A skydiver took 40 seconds to drop 120 feet. What is the skydiver’s rate of descent?

Here each tea mug has 60 milliliters of tea.

What is division?

A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.

2.4 liters of tea were equally distributed to 40 mugs.

2400 milliliter of tea.

So each tea mug has = 2400/40 = 60 milliliters of tea.

Hence, each tea mug has 60 milliliters of tea.

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Answer:

x = 2; y = 10

Step-by-step explanation:

y = 5x

2x + 3y = 34

You have a system of equations. Since the first equation is already solved for y, we can easily use the substitution method. Substitute 5x for y in the second equation.

2x + 3y = 34

2x + 3(5x) = 34

2x + 15x = 34

17x = 34

x = 2

Now substitute 2 for x in the first equation.

y = 5x

y = 5(2)

y = 10

Solution: x = 2; y = 10

The car's value will decreases to $6,200 in about 8.65 years.

First, let's find the annual depreciation of the car. The car is purchased for $19,000 and depreciates at 7.75% per year, so the annual depreciation is:

⇒ 0.0775 x $19,000 = $1,478.50.

Now that we know the annual depreciation of the car, we can divide the difference in value by the annual depreciation to find out how long it will take for the value of the car to reach $6,200.

The value of the car decreases from $19,000 to $6,200, so the difference in value is :

⇒ $19,000 - $6,200 = $12,800.

Dividing this difference by the annual depreciation of $1,478.50:

⇒ $12,800 / $1,478.50 = 8.65 years.

Therefore, it will take approximately 8.65 years for the value of the car to reach $6,200.

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When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

There are a total of four components in a time series model.

Trend, Seasonal, Cyclical, and Error.

Seasonal Component is a wavelike pattern that is repeated throughout a time series and has a recurrence period of at most one year.

Cyclical Component is a wavelike pattern within the time series that repeats itself throughout the time series and has a recurrence period of more than one year.

Error Term represents the changes in time series data that are unpredictable and can't be associated with a seasonal , cyclical component.

Trend Component is the long-term increase or decrease in a variable being measured over time.

When a relationship is plotted on a graph, a linear relationship results in a straight line; a nonlinear relationship, on the other hand, results in a curve.

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The summation notation of the sum is given as follows:

[tex]\sum_{i = 1}^{6} \frac{(-1)^{i-1}}{3^i}[/tex]

The summation notation of the sum is written considering the patterns of the terms that compose the terms.

First we look at the fact that the sum has six terms, and the first term is considered as having index 1, hence:

[tex]\sum_{i = 1}^{6}[/tex]

Then we consider that the signal is alternating, with the terms with odd indices being positive and those with even indices being negative, hence the numerator is of:

[tex](-1)^{i - 1}[/tex]

(any of -1 or +1 would work here).

Then we considering that the denominator is composed by the powers of 3, hence it is given by:

[tex]3^i[/tex]

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Step-by-step explanation:

I will help you sir.

Given

Opposite Sides are Congruent

Reflexive

SSS

CPCTC

Answer:

(1)

Step-by-step explanation:

This is because (x-7)²=(x-7)(x-7), which when expanded using the FOIL method, is equal to x²-7x-7x+49=x²-14x+49.

The lengths of AC and AD using the concept of similar triangles are; AC =  12.5 and AD = 3

We are given that;

∆BDE is a similar triangle to ∆BAC.

This means that their sides are proportional. Thus, we can say that;

BD/BA = BE/BC

Thus;

2/BA = 4/(6 + 4)

BA = 2 × 10/4

BA = 5

Similarly;

BE/BC = DE/AC

4/10 = 5/AC

AC = 5 × 10/4

AC = 25/2

Finally,

AC = 25/2 = 12.5.

Thus;

AD = BA - BD = 5 - 2 = 3.

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The values of the x of the given equation [tex]x^{2} + 6x + 1 = 0[/tex]  using quadratic formula is -10 and -2.

The quadratic formula helps us solve any quadratic equation. First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula:

(-b±√(b²-4ac))/(2a)

Given equation;

[tex]x^{2} + 6x + 1 = 0[/tex]

Using  quadratic formula

x = [tex]-b[/tex] ± [tex]\frac{\sqrt{(b^{2} - 4 (ac) } }{4a}[/tex]

Substitute the values a = 1, b = 6, c = 1, we get;

x = [tex]-6[/tex] ± [tex]\frac{\sqrt{( (6) ^{2} - 4. 1.1)} }{2*1}[/tex]

x = -6 ± 4

x = -6 - 4      &    x = -6 + 4

  = -10                = -2

x = -10,  -2

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The values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

Expression 10x – x²

The expression can be written as

10x – x² = p – (x – q)²

10x – x² = p - x² - q² + 2xq

10x – x² = - x² + 2xq + p - q²

Compare the quantities on both sides,

10x = 2xq and 0 = p - q², p = q²

q = 10x / 2x = 5

p = 5² = 25

Therefore, the values of p and q, if Expression 10x – x² can be written as p – (x – q)² are 25 and 5.

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Answer: let d=# of dimes

let n= # of nickels

n+d=11

5n+10d=80

5d+25

5 dimes and 6 nickels

Answer:

where is your circle graph

Step-by-step explanation:

i need the graph in order to solve this

Answer:

4 1/2 ft

Step-by-step explanation:

18 = 4s

Divide both sides by 4.

18/4 = 4s/4

9/2 = s

4 1/2 = s

The side of the table is 4 1/2 ft.

The answer to this Question is YES. Inequalities do show the relation between Numbers.

What are Inequalities?

Inequalities are the operators the we want to compare the data when equality is not valid

Solution:

The Inequalities shows nice relation between numbers like when we say for example 2 and 4 we know that 2 is not equal to 4 but we know that

2 is less than 4 in this case inequalities help us to develop relations between numbers that are not equal

Inequalities are also used in inequations where they represents large set of data .

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As per the concept of hypothesis testing, the p-value of the test static is  0.0837

Hypothesis testing:

In statistics, when the alternative hypothesis is of the "greater than or greater than or equal to" type, the p-value can be calculated by calculating the probability of the z statistic being greater than the test statistic value.

Given,

Here we have the mayor of a town has proposed a plan for the annexation of a new community. and the political study took a sample of 800 voters in the town and found that 63% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 60%. testing at the 0.02 level.

Here we need to find the p-value of the test statistic.

While we looking into the given question we have identified the following hypothesis,

=> H0 : p <=0.6

=> H1: p > 0.6

And the value of alpha=0.02 p{reject H0 | H0 true} test statistic is a z from a 1 way 1 proportion test

So, the z value is z> 7.1286

Then the z value is calculated as,

=> 0.03/sqrt(0.6*0.63/800)

=> z = 1.3801

Therefore, the reject H0, the true proportion is greater than 60% and the p-value is 0.0837

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The midpoint of the line AN is (3(1/2) , -1).

What is midpoint?

Midpoint of the line(x , y) = (x₁ + x₂ / 2) , (y₁ + y₂ / 2)

x₁  = 2, x₂ = 5

y₁ = -3, y₂ = 1

So,

Midpoint of the line(x , y) = (2+5/2) , ((-3)+1 / 2)

= (7/2 , -2/2)

= (7/2, -1)

We can write 7/2 as 3(1/2)

Hence, the midpoint of the line AN is (3(1/2) , -1)

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No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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The measure of ∠WRS is 25°.

What is meaning of intersect point?

A graph intersection is a location where two or more graphs meet. It is a point that is the answer to an equational system. The intersection of two curves is the sole application of the TI series.

Given the points on a line are T, R, W.

The points on another line are V, R, S.

Both lines intersect at R.

Then another line that extends from point R to point Z between ∠VRW.

The angle ∠VRT is 5x° and the angle ∠TRS is (25x + 30)°.

∠VRS is a linear angle means ∠VRS = 180°.

Again,

∠VRS = ∠VRT + ∠TRS

Putting the value of ∠VRS, ∠VRT, ∠TRS

180° =  5x° + (25x + 30)°

180 =  30x + 30

Subtract 30 from both sides:

150 = 30x

Divide both sides by 30:

x = 5.

∠WRS is vertically opposite angle of ∠VRT.

Therefore ∠WRS = ∠VRT = 5x° = (5×5)° = 25°

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The value of 'x' for the given (alternate exterior angles) is found as 9.

For the stated question.

-1 + 14x = 12x + 17 (alternate exterior angles)

Simplifying,

14x - 12x = 17 + 1

2x = 18

x = 9

Thus, the value of 'x' for the given (alternate exterior angles) is found as 9.

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Answer:

yellow = red - 3 and green = yellow x 2 and red = yellow + 3

or

green= (red-3) x 2

Step-by-step explanation:

Three fewer yellow than read is the same as saying red -3

twice as many green as yellow is the same as yellow x 2

if green is yellow x 2 you can substitute yellow for the equation to find yellow

you can flip the equation for yellow around by doing inverse operations. To have the equation equal red you need to move the three by doing its inverse. The opposite of subtraction is addition so you'd add 3 to each side, getting rid of the -3 and isolating the red to make the equation red=yellow+3

Answer:

9 laps

Step-by-step explanation:

75% of something is the same as three-fourths, or multiplying by 0.75

12 x 0.75 = 9

or you can divide by 4 and then multiply by three if you know what to separate the original number into

12/4 = 3     3 x 3 = 9

Answer:

5 1/7 pages in one hour. And what does "A.B.C.D." Mean?

Step-by-step explanation:

It is insufficient proof that more than half of the students at the school recycle.

Given :

suppose that in the sample, 55 students said that they recycle.

It is insufficient proof that more than half of the students at the school recycle because: "Yes" was replied by 55 out of 100 pupils.

= 55 / 100

= 0.55

We can see that the proportion 0.55 of has a lot of dots above it in the dot plot.

As a result, a proportion of 0.55 is quite likely to be obtained when the genuine proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students recycle.

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The giant box's surface area dwarfs that of the little box by = 8 times bigger than the tiny box.

The cube's surface area is calculated as six times the square of its side lengths. 6a2, where an is the cube's side length, serves as its representation. In essence, it is the overall surface area. Study Cube Volume as well.

given

Large boxes with a side length of 6 feet are produced by Z-Grand Shipping Company.

The business also produces little boxes with 3-foot sides.

surface are of large box is = 6*6*6

= 216 feet3

surface area of small box = 3*3*3

= 27 feet3

The giant box's surface area dwarfs that of the little box by = 8 times

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Answer:

The number is 28.35

Step-by-step explanation:

45% of 36

[tex]\frac{x*y}{100}[/tex]

= [tex]\frac{45*36}{100}[/tex]

= [tex]\frac{2835}{100}[/tex]

= 28.35

A random variable is a quantitative outcome of a chance experiment.

A probability distribution includes the likelihood of each possible outcome.

A random variable is a variable whose value is determined by chance or randomness. It is often used to represent a numerical outcome of a chance experiment, such as the result of a coin toss, the roll of a die, or the outcome of a survey. Random variables can take on any numerical value, but it is often useful to assign probabilities to each possible value. This probability, known as a probability distribution or probability density function, describes the likelihood that a given value of the random variable will occur.

A normal distribution is a type of probability distribution that is symmetrical and bell-shaped, with the mean, median, and mode all equal. The values of the distribution are spread out around the mean, with the majority of the values within one standard deviation of the mean. A normal distribution is also known as a Gaussian distribution, as it was discovered by Carl Friedrich Gauss in the early 19th century.

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The measure of angle 3 is given as follows:

m < 3 = 55º.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles in this problem are listed as follows:

The measure of angle 1 is given as follows:

m < 1 = 55º.

Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:

m < 3 = 55º.

As angle 3 is congruent to angle 1.

Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.

The diagram is given by the image shown at the end of the answer.

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Therefore the probability that  she buys at least one of the previous items is 0.1333

The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.

Given:

event A: she buys  red dress.

event B: she buys a blue dress.

event C: she buys a necklace.

the probability she will buy a red dress is 0.2,

the probability she will buy a blue dress is 0.4

there is 10% chance  she will buy a necklace =0.10

The probability she wants to buy at most one dress,

P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)

P(A or B or C) =0.568

the probability she buys at least one of the previous items is

[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex] = [tex]\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}[/tex]

 [tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex]= 2/15 =0.133

Therefore the probability that  she buys at least one of the previous items is 0.1333

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Answer:

  C.  4

Step-by-step explanation:

You want the midpoint between -3 and 11 on the number line.

The midpoint is the average of the end point coordinates:

   (-3 +11)/2 = 8/2 = 4

The midpoint is 4.