skydiver jumps from a pant at 11,00 feet above the ground and descends at a rate of 15 feet per second and skydiver b jumps after 60 seconds and is 10,100 feet above the ground. in 3 minutes skydiver b is 8,300 feet above the found where are both skydivers going to after 2 minutes.

Answer:

x=72

y=54

Step-by-step explanation:

1st question. y=54 because it is a bisector of the 108 degree angles. (a polygon's interior angles add to number of sides minus 2 times 180)

There are two ys, so they add up to 108. A triangle's interior angles add to 180. 180-108 =72 x=72

2nd question, x is 72 ( it says x is the same measure) so 180-72=2y.

y still equals 54

Answer:

this is so easy

Step-by-step explanation:

3000* (15) (300) divided by 20 x 60 100ft  divided by 40

Answer:

1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.

2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.

3. The solution to the initial value problem is y = t^2 + 4/3.

Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Answer:

It is 18 because if you look at the side the small one says 3 the big one says 6 so if you multiply the 9 square feet by 2 thats your answer

Answer:

A=36

Step-by-step explanation:

Hi love ,

so we now that the are of a triangle is : 1/2bh

the smaller triangle shows that : 9 = 1/2b*3

so b =6

and if the 3 became 6 then 6 will become 12

base of the smaller triangle = 6

base of the larger triangle = 12

Area of Larger triangle = 1/2 * 12*6

= 1/2*72 = 36

A=36

Answer: Answer: 2000 was invested into 6%, 5000 was invested Into 8%

Step-by-step explanation:

8% of 5000 = 400

6% of 200 = 120

In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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Answer:

Solutions given;

Using cosine rule

b²=a²+c²-2*a*c*cos B°

b²=15²+8²-2*15*8*cos39

b²=102.48

b=\( \sqrt{102.48} \)

b=10.12

b=10.1

Using sine rule

\( \frac{sin A}{BC} = \frac{sin B}{AC} =\frac{sin C}{AB} \)

\( \frac{sin 29°}{15} =\frac{sin C}{8} \)

Doing criss cross multiplication

Sin C=\( \frac{sin 29°}{15} ×8\)

m<C=Sin -¹(0.29)

m<C=14.98

m<C=15°is a required answer.

Answer:

Step-by-step explanation:

number of committees=9C4×30C2

=(9×8×7×6)/(4×3×2×1)×(30×29)/(2×1)

=63×30×29

=54810

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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The only equation from the options given which shows exactly one solution is x = 2

Evaluating the options given :

Therefore, only the equation x =2 gives exactly one solution for the value of x

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Answer:

1/2 is the same number as 0.5, so (1/2)% is the same as 0.5%. “Percent” means “per 100”, so 50% = 50/100 = 1/2. (1/2)% = (1/2)/100 = 1/200. In other words, 50% is the same as 1/2, but is not the same as (1/2)%.

Step-by-step explanation:

Answer:

110

Step-by-step explanation:

Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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By considering these rules and properties of integers, the correct result of 6 was obtained.

When writing the response, I considered the following information:

The product or quotient of two integers with different signs is negative. This rule was used to determine that 2(-12) equals -24, not 24.

To subtract an integer, add its opposite. This rule was applied when subtracting -30 from -24, resulting in -24 - (-30) = -24 + 30.

To add integers with opposite signs, subtract the absolute values. The sum has the same sign as the integer with the greater absolute value.

This rule was used to calculate -24 + 30 = 6, where the absolute value of 30 is greater than the absolute value of -24.

By considering these rules and properties of integers, the correct result of 6 was obtained.

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Answer:

C. 65

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

180-62-53 = 65

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

Answer:

Step-by-step explanation:

Required equation is:

Solution:

The order from smallest to largest is 0.079 inches, 0.7 inches, 0.7091 inches, 0.762 inches.

What is a sequence?

A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for a more in-depth discussion.

To arrange the given numbers in order from smallest to largest, we can simply compare them to each other and order them accordingly:

0.079 inches < 0.7 inches < 0.7091 inches < 0.762 inches

Therefore, the order from smallest to largest is 0.079 inches, 0.7 inches, 0.7091 inches, 0.762 inches.

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Answer:

8 roses

Step-by-step explanation:

First start by subtracting $18.69 by $5.25 because you already know how much the carnations cost and how much the bouquet cost in all. When you subtract 18.69 by 5.25 you should get $13.44. If each rose cost $1.68 then divide 13.44 by 1.68 to get the amount of roses in the bouquet.

Answer:

Explained below.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

\(\mu_{\hat p}=p\)

The standard deviation of this sampling distribution of sample proportion is:

\(\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}\)

A random sample of n = 658 items is sampled randomly from this population.

As the sample size is large, i.e. n = 658 > 30, the Central limit theorem can be applied to approximate the sampling distribution of sample proportion by a Normal distribution.

Compute the mean and standard deviation as follows:

\(\mu_{\hat p}=0.61\\\\\sigma_{\hat p}=\sqrt{\frac{0.61(1-0.61)}{658}}=0.019\)

(a)

Compute the probability that the sample proportion is greater than 0.63 as follows:

\(P(\hat p>0.63)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.63-0.61}{0.019})\\\\=P(Z>1.05)\\\\=1-P(Z<1.05)\\\\=1-0.85314\\\\=0.14686\\\\\approx 0.1469\)

(b)

Compute the probability that the sample proportion is between 0.60 and 0.66 as follows:

\(P(0.60<\hat p<0.66)=P(\frac{0.60-0.61}{0.019}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.66-0.61}{0.019})\\\\=P(-0.53<Z<2.63)\\\\=P(Z<2.63)-P(Z<-0.53)\\\\=0.99573-0.29806\\\\=0.69767\\\\\approx 0.6977\)

(c)

Compute the probability that the sample proportion is greater than 0.592 as follows:

\(P(\hat p>0.592)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}>\frac{0.592-0.61}{0.019})\\\\=P(Z>-0.95)\\\\=P(Z<0.95)\\\\=0.82894\\\\\approx 0.8289\)

(d)

Compute the probability that the sample proportion is between 0.57 and 0.60 as follows:

\(P(0.57<\hat p<0.60)=P(\frac{0.57-0.61}{0.019}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.60-0.61}{0.019})\\\\=P(-2.11<Z<-0.53)\\\\=P(Z<-0.53)-P(Z<-2.11)\\\\=0.29806-0.01743\\\\=0.28063\\\\\approx 0.2806\)

(e)

Compute the probability that the sample proportion is less than 0.51 as follows:

\(P(\hat p<0.51)=P(\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.51-0.61}{0.019})\\\\=P(Z<-5.26)\\\\=0\)

Answer:

x = 20

Step-by-step explanation:

We know that the vertically opposite angles are equal.

Accordingly,

41 = 2x + 1

Subtract 1 from both sides.

41 - 1 = 2x

40 = 2x

Divide both sides by 2.

x = 20

According to the information, the missing number from the box is number 40.

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values  y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

m = (y2 - y1) / (x2 - x1)

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

What is the parallel lines?

Parallel lines are two lines in a plane that never intersect.

1. Orientation of Lines:

Parallel lines are lines that never intersect and remain equidistant from each other at all points.

When constructing parallel lines, the lines are drawn in the same direction and maintain the same distance between them throughout their entire length. They do not meet or cross each other.

On the other hand, perpendicular lines are lines that intersect at a right angle (90 degrees). When constructing perpendicular lines, the lines are drawn so that they intersect at a right angle, forming four right angles at the point of intersection.

2. Tools/Methods Used:

Constructing parallel lines and constructing perpendicular lines may require different tools or methods.

To construct parallel lines, one common method is to use a straightedge and a compass. A straightedge is used to draw a straight line, and a compass is used to measure and transfer distances to create additional parallel lines.

Therefore, By using the compass to measure a distance from the original line, and then transferring that distance to another point on the line, a parallel line can be drawn.

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Using the sinking fund formula and the information given, we have:

Answer:

275 cheeseburgers

Step-by-step explanation:

620-70=550

550/2=275

If a local hamburger shop sold a combined total of 620 hamburgers and cheeseburgers on Monday.  275 hamburgers were sold on Monday.

H = Number of hamburgers sold

C = Number of cheeseburgers sold

The total number of hamburgers and cheeseburgers sold on Monday is 620:

H + C = 620

There were 70 more cheeseburgers sold than hamburgers:

C = H + 70

Substitute the value of C from the second equation into the first equation:

H + (H + 70) = 620

Combine like terms:

2H + 70 = 620

Isolate 2H by subtracting 70 from both sides:

2H = 620 - 70

2H = 550

Divide both sides by 2 to find the value of "H":

H = 550 / 2

H = 275

Therefore  275 hamburgers were sold on Monday.

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The line of best fit for the data in the table is given as follows:

y = 1.68x - 48.61.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.

The points of the data-set in this problem are given as follows:

(77.4, 81), (78.1, 83), (80.4, 84.5) and (81.5, 89.1).

Inserting these points into a linear regression calculator, the line of best fit for the data in the table is given as follows:

y = 1.68x - 48.61.

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Answer:

\(y=\displaystyle\frac{2}{3}x\)

Step-by-step explanation:

Hi there!

The given linear equations are organized in slope-intercept form: \(y=mx+b\) where m is the slope of the line and b is the y-intercept (the value of y when x=0)

First, we can determine the slope using the following formula:

\(m=\displaystyle\frac{y_2-y_1}{x_2-x_1}\) where two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):

\(m=\displaystyle\frac{2-0}{3-0}\\\\m=\displaystyle\frac{2}{3}\)

Therefore, the slope of the line is \(\displaystyle\frac{2}{3}\). Plug this into \(y=mx+b\) as m:

\(y=\displaystyle\frac{2}{3}x+b\)

We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:

\(y=\displaystyle\frac{2}{3}x+0\\\\y=\displaystyle\frac{2}{3}x\)

I hope this helps!