Hi, can you help me to Analyze and solve this problem of math please!

16 is the number which is one-fifth of a number when one-fourth of that same number is 20.

As per the given data:

One-fourth of the number is resulted to 20.

Here we have to determine the result of one-fifth of the same number from the given options.

An expression for a portion of a whole is a fraction.

For any real numbers, the fractional component of x is defined.

Let the number be X.

One-fourth of a number is 20 which means:

Multiply the one-fourth fraction with an unknown number which results in the number 20.

\($\frac{1}{4}\)  (X) = 20

X = 20 × 4

X = 80

Now we have to determine that one-fifth of the same number.

Multiply the one-fifth fraction by 80.

We get:

= \($\frac{1}{5}\) (80)

= \($\frac{1}{5}\)   × 5 × 16

= 16

One-fifth of the number 80 is 16

Therefore Option (D) - 16 is the correct answer.

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Answer:

  not quadratic

Step-by-step explanation:

In a quadratic expression, the highest exponent of x is 2.

Here, the highest exponent of x is 1, so this expression is not quadratic.

Answer:

12r + 13 + 5r + = 13 + 17r

Step-by-step explanation:

If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.

Answer:

30 inches long

Step-by-step explanation:

width=5

length=6x5

6x5=30

length=30

Answer:

Hey there!

The correct answer would be f(x)=(x-3)^2

Let me know if this helps :)

\(\longrightarrow\)Let the the number of dimes be x

\(\longrightarrow\)So, the number of nickels = x+4

(as the number of nickels is four more than dimes)

Now,

\(\leadsto\)Total amount of money= $ 1.25

\(\quad\)= 125 cents \(\quad\)(1 dollar = 100cents)

\(\leadsto\)Amount of money in dimes(in cents)

\(\quad\)= 10x \(\quad\quad\quad\) (1 dime = 10 cents)

\(\leadsto\)Amount of money in nickels(in cents)

\(\quad\) = 5(x+4) \(\quad\quad\)(1 nickel = 5 cents)

further,

Total amount of money by nickels and dimes = 125 cents

\(\implies\)10x+ 5(x+4) = 125

\(\implies\)10x+5x+20 =125

\(\implies\)15x + 20 = 125

\(\implies\)15x = 105

\(\implies\)x = 7

\(\bull \)Number of dimes = x = 7

\(\bull\)Number of nickels = x+4

\(\quad\)= 7+4

\(\quad\)= 11

\(\\\)

\(\green\therefore \quad\)Sophia has 7 dimes and 11 nickels.

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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Hey there!

5x < -10

DIVIDE 5 to BOTH SIDES

5x/5 < -10/5

CANCEL out: 5/5 because it gives you 1

KEEP: -10/5 because it helps solve for the x-value

NEW EQUATION: x < -10/5

SIMPLIFY IT!

x < -2

It is an OPEN circle shaded to the RIGHT

Therefore, your answer should be:

Option A. x < -2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Based on the polynomial remainder theorem, the value of the function when x = 10 is 8434.

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder. This remainder that has been obtained is actually a value of P(x) at x = a, specifically P(a). So basically, x -a is the divisor of P(x) if and only if P(a) = 0. It is applied to factorize polynomials of each degree in an elegant manner.

Putting x = 10 into the function f(x)=x^4-2x^3+5x^2-7x+4

f(10) = \(10^{4} - 2(10)^{2} + 5(10)^{2} - 7(10) + 4\)

f(10) = 10000 - 2(1000) + 5(100) - 70 + 4

f(10) = 10000 - 2000 + 500 - 66

f(10) = 8000 + 434

f(10) = 8434

Thus, the remainder is 8434.

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Step-by-step explanation:

3x + y

3(1.5)+0.5

=5

!!!!!!!!!!

Answer:

5

Step-by-step explanation:

3x + y = ?

3 (1.5) + 1/2 = ?

4.5                         First let's convert 4.5 into a fraction

4.5 = \(\frac{9}{2}\)                    Then convert it has a mixed number

\(4\frac{1}{2}\) + \(\frac{1}{2}\) = 5

Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.

To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.

The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:

Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).

Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.

Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.

If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.

In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.

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Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

Answer:

i just want points

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer: .....

ok done. Thank to me :>

Check the picture below.

so let's use those two points for that domain.

\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0}\implies \cfrac{0~~ - ~~(-6)}{2}\implies \cfrac{6}{2}\implies 3\)

Answer:

The t-score that should be used to find the 90% confidence interval is 1.729.

Step-by-step explanation:

The (1 - α)% confidence interval population mean, when the population standard deviation is not known is:

\(CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}\)

The information provided is:

n = 20

α = 0.10

The degrees of freedom of t-statistic will be:

df = n - 1

   = 20 - 1

   = 19

Compute the critical value of t as follows:

\(t_{\alpha/2, (n-1)}=t_{0.10/2, 19}=1.729\)

*Use a t-table.

Thus, the t-score that should be used to find the 90% confidence interval is 1.729.

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Iḿ sorry I cannot be specific but it´s either  12.633 or 0.6.33

Sorry if it is not helpful

Answer:

350d ≥ 1400

Hope it helps

To find the margin of error, we can use the formula: E = z√((p(1-p))/n)

where z is the z-score for a 99% confidence level, p is the sample proportion, and n is the sample size.

From the table of standard normal distribution, the z-score for a 99% confidence level is 2.576.

Plugging in the values, we get:

E = 2.576√((0.696(1-0.696))/664) ≈ 0.0385

So the margin of error is 0.0385.

To find the confidence interval, we can use the formula:

p ± E

where p is the sample proportion and E is the margin of error.

Plugging in the values, we get:

0.696 ± 0.0385

So the 99% confidence interval for the true proportion of all Americans that say "the future of the nation is a significant source of stress for me" is (0.6575, 0.7345). In interval notation, this can be written as [0.6575, 0.7345].

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Answer:

second one

Step-by-step explanation:

just multiply by -9 and see which one fits in

Answer:

{1, -9, 81, -729, …}

Step-by-step explanation:

Geometric sequence is basically multiplying the previous number by the constant. So it is 1 x -9 = -9, -9 x -9 = 81, -81 x -9 = -729, and so on.

Answer:

x=3/2

Step-by-step explanation:

\(\cfrac{3x-1}{21} =\cfrac{2x-2}{12}\)

\(36x-12=42x-21\)

\(6x=9\)

\(x=\cfrac{3}{2}\)

Hope it helps! :)

Answer:

\(\displaystyle y = \frac{x - 1}{2}\)

General Formulas and Concepts:

Pre-Algebra  

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

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

Step 2: Solve for y

The value of x is 30 degrees as it is a complimentary angle. When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are said to be supplementary.

Complementary angles are two angles with a combined angle of 90 degrees, whereas supplementary angles have a combined angle of 180 degrees.

Reflex angles are those that are larger than 180 degrees and less than 360 degrees. So 270 degrees is a reflex angle.

Since it is a right angle triangle,

hence

\((2x+1)+29=90\\2x+1=61\\2x=60\\x=30\)

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Answer:

tara is 59 inches tall

Step-by-step explanation:

math

Answer:

(a)

\(\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}\)

(b)

\(\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}\)

Step-by-step explanation:

Given

\(\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {0} &{0.1}&{0.03} & {0.01} & {0.14} & {1} &{0.08}&{0.20} & {0.06} &{0.34}& {2} &{0.05}&{0.14} & {0.33} &{0.52 } \ \end{array}\)

Solving (a): Find PMF of y if x = 1

This implies that, we consider the dataset of the row where x = 1 i.e.

\(\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {1} &{0.08}&{0.20} & {0.06} &{0.34} \ \end{array}\)

The PMF of y given x is calculated using:

\(Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{P(x)}\)

When x = 1

\(P(x) = 0.34\) --- the sum of the rows

So, we have:

\(Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.34}\)

For i = 0 to 2, we have:

\(i = 0\)

\(P(y=0|x)=\frac{P(y=0\ \&\ x = 1)}{0.34}\)

\(P(y=0|x)=\frac{0.08}{0.34}\)

\(P(y=0|x)=0.2353\)

\(i =1\)

\(P(y=1|x)=\frac{P(y=1\ \&\ x = 1)}{0.34}\)

\(P(y=1|x)=\frac{0.20}{0.34}\)

\(P(y=1|x)=0.5882\)

\(i = 2\)

\(P(y=2|x)=\frac{P(y=2\ \&\ x = 1)}{0.34}\)

\(P(y=2|x)=\frac{0.06}{0.34}\)

\(P(y=2|x)=0.1765\)

So, the PMF of y given that x = 1 is:

\(\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|1)} &{0.2353}&{0.5882} & {0.1765}\ \end{array}\)

Solving (b): The interpretation of (b) is to find the PMF of y if x = 2

This implies that, we consider the dataset of the row where x = 2 i.e.

\(\begin{array}{ccccc}{} & {y} & { } & { }& { } & {x} & {0} & {1} & {2} & {total} & {2} &{0.05}&{0.14} & {0.33} &{0.52 }\ \end{array}\)

When \(x = 2\)

\(P(x) = 0.52\)

So, we have:

\(Py|x(yi)=P(y=y_i|x)=\frac{P(y=x_i\ \&\ x)}{0.52}\)

For i = 0 to 2, we have:

\(i = 0\)

\(P(y=0|x)=\frac{P(y=0\ \&\ x = 2)}{0.52}\)

\(P(y=0|x)=\frac{0.05}{0.52}\)

\(P(y=0|x)=0.0962\\\)

\(i =1\)

\(P(y=1|x)=\frac{P(y=1\ \&\ x = 2)}{0.52}\)

\(P(y=1|x)=\frac{0.14}{0.52}\)

\(P(y=1|x)=0.2692\)

\(i = 2\)

\(P(y=2|x)=\frac{P(y=2\ \&\ x = 2)}{0.52}\)

\(P(y=2|x)=\frac{0.33}{0.52}\)

\(P(y=2|x)=0.6346\)

\(P(y=0|x)=0.0962\\\)

\(P(y=1|x)=0.2692\)

\(P(y=2|x)=0.6346\)

So, the PMF of y given that x = 1 is:

\(\begin{array}{cccc} {y} & {0} & {1} & {2} & {p(y|2)} &{0.0962}&{0.2692} & {0.6346}\ \end{array}\)

Answer:

the answer is 12

Step-by-step explanation:

d=2r=2*6.2=12.4