Can anyone help me with this question?

Can Anyone Help Me With This Question?

Answers

Answer 1

a. Ex is read as "the expected value of all x values,"

What is sigma ?

Ex is a mathematical notation that represents the expected value of a random variable X. The expected value of X is the theoretical long-run average value of X that is expected to occur when X is repeatedly observed or measured under identical conditions. The expected value is calculated by summing the product of each possible value of X and its probability of occurrence. Mathematically, it is denoted as E(X) or Ex. The expected value is a fundamental concept in probability theory and statistics and is used in various applications such as decision-making, risk assessment, and financial analysis.

Sigma (written as Σ) is a mathematical symbol that represents the sum of a series of numbers or terms. It is often used in mathematics and statistics to denote a sum of a set of values. The symbol is written as an uppercase Greek letter sigma and appears as an elongated "S".

For instance, if we have a series of n numbers, a₁, a₂, ..., aₙ, then the sum of these numbers is represented by the following formula using the sigma notation:

∑ᵢ₌₁ⁿ aᵢ = a₁ + a₂ + ... + aₙ

Here, i is the index that takes on the values from 1 to n, and aᵢ is the ith term in the series. The sigma notation allows us to express the sum of the terms in a compact and convenient way. We can also use sigma notation to represent other types of mathematical expressions involving sums, such as infinite series or double sums.

b. Sigma * x² is read as "the sum of the squared values of all x values,"

c. Sigma (x- overline x ) is read as "the sum of the deviations from the mean x bar."

d. (Sigma*x)² is read as "the square of the sum of all x values."

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Related Questions

Recently a hardware store sold premium exterior house stain for $53.10 per gallon. Estimate how many gallons could be bought with $200.85.

Answers

Answer:

Step-by-step explanation:

Take the amount of money you have (big number).Divide how much each gallon of paint costs (little number).

200.85 / 53.10 = ~3.78 (3.782485875706215)
Answer:

3.785 gallons

Step by step explanation:

To estimate how many gallons of premium exterior house stain can be bought with $200.85, we need to divide the total amount of money by the cost of one gallon of stain:

Number of gallons = Total amount of money ÷ Cost per gallon

Substituting the given values, we get:

Number of gallons = $200.85 ÷ $53.10/gallon

Simplifying the expression by dividing the total amount of money by the cost per gallon, we get:

Number of gallons = 3.785 gallons

Therefore, an estimated 3.785 gallons of premium exterior house stain could be bought with $200.85.

Question 1 Evaluate the determinant of A = -4 3 0 11 7 -9 8 -2 5 *​

Answers

According to the given information, we have value,   the determinant of matrix A is -647.

What is an expression?

In mathematics and computer programming, an expression is a combination of one or more values, variables, operators, and functions that are evaluated to produce a result.

Expressions can be as simple as a single value, such as "5", or as complex as a combination of multiple operators and functions, such as "2 + 3 * sin(4)".

According to the given information:

To evaluate the determinant of the given 3x3 matrix A, we can use the formula:

det(A) = a11(a22a33 - a23a32) - a12(a21a33 - a23a31) + a13(a21a32 -a22a31)

where aij represents the entry in the ith row and jth column of matrix A.

Using this formula, we get:

det(A) = (-4)(7(5) - (-9)(-2)) - (3)(11(5) - (-9)(8)) + (0)(11(-2) - 7(8))

det(A) = (-4)(59) - (3)(137) + (0)(-66)

det(A) = -236 - 411 + 0

det(A) = -647

Therefore, according to the given information, we have value,   the determinant of matrix A is -647.

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Find cos 2a if 2 cos 3α = cos a

Answers

Therefore , the solution of the given problem of trigonometry comes out to be using the formula 8 cos³ a - 6 cos a - 1.

What is trigonometry?

According to some, the growth of astrophysics was aided by the blending of various disciplines. Many metric problems may be solved or the results of a computation may be ascertained with the help of precise mathematical techniques. Trigonometry is the study of all six basic geometric computations. They go by a variety of titles and acronyms, including sine, variation, angle, and others. (csc).

Here,

To determine cos 2a in terms of cos a, we can use the double angle cosine formula as follows:

=> cos 2a = 2 cos² a - 1

Given that 2 cos 3 = cos a, we can reformat this as follows:

=> cos 3α = (1/2) cos a

Now, we can express cos 3 in terms of cos using the triple angle formula for cosine:

=>  cos 3α = 4 cos³ α - 3 cos α

=>  4 cos³ α - 3 cos α = (1/2) cos a

=>  8 cos³ α - 6 cos α = cos a

=>  cos 2α = 2 cos² α - 1

=>  cos 2α = 2 (cos² α - 1/2)

=>  cos 2α = 2 [(8 cos α - 6 cos α)/2 - 1/2]

=> cos 2α = 8 cos³ α - 6 cos α - 1

As a result, cos 2a can be calculated using the formula 8 cos³ a - 6 cos a - 1.

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What number gives a result of −1 when 10 is subtracted from the quotient of the number and 4?

Answers

Therefore , the solution of the given problem of expressions comes out to be when 10 is subtracted from the product of the number and 4, 36 is the number that produces a result of -1.

What does an expression actually mean?

Once numbers have been moving, estimates ought to be made by adding, pausing, and lowering variable but instead of doing so at random. They might only be able to assist one another by sharing information, resources, or answers to problems. In addition to arithmetic operations like addition, subtraction, combination, and combination, a statement of truth also includes formulas, parts, and notations.

Here,

Call the unidentified number "x" for now. The problem statement can then be converted into an equation as follows:

=>  (x/4) - 10 = -1

We can start by adding 10 to both sides of the equation before we solve for x:

=>  (x/4) - 10 + 10 = -1 + 10

Simplifying:

=>  x/4 = 9

Finally, we can find x by multiplying both sides of the equation by 4:

=> x = 36

Therefore, when 10 is subtracted from the product of the number and 4, 36 is the number that produces a result of -1.

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If
r=2x+5 Find the value of S, given the equation S=4r2

Answers

The value of S, given the equation S = 4r^2 and r = 2x + 5, is: S = 16x^2 + 80x + 100

How to determine the value of S

From the question, we have the following parameters that can be used in our computation:

r = 2x + 5

S = 4r^2

If r = 2x + 5, we can substitute this expression for r in the equation S = 4r^2:

S = 4(2x + 5)^2

Simplifying the expression inside the parentheses, we get:

S = 4(4x^2 + 20x + 25)

Expanding the expression, we get:

S = 16x^2 + 80x + 100

Therefore, the value of S, given the equation is: S = 16x^2 + 80x + 100

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a manufacturer produces three models of bluetooth earbuds… below

Answers

The price for each product is given by matrix BA in which price of manufacturer A is $1,106,150 and price of manufacturer B is 1,387,250.

Explain about the multiplication of matrix?

If the column count in the first matrix equals the number of rows there in second matrix, the product of the two matrices will be known.

The resultant matrix is going to have the exact number of rows in comparison to the initial matrix and the same quantity of columns also as second matrix if the product is defined.

Given value for the manufacturers A and B are-

A =   [tex]\left[\begin{array}{ccc}3,800&4,200\\5,500&12,500\\8,000&6,400\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}45.50&55.50&78.50\\\end{array}\right][/tex]

Multiply matrix A with Matrix B

BA =  [tex]\left[\begin{array}{ccc}45.50&55.50&78.50\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3,800&4,200\\5,500&12,500\\8,000&6,400\end{array}\right][/tex]

BA =  [tex]\left[\begin{array}{ccc}45.50*3,800 + 55.50*5,500 + 78.50*8,000&45.50*4,200+55.50*12,500+78.50*6,400\end{array}\right][/tex]

On solving

BA = [tex]\left[\begin{array}{ccc}1106,150&1387,250\end{array}\right][/tex]

Thus, the price for each product is given by matrix BA in which price of manufacturer A is $1,106,150 and price of manufacturer B is 1,387,250.

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find the value of X for which r ll s then find the m<1 and m<2

Answers

Based on the corresponding angles theorem, the value of x for which r ll s is calculated as: x = 15

m<1 = 64°; m<2 = 64°

What is the Corresponding Angles Theorem?

The corresponding angles theorem states that when a transversal intersects two parallel lines, the pairs of corresponding angles are congruent.

Based on the corresponding angles theorem, for r to be parallel to s, therefore:

m<1 = m<2

Substitute and solve for x:

79 - x = 94 - 2x

2x - x = 94 - 79

x = 15

Substitute the value of x to find the angle measures:

m<1 = 79 - x = 79 - 15 = 64°

m<2 = 94 - 2x = 94 - 2(15) = 64°

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Complete Question:

Find the value of x for which r || s. Then find m<1 and m<2.

m<1 = 79 - x

m<2 = 94 - 2x

What is the additive inverse of 7x – 20?

Answers

The additive inverse would be 20 - 7x

5; x; y is an arithmetic sequence and x; y; 81 is a geometric sequence. all terms in the sequence are integers. calculate the value (s) of x and y​

Answers

The value (s) of x and y​ are 25 and 45

x=25,y=45

sequence

A function which is a subset of the integers. In other words the sequence is an ordered set of numbers

Arithmetic sequences: which has constant difference between the termsGeometric sequences: found by multiplying the previous term by a constantRatio

The ratio is used to compare two or more items based on their size

5;x;y

x;y;81

let d be the common difference of A.S

x-5=d

y-x=d

y-5=2d

y-5=2(x-5)

y=2x-5

x,2x-5,81

common ratio r=> 2x-5/x= 81/2x-5

now solve for x

(2x-5/x)^2=81x

4x^2-101x+25=0

(4x-1)(x-25)

x=25

y=2*25-5

y=45

x=25,y=45

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State 2 reasons why statistics are important in our everyday lives and briefly explain how they are used?​

Answers

It is mostly used to keep records, calculate probabilities, and provide knowledge.

Basically, it helps us understand the world a little bit better through numbers and other quantitative information. Thus, the application of statistics is evident in our everyday activities.

18 point need helpppp

Answers

the measure of the angle will be ∠BAC= 61°

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The sum of all angle of triangle = 180

In this given triangle ∠ADE =7x and ∠BAC = 3x+10

7x + 3x+10 =180

10x+10 = 180

10x = 170

x = 17

∠BAC = 3x+10 = 51+10 = 61°

Hence the measure of the angle will be ∠BAC= 61°

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WILL MARK BRAINLIEST
Use the function below to find F(3)
F(x)=(1/5)^x

Answers

The value of the function F(3) will be 1/125. It is obtained by putting the value 3 in the place of x.

What is a function?

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

A function is represented by the two variables one is dependent and another one is an independent function. The relation between them is shown as y if dependent and x is the independent variable.

F(x)=(1/5)ˣ

F(3)=(1/5)³

F(3)=1/125

Hence, the value of the function F(3) will be 1/125.

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How long will it take $1000 invested at 2.6%
compounded monthly to grow to $2700?

Answers

For $1,000 invested at 2.6% compounded monthly to grow to $2,700 (Future Value), it will take 38 years and 3 months.

What is compounding?

Compounding refers to the system of charging interest on accumulated interest.

Compound interest is different from the simple interest system that charges interest only on the principal for each period.

With compounding, interest is computed on the principal and the accumulated interest.

To determine the period for the investment to grow to the future value of $2,700, we use an online finance calculator as follows:

I/Y (Interest per year) = 2.6%

PV (Present Value) = $1,000

PMT (Periodic Payment) = $-0

FV (Future Value) = $-2700

Results:

N = 458.920 months

= 38 years 3 months (458.92/12)

Total Interest = $1,700.0

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A scuba diver jumps into the water off the coast of Key West to see how deep he can descend and return to the source in about 7.3 minutes. After 60 seconds, he reaches a depth of 4 meters. At 4 minutes, he's at 22 meters from sea level. Upon his return to sea level, the diver noticed he was back at 4 meters below sea level after 7 minutes. The distance, in meters, the scuba diver traveled from sea level is a function of t, time, in minutes, can be modeled by a quadratic function. What is the quadratic function of the distance of the diver from sea level, d, as a function of t, time in minutes, in vertex form?​

Answers

The quadratic function of the distance traveled by the scuba diver from sea level, d, as a function of t, time in minutes, in vertex form is:[tex]$f(t) = 0.0113(t - 4)^2 - 4$[/tex]

How to find the quadratic function of this problem?

To write the quadratic function of the distance traveled by the scuba diver from sea level, we can use the vertex form of a quadratic function, which is:

[tex]$f(t) = a(t - h)^2 + k$[/tex]

where (h, k) is the vertex of the parabola, and a determines whether the parabola opens up or down.

In this case, we know that the vertex is at (4, -4), because the diver reaches a depth of 4 meters at 60 seconds (or 1 minute), and returns to that depth at 7 minutes (or 420 seconds), which means that the vertex is halfway between those two times:

h = (1 + 7) / 2 = 4

k = -4

We can also determine the value of a by using the other point given, at t = 4 minutes (or 240 seconds), when the diver is at a depth of 22 meters.

We can plug in these values to solve for a:

[tex]$22 = a(240 - 4)^2 - 4$[/tex]

[tex]$26 = 2304a$[/tex]

[tex]$a = 26 / 2304 = 0.01128472222$[/tex]

Therefore, the quadratic function of the distance traveled by the scuba diver from sea level, d, as a function of t, time in minutes, in vertex form is:

[tex]$f(t) = 0.0113(t - 4)^2 - 4$[/tex]

Note that the "0.0113" value has been rounded to five decimal places.

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A zebra runs 15 miles in 30 minutes. The zebra runs at a constant rate. At what rate in feet per second does the zebra run?

Answers

To convert miles per minute to feet per second, we need to use the following conversion factors:

1 mile = 5280 feet
1 minute = 60 seconds

So, we can calculate the zebra's speed as follows:

Speed = (Distance ÷ Time) × (Conversion factor for distance ÷ Conversion factor for time)

Speed = (15 miles ÷ 30 minutes) × (5280 feet per mile ÷ 60 seconds per minute)

Speed = 0.5 miles per minute × 88 feet per second

Speed = 44 feet per second

Therefore, the zebra runs at a rate of 44 feet per second.

NO LINKS!!! URGENT HELP PLEASE!!!

Please help me with #1 and 3

Answers

Answer:

[tex]\textsf{1)} \quad f(x)=3 \left(\dfrac{1}{2}\right)^x[/tex]

[tex]\textsf{3)} \quad f(x)=2 (3)^x[/tex]

Step-by-step explanation:

Exponential Function

The general formula for an exponential function is:

[tex]\boxed{f(x)=ab^x}[/tex]

where:

a is the initial value (y-intercept).b is the base (growth/decay factor) in decimal form.

Question 1

From inspection of the graph, this is a exponential decay function.

The end behaviours of the function are:

As x → -∞, f(x) → +∞As x → +∞, f(x) → 0

The y-intercept is (0, 3), so a = 3.

Another point on the curve is (-2, 12).

Substitute a = 3 and point (-2, 12) into the formula and solve for b:

[tex]\implies y=ab^x[/tex]

[tex]\implies 12=3 \cdot b^{-2}[/tex]

[tex]\implies 4= b^{-2}[/tex]

[tex]\implies 4= \dfrac{1}{b^{2}}[/tex]

[tex]\implies b^2= \dfrac{1}{4}[/tex]

[tex]\implies b= \dfrac{1}{2}[/tex]

Therefore, the equation of the exponential function is:

[tex]f(x)=3 \left(\dfrac{1}{2}\right)^x[/tex]

Question 3

From inspection of the graph, this is a exponential growth function.

The end behaviours of the function are:

As x → -∞, f(x) → 0As x → +∞, f(x) → +∞

The y-intercept is (0, 2), so a = 2.

Another point on the curve is (1, 6).

Substitute a = 2 and point (1, 6) into the formula and solve for b:

[tex]\implies y=ab^x[/tex]

[tex]\implies 6=2 \cdot b^1[/tex]

[tex]\implies 6=2 \cdot b[/tex]

[tex]\implies b = 3[/tex]

Therefore, the equation of the exponential function is:

[tex]f(x)=2 (3)^x[/tex]

You need gallon of fertilizer to cover a lawn. What is the least amount of money that you
can pay and have enough fertilizer?
LAWN
PERTILIZER
128 fluid ounces
$40
LAW
16 fluid ounces
$11

Answers

The cheaper option is buying a single bottle of 128 fluid ounces for $40.

What is the least amount of money that you can pay?

Here we know that you need gallon of fertilizer to cover a lawn. And we also know the prices for the fertilizers, we know that 128fluid ounces cost 40 dollars while 16 fluid ounces costs $11.

First, let's do a change of units to gallons to fluid ounces, we know that:

1 gall = 128 fluid ounces.

Then if you need exactly one gallon, the cheaper option is just buy one of the bottles of 128 fluid ounces for $40, because if you buy the smaller ones you will need to buy:

128/16 = 8 of these, for a total of 8*$11 = $88

While if you buy the big bottle you only spend $40.

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2. Given that V = {2, 4, 6, 8} and Q = {4, 6}. Find Q1 the complement of Q

Answers

Answer:

{2, 8}

Step-by-step explanation:

V union Q ={ 2,4,6,8}

V only ={2,8}

Q only ={None}

V intersection Q = {4,6}

so Q complement = V only ={2 and 8}

You have $x. You spend $3 to play golf. You have $8 left.

Which equation would you use to determine the amount of money you started with?

Answers

Answer:

x-3=8
8+3=11
You started with $11

What is the result when the number 44 is decreased by 25%?

Answers

To decrease 44 by 25%, we can first find what 25% of 44 is and then subtract that amount from 44:

25% of 44 = 0.25 x 44 = 11

So, the amount that 44 is decreased by 25% is 11.

Subtracting 11 from 44, we get:

44 - 11 = 33

Therefore, the result when the number 44 is decreased by 25% is 33.

What equation goes with what table?

Answers

Fοr the table 1 data pοints, the cοrrect equatiοn is Equatiοn 3:  y = -5x + 3.

What is an equatiοn?

A mathematical definitiοn οf an equatiοn is a claim that twο expressiοns are equal when they are jοined by the equals sign ("=").

Table 1 cοntains the data pοints -

x = -1, 0, 1, 2

y = 8, 3, -2, -7

Substitute the value οf x = -1 intο the fοur equatiοns tο οbtain the value οf y as 8.

Equation 1 is [tex]y = 5^x[/tex]

On substituting the value of x = -1 -

[tex]y = 5^{-1}[/tex]

y = 0.2

Therefore, equation 1 is incorrect.

Equation 2 is y = 5x - 2.

On substituting the value of x = -1 -

y = 5(-1) - 2

y = -5 - 2

y = -7

Therefore, equation 2 is incorrect.

Equation 3 is y = -5x + 3.

On substituting the value of x = -1 -

y = -5(-1) + 3

y = 5 + 3

y = 8

Therefore, equation 3 is correct.

Equation 4 is [tex]y = 5(0.2)^x[/tex]

On substituting the value of x = -1 -

[tex]y = 5(0.2)^{-1}[/tex]

[tex]y = 1^{-1}[/tex]

y = 1

Therefore, equation 4 is incorrect.

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total selling price for 5 shares of stocks at 90 1/8?

Answers

the total selling price for 5 shares of stock at $90 1/8 is $450.63.

How to calculate?

To calculate the total selling price for 5 shares of stock at $90 1/8, we need to multiply the price per share by the number of shares.

Let's first convert $90 1/8 to an improper fraction:

$90 1/8 = $721/8

Now we can multiply by 5 to get the total selling price:

Total selling price = 5 x $721/8

To simplify the calculation, we can first multiply 5 by the numerator:

Total selling price = $3605/8

We can leave the answer as a fraction or convert it to a decimal:

Total selling price = $450.63

Therefore, the total selling price for 5 shares of stock at $90 1/8 is $450.63.

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Simplify: (-7x + 5) - (2x^2 - 8x + 6). Name by degree and by terms.

Answers

Answer:

Step-by-step explanation:

18+11*65=2

Which equation has the solution set (1, 3)? A. x² + 4x + 3 = 0 B. x² + 4x − 3 = 0 C. x² - 4x - 3 = 0 x² - 4x +3=0​

Answers

Answer:

The equation that has the solution set (1, 3) is D. x² - 4x +3=0​.

Step-by-step explanation:

To find out which equation has the solution set (1, 3), we can substitute x = 1 and x = 3 into each equation and see which one gives us 0.

A. x² + 4x + 3 = 0

Substituting x = 1: (1)² + 4(1) + 3 = 8 ≠ 0

Substituting x = 3: (3)² + 4(3) + 3 = 24 ≠ 0

B. x² + 4x − 3 = 0

Substituting x = 1: (1)² + 4(1) − 3 = 2 ≠ 0

Substituting x = 3: (3)² + 4(3) − 3 = 18 ≠ 0

C. x² - 4x - 3 = 0

Substituting x = 1: (1)² - 4(1) - 3 = -6 ≠ 0

Substituting x = 3: (3)² - 4(3) - 3 = 0

D. x² - 4x +3=0​

Substituting x = 1: (1)² - 4(1) + 3 = 0

Substituting x = 3: (3)² - 4(3) + 3 = 0

The equation that has the solution set (1, 3) is D. x² - 4x +3=0​.

Hannah has a bag that contains pineapple chews, apple chews, and peach chews. She performs an experiment. Hannah randomly removes a chew from the bag, records the result, and returns the chew to the bag. Hannah performs the experiment 20 times. The results are shown below:
A pineapple chew was selected 5 times.
A apple chew was selected 7 times.
A peach chew was selected 8 times.
Based on these results, express the probability that the next chew Hannah removes from the bag will be a flavor other than peach as a percent to the nearest whole number.

Answers

The  probability that the next chew Hannah removes from the bag will be a flavor other than peach is 60%.

What is Probability?

The probability of an event is a number used in science to describe how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

According to question:

The total number of chews that Hannah removed from the bag is 20.

Out of these 20 chews, a peach chew was selected 8 times, so the number of non-peach chews is 20 - 8 = 12.

Therefore, the probability that the next chew Hannah removes from the bag will be a flavor other than peach is 12/20 = 0.6.

To express this probability as a percentage, we multiply it by 100 and round it to the nearest whole number:

0.6 * 100 = 60

So the probability that the next chew Hannah removes from the bag will be a flavor other than peach is 60%.

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Last month, Jill worked out for 25 minutes. Whenever she worked out in the morning. She also worked out in the afternoon for 1800 minutes. She worked out for a total of 2550 minutes. write and solve an equation to determine how many days she worked out in the morning.

Answers

Therefore , the solution of the given problem of unitary method comes out to be Jill exercised every morning for 30 days as a result.

Define unitary method.

By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.

Here,

Let's designate the quantity of morning workout days Jill completed "x".

Jill exercised for a total of 2550 minutes, so her morning and afternoon workouts together accounted for the following amount of minutes:

25x + 1800

Additionally, we are aware that this sum equals 2550:

25x + 1800 = 2550

We can first identify the variable component on one side of the equation by deducting 1800 from both sides in order to find x:

25x = 2550 - 1800

25x = 750

Then, by multiplying both sides by 25, we can find the value of x:

=> x = 750/25

x = 30

Jill exercised every morning for 30 days as a result.

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[tex](\sqrt{3}) sec2x+2=0[/tex]

Answers

Using the graphing tool, we have graphed the function [tex]$\rm({\sqrt{3}}) \sec2x+2=0$[/tex].

What is a function?

A functiοn in mathematics is a rule that designates a certain element frοm a different set, knοwn as the range tο each element in the dοmain οf a set. Typically, a functiοn is represented by a symbοl like f(x), where x is an element frοm the dοmain and f(x) represents the οutput fοr that element frοm the range.

What is graph?

In discrete mathematics, and mοre specifically in graph theοry, a graph is a structure amοunting tο a set οf οbjects in which sοme pairs οf the οbjects are in sοme sense "related". The οbjects cοrrespοnd tο mathematical abstractiοns called vertices and each οf the related pairs οf vertices is called an edge.

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Complete question:

Graph the given function using a graphing tool.

[tex]$\rm({\sqrt{3}}) \sec2x+2=0$[/tex]

Determine whether the equation represents a direct variation. If it does, find the constant variation.
3y=5x+4

Answers

The equation does not represent a direct variation.

Does the equation represent a direct variation?

A direct variation between two variables x and y can be written as:

y = k*x

Where k is what we know as the constant of variation or constant of proportionality.

Something important about these equations is that always pass through the point (0, 0).

y = k*0

y = 0

Now let's look at our equation:

3y = 5x + 4

When we take x = 0 we will get:

3y = 5*0 + 4

3y = 4

y = 4/3

It passes through (0, 4/3)

Then this is not a direct variation.

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Peter is one year older than Patrick. The product of their ages is 506. How old is Peter?

Answers

x(x+1)=506

x^2+x-506=0

(x+23)(x-22)=0

x=22


Peter is 23 years old.

Answer:x(x+1)=506

x^2+x-506=0

(x+23)(x-22)=0

x=22

Peter is 23 years old

Step-by-step explanation:

Find the missing length indicated.
64 48 fast if possible!!!

Answers

The value of x for the given right angled triangle is x = 36.

What is Pythagoras Theorem?

According to Pythagoras's Theorem, the square of the hypotenuse side of a right-angled triangle is equal to the sum of the squares of the other two sides. Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides. The hypotenuse in this case is the longest side since it forms the reverse of a 90° angle. When a right triangle's sides (let's say, a, b, and c) positive integer values are squared, they are used to create an equation known as a Pythagorean triple.

The given triangle is divided into two right angled triangles.

For the triangle whit the side lengths as 48 and 64, we use the Pythagoras theorem to find the hypotenuse.

c² = a² + b²

Substituting the values:

c² = (48)² + (64)²

c = 80

Now, for triangle with sides 48 and x we have:

l² = (48)² + x²

l² = 2304 + x²

Now, for the triangle with hypotenuse (64 + x) we have:

(64 + x)² = (80)² + (2304 + x²)

4096 + 128x + x² = 6400 + 2304 + x²

128x = 4608

x = 36

Hence, the value of x for the given right angled triangle is x = 36.

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