suppose y varies directly as x. suppose also that y=34 when x=17. find y when x=56.

On solving the provided question, we can say that Probability (marble in blue) = 4/14 and Probability (marble in red ) = 10/14

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

total marble = 14

total red = 4

total blue = 10

Probability (marble in blue) = 4/14

Probability (marble in red ) = 10/14

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Answer:

-19 - (-25) = 6

Step-by-step explanation:

-19 - (-25) =

-19 + 25 = 6

Answer:

Step-by-step explanation:

-5(3m² + 7n²) + 8n²

Expand brackets.

-15m² + -35n² + 8n²

Combine like terms.

-15m² + -27n²

Answer:

\(\boxed{\red{= - 3(5 {m}^{2} + 9 {n}^{2} )}}\)

Step-by-step explanation:

\( - 5(3 {m}^{2} + 7 {n}^{2} ) + 8 {n}^{2} \\ - 15 {m}^{2} - 35 {n}^{2} + 8 {n}^{2} \\ = - 15 {m}^{2} - 27 {n}^{2} \\ = - 3(5 {m}^{2} + 9 {n}^{2} )\)

Answer:

Division can be thought of as the opposite of multiplication. Let's say you want to divide 8 by 2. Another way to think of this example is what can be multiplied by 2 to equal 8? 4 does. There are many different methods to come up with a solution. I honestly cannot explain division with one universal method. Start with thinking about what is division. It took me awhile to figure it out, unfortunately I don't think I can help much that's what I can explain.  Anybody with more knowledge than my 10th grade math skills please help? This is important.

Step-by-step explanation:

Step-by-step explanation:

When we divide any number, divisor must be smaller than the number of dividend. Subtract the product from the number of dividend every time and then take the next number until all number finished. Quotient is always written above the line and product below the number of dividend.

Answer:

32 cubic feet

Step-by-step explanation:

The formula for a cylinder is \(\pi r^{2} h\).

The radius of the cylinder is equal to 1.5 feet, since it is \(\frac{diameter}{2}\).

Plugging in, the cylinder's full volume is  \(6\pi 1.5^2\) which is approximately 42.4 cubic feet.

To find the amount of water when it is 3/4 full, multiply 42.4 x .75, to get around 31.8, and 32 when rounded

Answer:

0.26

Step-by-step explanation:

A (x , y), radius of circle = 1

y/radius = y/1 = sin 15°

y = 0.26

Answer:

sin 165..........

Step-by-step explanation:

Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one variable that is squared but no variables that are raised to a higher power. The general form of a quadratic equation in one variable (usually represented by x) is:

�

�

2

+

�

�

+

�

=

0

,

ax

2

+bx+c=0,

where a, b, and c are constants (numbers) and a is not equal to zero. The term ax^2 is called the quadratic term, bx is the linear term, and c is the constant term.

To solve a quadratic equation, we can use the quadratic formula:

�

=

−

�

±

�

2

−

4

�

�

2

�

.

x=

2a

−b±

b

2

−4ac

​

​

.

This formula gives us the solutions (values of x) for any quadratic equation in the standard form. The expression under the square root, b^2 - 4ac, is called the discriminant of the quadratic equation.

The discriminant can tell us a lot about the nature of the solutions of the quadratic equation. If the discriminant is positive, then the quadratic equation has two distinct real solutions. If the discriminant is zero, then the quadratic equation has one real solution, called a double root or a repeated root. If the discriminant is negative, then the quadratic equation has two complex (non-real) solutions, which are conjugates of each other.

Using concepts of Probability, we got 13/17 is the probability of selection of diagonal which is not shortest nor longest.

We know very well that icosagon has 20 sides.

If any diagonal is possible, it can be possible by connecting two points, so to choose r objects from n objects can be done by \(^nC_r\) ways=\(\frac{n!}{r!.(n-r)!}\)

So, number of ways to choose diagonal =\(^2^0C_2\)

After that we need to subtract 20 ways as single point can lead to diagonal making.

So, total number of ways to choose 20 diagonals=\(^2^0C_2\)-20 = 170

Now, talking about the shorter diagonal

so, shorter diagonal =Diagonal connecting(A₁A₃, A₂A₄,.....) =20 diagonals.

Now, talking about longer diagonal=Diagonal connecting(A₁A₈,A₂A₉.........)=20 diagonals

So, we have total chances of selection and possible number of chances of selection of shorter and longer diagonal

So, according to the formula of Probability=\(\frac{Favorable outcomes}{Total Outcomes}\)

Probability=[(Total ways to select diagonals-(Ways to select shorter diagonal)-Ways to select longer diagonal)]/(Total number of ways)

=>Probability=(170-20-20)/170

=>Probability=130/170

>Probability=13/17

Hence, the probability of selecting a  diagonal such that it is not shortest nor longest is 13/17.

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Answer:

C. 2/3 x 2/3

Step-by-step explanation:

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as = 2 * 10^-7

A canonical, normal, or standard form of a mathematical object is a conventional manner of presenting that item as a mathematical expression in mathematics and computer science. It is frequently the one that gives the simplest representation of an item and allows it to be identified in a unique fashion.

A quantity is said to be stated in standard form if it is written as the product of a power of ten and a number higher than or equal to one but less than ten (or scientific notation).

The expression (3.6 * 10^-5) / (1.8 * 10^2) can be calculated as follows:

=3.6 * 10^-5 / (1.8 * 10^2)

= (3.6 / 1.8) * (10^-5 / 10^2)

= 2 * 10^-7

Therefore, the answer in standard form is 2 * 10^-7.

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Answer:

C.) AFD measures 30°

Step-by-step explanation:

it is 150 degrees

Answer:

the answer is C

Step-by-step explanation:

A)  angle EFC is 80 degrees so a is a true statement

B) angle BFC is 60 degrees and angle DFE is 30 degrees 60+30=90 so that's a true statement

D) angle AFB is 40 degrees and angle CFD is 50 degrees  40+50=90 so that a true statement

that leaves C and angle AFD is more than 30 degrees its 150 degrees

The period of the sinusoidal function is equal to 10 units.

In this problem we find the representation of a sinusoidal function set on Cartesian plane. The period of the function described above is equal to the horizontal distance between two peaks of the graph described in the figure.

Then, we can determine the period by means of the following subtraction formula:

T = Δx

T = 11 - 1

T = 10

In a nutshell, the sinusoidal function has a period equal to 10 units.

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Answer:

A) $12.80 per pound of chocolate

Step-by-step explanation:

As, 2 1/2 pounds = 5/2 = 2.5

So for 2.5 pounds = $32

For 1 pound = 32/2.5 = 12.80

So, = 12.80

a0 is the regression term that describes the constant or intercept in the linear regression equation.

In a simple linear regression model, the equation takes the form of y = a0 + a1x + e1, where y is the dependent variable (or response variable), x is the independent variable (or predictor variable), a0 is the intercept or constant term, a1 is the coefficient of the independent variable, and e1 is the error term.

The intercept term, a0, represents the value of the dependent variable when the independent variable is zero. For example, in a linear regression model that predicts salary based on years of experience, the intercept would represent the starting salary for someone with zero years of experience. The intercept is an important component of the regression equation because it allows us to make predictions for values of x that are outside the range of our observed data.

The coefficient, a1, represents the change in the dependent variable for each one-unit increase in the independent variable. In the salary example, the coefficient would represent the average increase in salary for each additional year of experience.

Both the intercept and coefficient are estimated from the data using methods such as least squares regression. Once these values are estimated, we can use them to make predictions for new values of x.

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Answer:

11 feet wide

Step-by-step explanation:

Answer:

32−(−19)

=32−(−19)

=32+19

=51

Step-by-step explanation:

hope this helps

The value of x is 4.8cm.

Here BD // EF and BF // DE

So from this, we have ∠ABF = ∠EFC

Let's take two triangles ΔABC and ΔFCE

∠C =∠C (common angle)

∠ABC = ∠EFC

So ΔABC ≅ ΔEFC

So ∠BAC = ∠FEC

AB/ EF = BC/ FC

AB = 8cm, EF =x, BC = 12cm, FC= 12-x

8/x = 12/ 12-x

2/x = 3/ 12-x

24 - 2x = 3x

5x = 24

x = 4.8cm

Therefore the value of x is 4.8cm.

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Answer:

  (a)  x=−20 1/2

Step-by-step explanation:

Multiply by the product of the denominators and solve the resulting linear equation in the usual way.

  \(\dfrac{2}{7}=\dfrac{-5}{x+3}\\\\2(x+3)=-5(7)\qquad\text{multiply by $7(x+3)$}\\\\2x+6=-35\qquad\text{simplify}\\\\2x=-41\qquad\text{subtract 6}\\\\\boxed{x=-20\dfrac{1}{2}}\qquad\text{divide by 2}\)

The height of the room is 5 m.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Length = 7 m

Width = 2 m

Height = x

Four walls of a room will have,

Two walls of length x height.

Two walls of Width x height.

Now,

Area four walls of the room = 90 m

2 (length x height) + 2 (Width x height) = 90

2 (7x) + 2 (2x) = 90

14x + 4x = 90

18x = 90

x = 5

Thus,

Height of the room = 5 m.

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Answer:

Step-by-step explanation:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base Area * Height

To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:

A = (3√3/2) * s^2

where s is the length of one side of the hexagon. Substituting s = 10, we get:

A = (3√3/2) * 10^2 = 259.80 square units (approx)

Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:

V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)

Therefore, the approximate volume of the pyramid is 1039.20 cubic units.

The value of the angle U in the triangle is 92.10 degrees.

The angle U in the triangle can be found using cosine rule as follows:

Let's use cosine formula to find the angle U

c² = a² + b² - 2ab cos C

Hence,

Therefore,

a = 58.8

b = 38.4

c = 71.4

Hence,

71.4²  = 58.8² +  38.4² - 2(58.8)(38.4) cos U

5097.96 = 3457.44 + 1474.56 - 4515.84 cos U

5097.96 - 4932 =  - 4515.84 cos U

165.96 = - 4515.84 cos U

divide both sides by - 4515.84

cos U = 165.96 / - 4515.84

cos U = - 0.03675063775

U = cos⁻¹ - 0.03675063775

U = 92.1032274244

Therefore,

U = 92.10 degrees

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The correct hypothesis for the test made in this problem are given by:

H0: p = 0.25, Ha: p > 0.25.

At the null hypothesis, we test if the researcher is not correct, that is, if the proportion is of 25%, hence:

\(H_0: p = 0.25\)

At the alternative hypothesis, we test if there is enough evidence for the researcher's claim, that is, if the proportion is greater than 25%, hence:

\(H_a: p > 0.25\)

Hence the correct option is:

H0: p = 0.25, Ha: p > 0.25

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Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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