sides by 4√2:

[tex]\implies 1\cdot 4\sqrt{2}=\dfrac{y}{4\sqrt{2}}\cdot 4\sqrt{2}[/tex]

[tex]\implies 4\sqrt{2}=y[/tex]

[tex]\implies y=4\sqrt{2}[/tex]

Check the picture below.

The length of segment PM would be 12 units

I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.

We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.

Our equation QM = (SM)(RM) (PM)

We now enter the information and resolve: (10)(18) = (15)(x) (x)

(10)(18) = 180

(15)(x) = 15x

180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x

x = 12

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The responses for the solution to the equations are evaluated as follows;

First equation; The response is not the solution to the equation;

Second equation; The response, f = 9 is the solution to the equation

An equation is the representation of a mathematical statement indicating the equality of two expressions.

The equations are;

First equation; 52 + G = 45 + 11

The response to the first equation is; G = 3

The solution for the first equation is found as follows;

52 + G = 45 + 11

G = 45 + 11 - 52 = 4

The solution to the equation 52 + G = 45 + 11 is; G = 4

Therefore, the response in not the solution to the equation, the solution to the equation is; G = 4

The second equation is; 13 + 14 = 3·f

The response for the above equation in the question is; f = 9

Plugging in f = 9 into the second equation, we get;

13 + 14 = 3 × f = 3 × 9 = 27, which is correct

The solution to the second equation can also be found by solving the equation as follows;

13 + 14 = 3·f

27 = 3·f

f = 27/3 = 9

f = 9

Therefore the response in the question for the second equation is the correct solution to the equation, 13 + 14 = 3·f, where, f = 9

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The correct option to represents downloads and rentals this person purchases is, (6, 14) and (8, 12).

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

We have to given that;

A digital download, x, costs $3 and a digital rental, y, costs $2 for a song. a person has $48 maximum to spend in a month.

Now, Let (x, y) represent number of downloads and rentals this person purchases.

Hence, We can formulate;

⇒ 3x + 2y ≤ $48

So, We can check all the options which satisfy the above equation.

By option C; (x, y) = (6, 14)

⇒ 3x + 2y ≤ $48

⇒ 3×6+ 2×14 ≤ $48

⇒ 18 + 28 ≤ 48

⇒ 46 ≤ 48

Hence, This option satisfy the equation.

By option D; (x, y) = (8, 12)

⇒ $3x + $2y ≤ $48

⇒ 3×8 + 2×12 ≤ 48

⇒ 24 + 24 ≤ 48

⇒ 48 = 48

Thus, It satisfy the equation.

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the standard deviation for activity e is 6.8

What is the probability of finishing the project by the 24th day or less?

Recall that:

z = (Specified Time - Path's mean)/Path's Standard Deviation.

Hence for z₂₁

(21 − 20.5)/1.118   = 0.447 ≈ 0.45.

Hence the probability is:   P(Z<0.45) =0.6736

(21 − 21.5)/1.344 = −0.3721 ≈ −0.37

Hence the probability is:  P(Z<-.37) = 0.3557

(21 − 19.5)/.726 = 2.066 ≈ 2.07

Hence the probability is: P(Z<2.07) = 0.9808

Following through on the above, the project will be finished in less than 21 days is given as:

P = 0.23499920921

P ≈ 0.2350

the standard deviation for activity e is 6.8

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Answer:

Step-by-step explanation:

a) The probability that the point selected at random lies in ∆ADM is 1/4. This is because ∆ADM is one of the four equal parts of the square ABCD.

b) The probability that the point selected at random lies in ∆ADM but not in ∆ADN is 1/8. This is because ∆ADM and ∆ADN are two of the four equal parts of the square ABCD, and the union of these two parts forms one quarter of the square. Hence, the probability of the point lying in one of these parts but not in the other is 1/8.

c) The probability that the point selected at random lies neither in ∆ADM nor in ∆ADN is 3/4. This is because the union of ∆ADM and ∆ADN forms one quarter of the square ABCD, while the remaining three quarters of the square lie outside of both ∆ADM and ∆ADN. Hence, the probability that the point lies outside of both these parts is 3/4.

Using the formula of length of an arc, the radius of the circle is 3 units

The length of an arc is a measure of the distance along the curved path of the arc. It is a portion of the circumference of the circle of which the arc is a part.

It can be calculated using the following formula:

Length of arc = (Arc angle / 360) * Circumference of the circle

Where:

Arc angle is the measure of the angle formed by two radii at the center of the circle. It is measured in degrees.

Circumference of the circle is the distance around the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

Alternatively, the length of an arc can also be calculated using the formula :

Length of arc = (Arc angle/360) * 2πr

Also, the formula of length of an arc is given as

s = rθ

s = length of arc

r = radius of arc

θ = angle in radians

In the question given, we can substitute the values and solve for the radius.

s = rθ

3π / 2 = r * π/2

r = (3π / 2) / (π / 2)

r = 3

The radius of circle is 3 units

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Categorical variables are grouped into categories, ordinal variables can be ordered, continuous variables have infinite values, and discrete variables have a finite number of values.

Categorical or nominal variables are variables that can be grouped into categories. These categories can represent anything that is not quantitative, such as gender, race, or religion. Ordinal variables are variables that can be ordered or ranked. These variables are typically used to measure preferences or attitude, such as ratings or rankings. Continuous variables are variables with an infinite number of possible values, such as height, weight, or temperature. These variables can have any value within a given range. Discrete variables are variables with a finite number of possible values, such as integers or counts. These variables are typically used to count the number of occurrences of a particular event or outcome. All four of these types of variables are important for understanding data and making predictions or decisions based on that data.

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The expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. The expression can be rewritten as (1-2g)5h, which is the same expression but with fewer symbols.

1. Simplify the expression inside the parentheses: (1-2g)

2. Multiply what is inside the parentheses by 5: (1-2g)5

3. Multiply the result by h: (1-2g)5h

This expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. To simplify it, first we need to simplify the expression inside the parentheses. To do this, we subtract two times g from one, which gives us the result of 1-2g. We then multiply the result by 5, which gives us the result of (1-2g)5. Finally, we multiply the result by h, which gives us the final result of (1-2g)5h. This is the same expression as the original, but with fewer symbols. The result of the expression is the product of the five, the difference of one and two times g, and h.

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The product of three numbers is 12,295.

We are given that the sum of three numbers x, y, and z is 165, so we can write:

x + y + z = 165

We are also told that when the smallest number x is multiplied by 7, the result is n. So we can write:

x * 7 = n

It is also given that the value n is obtained by subtracting 9 from the largest number y, so we can write:

y - 9 = n

And that this number n also results by adding 9 to the third number z, so we can write:

z + 9 = n

We have 3 equations with 3 unknowns, we can use these equations to solve the problem.

From the equation x * 7 = n, we can substitute n = y-9, and we get:

x * 7 = y - 9

From the equation z + 9 = n, we can substitute n = y-9, and we get:

z + 9 = y - 9

Now we have 2 equations with 3 unknowns x,y,z.

To solve for the third unknown, we can use the equation x + y + z = 165 and substitute the values that we know from the previous equations:

x + (y - 9) + (z + 9) = 165

Solving for x we get:

x = (165 - (y-9) - (z+9)) = (165 - y + 9 - z - 9) = (165 - y - z + 18) = (183 - (y+z))

Now we can substitute this value into one of the previous equations:

(183 - (y+z)) * 7 = y - 9

Solving for y and z we get:

y = 95 and z = 71

And the product of the three numbers is:

x * y * z = (183 - (y+z)) * y * z = (183 - (95 +71)) * 95 * 71 = (183 - 166) * 95 * 71 = 17 * 95 * 71 = 12,295

So the product of three numbers is 12,295.

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Chad used the scale of 1 scale inch which is equal to 9 feet.

In the conventional system of measuring, an inch is a unit of length. Either in or " can be used to denote length in inches. For instance, 16 in or 16" can be used to write 5 inches.

Given that,

The length of the gym in real life = 81 feet

The length of the gym in scale drawing = 9 inches

1 scale inch = length of the gym in real life/length of the gym in the scale drawing

1 scale inch = 81/9 = 9

Thus, Chad used the scale of 1 scale inch which is equal to 9 feet.

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i)The amount of petrol sold by the petrol station on a particular day is 21,600 L

II) Number of customers who would expect to buy 44 L of petrol is 2.28

i)The amount of petrol sold by the petrol station on a particular day can be estimated using the following equation:

Total petrol sold = Mean amount of petrol per customer x Number of customers

= 36 L x 600 customers

= 21,600 L

ii) To find the number of customers who would expect to buy 44 L of petrol, we need to find the probability of a customer buying that amount. We can use the standard normal table and the z-score formula (z = (x - mean) / std dev) to calculate the probability of a customer buying 44 liters of petrol.

z = (44 - 36) / 7 = 2.57

Using the standard normal table, we can find that the probability of a customer buying 44 liters of petrol is about 0.0038 or 0.38%.

Therefore, we can estimate that about 2.28 customers would expect to buy 44 liters of petrol on that day by multiplying the probability of buying 44 liters of petrol by the total number of customers.

Number of customers who would expect to buy 44 L of petrol = 0.38% * 600 = 2.28

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The complete question is:

The amount of petrol bought by a customer at a petrol station is normally distributed with mean 36 L and standard deviation 7 L.                                                                                                              on a particular day, the petrol station has 600 customers. i) how much petrol would you expect the petrol station to sell on this day? ii) how many customers would you expect to buy 44 l of petrol?          

Therefore , the solution of the given problem of equation comes out to be  y = 23.78t - 5t²

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,
Given :parametric equation

x be the speed of water

t be the time

v be the speed of dolphin

=> x = (vcosx)t +x₀

=> v = 32

=> x = 48

=> x = (32 X cos 48)t + 0

=> x = 21.41t

thus,

=>  y = (vsintx)t - 1/2gt² + y₀

=>   y₀ = 0

=>  v = 32

=> x = 48

=> g = 10

=> y = (32sin48)t -1/2 *10*t² +0

=>  y = 23.78t - 5t²

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Answer:

x = 2.5, y = 0.5

Step-by-step explanation:

[tex]10x - 16y = 17\\3x + 3y = 9[/tex]

Isolate for x or y on the equation of choice (Just choose a random one)

[tex]3y = 9 - 3x\\y = 3 - x[/tex]

Sub new equation into the other equation

[tex]10x - 16(3-x) = 17\\10x -48 + 16x = 17\\26x = 65\\x = 2.5[/tex]

Sub x into new equation

[tex]y = 3 - x\\y = 0.5[/tex]

To implement string matching algorithm, we can use naive algorithm and write the program in C.

To conduct the string matching we can use naive algorithm. Among the pattern finding algorithms, naive pattern searching is the most basic. It looks for all characters in the main string that match the pattern.

The program in C:

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

#include <stdio.h>

#include <string.h>

int match(char [ ], char [ ]);

int main() {

 char x[200], y[200];

 int po;

 printf("Write your text\n");

 gets(x);

 printf("Write thepattern you want to find\n");

 gets(y);

 pos = match(x, y);

 if (pos != -1) {

   printf("Found at location: %d\n", pos + 1);

 }

 else {

   printf("No match.\n");

 }

 return 0;

}

int match(char text[], char pattern[]) {

 int p, q, r, text_long, pattern_long, pos = -1;

 text_long    = strlen(text);

 pattern_long = strlen(pattern);

 if (pattern_long > text_long) {

   return -1;

 }

 for (p = 0; p <= text_long - pattern_long; p++) {

   pos = r = p;

   for (q = 0; q < pattern_long; q++) {

     if (pattern[q] == text[r]) {

       r++;

     }

     else {

       break;

     }

   }

   if (q == pattern_long) {

     return pos;

   }

 }

 return -1;

}

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The equation has B. No solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, given that,

1/4*(-16r-28)= - 4r - 7

-16r - 28 = -16r-28

this statement is not true.

so, The equation has B. No solution.

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1956 'words' of any length can be formed from the letters of the word SECOND.

Number of letters =6

Number of single letter word =⁶P₁

Two lettered word =  ⁶P₂

​Three lettered word =  ⁶P₃

​Four lettered word =  ⁶P₄

​Five lettered word=  ⁶P₅

​Six lettered word=  ⁶P₆

​Total possible words

=6+30+120+360+720+720

=1956.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a function that rearranges a set; it is not an arrangement in and of itself. It is a bijection from a set to itself. Permutations are the arrangements themselves, according to an older and more fundamental perspective. The terms active and passive are occasionally attached to the term permutation to distinguish between these two, but older terminology uses the terms replacements and permutations.

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By solving a simple linear equation, we will see that there are 1666667 grains of salt on 100 grams

We want to see how many grains of salt would be in 100 grams, only by knowing that the mass of a salt grain is 0.06 mg

Where:

1mg = 0.001g

Then the mass of x grains of salt, is given by the function below:

m(x) = x*0.06 mg

m(x) = x*0.00006 g

Now we want to find the value of x such that the mass is 100 grams, then we can write the equation:

x*0.00006 g = 100g

Solving that equation for x, we will get:

x = 100g/0.00006 g

x = 1666667

So there are about 1666667 grains of salt on 100 grams of salt.

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Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4