The measures of the triangle of the angles of a triangle are shown in the figure below. Solve for x.

The measure of the angle marked "C" based on the information will be 42.8°.

It should be noted that to find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,

sinA / a = sinB / b = sinC / c

where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.

Given ∠A = 61°, c = 35, a = 45

∴( sinA)/a = (sinC)/c

(sin 61° )/ 45 = (sin C) / 35

sin c = ((sin 61°) / 45) × 35

sin c = 0.68

c ≈ 42.8°

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Answer: 1=53,2=96,0=100,2=70

Step-by-step explanation: Pretty easy there Parrell lines which equals 180 in angles so for example the first one is a corresponding angle cause 53 on angle A is the same on angle B

Second one equation to find this answer is 180-84=96

You'll learn the rest soon I hope this helps

Answer: The answer is E, or ≠.

Step-by-step explanation:

The symbol (≠) indicates that a number does not equal the other number. The correct option is E.

I hope this helped! A brainilist is appreciated and helpful! <3

Answer:

all of them

Step-by-step explanation:

i hope you find it helpful

The area of the shaded portion was estimated to be around 400 square feet, so 400 square feet were covered in sod.

The shaded portion of the garden was estimated to be around 400 square feet. To cover this area with sod, the soil was prepared by removing any existing vegetation, rocks, and debris. The soil was then leveled and covered with a layer of fertilizer. After that, the sod was laid on top of the soil, with the roots facing down. The sod was then watered and rolled to ensure the sod was securely attached to the ground. The entire process of sodding the garden was completed in 400 square feet, providing an even layer of grass for the area. This will help to keep the garden beautiful and healthy for years to come.

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Option b. best represents the data of scatter plots.

A scatter plot is a type of graph used to display the relationship between two numerical variables. It is also called a scatter diagram or scatter graph.

The best scatter plot to represent the given data would be:

b. A graph shows rainfall increases (in centimeters) from 1.5 to 15 in steps of 1.5 and the number of months on the x-axis.

Points at  (1, 1.1),  (2, 1.3),  (3, 1.8),  (4, 2.6),  (5, 3.7),  (6, 4.5),  (7, 5.7),  (8, 7.1),  (9, 8.9),  (10, 12.3)

This scatter plot correctly shows months on the x-axis and the corresponding increase in rainfall (in centimeters) on the y-axis. The range of the y-axis from 1.5 to 15 in increments of 1.5 is appropriate for the data provided. Additionally, this plot correctly represents all the data points provided without any errors.

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According to the solution we have come to find that, There are 50 gallons of water in the tank after 15 minutes.

what is calculus?

Calculus is a branch of mathematics that deals with rates of change and how things change over time. It has two main branches: differential calculus and integral calculus.

Differential calculus deals with instantaneous rates of change and how things change at a particular moment or instant. It involves concepts such as derivatives, limits, and rates of change.

Integral calculus deals with the accumulation of quantities and how things add up over time. It involves concepts such as integrals, area under a curve, and accumulation of volumes.

a. To calculate the rate of change, we need to find the slope of the line connecting the two given points on the table. Using the formula for slope, we get:

slope = (change in y) / (change in x)

slope = (70 - 90) / (6 - 3)

slope = -20 / 3

Expressing the slope as a ratio, we get:

rate of change = -20/3

b. The rate of change is negative, indicating that the amount of water in the tank is decreasing over time. Water is leaving the tank. We know this because the slope of the line is negative, meaning that as time goes on, the amount of water in the tank is decreasing at a constant rate.

c. To find the amount of water in the tank after 15 minutes, we need to first find the equation of the line that passes through the two given points. Using the point-slope form of the equation of a line, we get:

y - 90 = (-20/3)(x - 3)

Simplifying, we get:

y = (-20/3)x + 110

Now we can substitute x = 15 to find the amount of water in the tank after 15 minutes:

y = (-20/3)(15) + 110

y = 50

Therefore, there are 50 gallons of water in the tank after 15 minutes.

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So, option (a), a sample size of 700, should be chosen in order to attain a margin of error of no more than 2.5% with 90% confidence.

The statistical concept of margin of error describes the range in which the real value of a population parameter is assumed to lie based on a sample. The degree of uncertainty or error related to a specific sample size and confidence level is given as a plus or negative percentage or number. The genuine percentage of support in the population as a whole is assessed to be between 47% and 53% with 95% confidence, for instance, if a pollster surveys 1,000 individuals and finds that 50% of them favor a certain political candidate with a margin of error of 3%.

given

We can use the following formula to get the sample size required for a specified margin of error with a particular level of confidence:

[tex]n = (Z^2 * p * q) / E^2[/tex]

When we enter the values, we obtain:

[tex]n = (1.645^2 * 0.73 * 0.27) / 0.025^2[/tex]

n ≈ 643.71

We should round up to the nearest choice, which is 700, because the sample size must be an integer.

So, option (a), a sample size of 700, should be chosen in order to attain a margin of error of no more than 2.5% with 90% confidence.

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The complete question is:-   Based on earlier studies, it is believed that the proportion of California high school students favoring a four-day school week (8:00 am to 4:30 pm) is 73%. You plan on doing a follow up study. Money is a concern in your study, so you cannot afford to be conservative with your approach. A professional polling company offers to perform the survey for you, and show you the following sample size options. The larger the sample size, the more expensive the survey will be. Which size will you choose if you want a margin of error of no more than ± 2.5% with 90% confidence?

a. 700

b. 800

C. 900

d. 1,000

e. 1,100

so the garden is a parallelogram and the whole area is a rectangle, now, if we just get the whole area and then subtract the area of the parallelogram from it, in effect making a whole in the rectangle, what's leftover is the area of the walkway, Check the picture below.

The total volume of the hemisphere mounted on the cuboid is 3574.76 cubic yards.

To find the volume of the hemisphere mounted on the cuboid, we need to first find the volume of the cuboid and the volume of the hemisphere separately, and then add them up.

The volume of the cuboid is given by the formula:

V_cuboid = l x w x h

where l, w, and h are the length, width, and height of the cuboid, respectively. Substituting the given values, we get:

V_cuboid = 17 yd x 14 yd x 12 yd

V_cuboid = 2856 cubic yards

Next, we need to find the volume of the hemisphere. The diameter of the hemisphere is given as 14 yd, which means that the radius is 7 yd. The volume of the hemisphere is given by the formula:

V_hemisphere = (2/3) x π x [tex]r^{3}[/tex]

V_hemisphere = (2/3) x 3.14 x [tex]7^{3}[/tex]

V_hemisphere = 718.76 cubic yards

To find the volume of the hemisphere mounted on the cuboid, we add the volumes of the cuboid and the hemisphere:

V_total = V_cuboid + V_hemisphere

V_total = 2856 + 718.76

V_total = 3574.76 cubic yards

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Answer:

this may help!

Step-by-step explanation:

next time you have trouble with a graphing problem, you can just use the desmos graphing calculatator!

Step-by-step explanation:

Plot these set of points:

For x=-2, y=-7. So, plot (-2, -7)

Next, take x=0, so y=-3. Plot (0,-3)

Now make a straight line connecting the points from x=-2 to x=2, and draw a dot on every increment of x by 1. So, the graph should look like so:

Answer:

10:42

Step-by-step explanation:

Answer:

The numbers are 30, 60, and 10

Step-by-step explanation:

Let's start by assigning variables to the three numbers.

We can call them x, y, and z.

From the problem, we know that:x + y + z = 100

We also know that the first number is a multiple of 15, so we can write:

x = 15a, where a is some integer.

Furthermore, we know that the second number (y) is ten times the third number (z), so we can write:

y = 10z

Now we can substitute equations (2) and (3) into equation (1) to get an equation in terms of z:

15a + 10z + z = 100

Simplifying, we get:

15a + 11z = 100

To find a possible solution for this equation, we can try different values of a and see if we get a whole number solution for z.

Let's start with a = 1. Substituting a = 1, we get:

15(1) + 11z = 100

z = (100 - 15)/11

z = 8.64

Since z is not a whole number, we need to try a different value of a.Let's try a = 2.

Substituting a = 2, we get:15(2) + 11z = 100

z = (100 - 30)/11

z = 6

Now we have a whole number solution for z. Substituting z = 6 into equations (2) and (3), we get:x = 15a = 15(2) = 30

y = 10z = 10(6) = 60So the three numbers are 30, 60, and 10.

The value of both missing angles are calculated as: ∠1 = 41° and ∠2 = 139°

We know that the sum of angles on a straight line sums up to 180 degrees.

Thus, from the given diagram, we can say that:

∠1 + ∠2 = 180

We are told that ∠2 is 16 more that 3 times ∠1.

Thus:

∠2 = 3(∠1) + 16

Thus:

3(∠1) + 16 + ∠1 = 180

4(∠1) = 180 - 16

∠1 = 164/4

∠1 = 41°

∠2 = 180 - 41

∠2 = 139°

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Answer: a

Step-by-step explanation:

7(x -5)

12 + x

Answer: [6, 25]

Explanation:

If Gerald takes a 700-mile round trip, then he is credited with 1400 miles flown (700 miles each way). To attain Gold status, Gerald needs to fly between 8400 and 35000 miles per year. Let's call the number of round trips Gerald needs to take "x". Then, we can set up an inequality to represent the number of miles he needs to fly:

8400 ≤ 1400x ≤ 35000

Dividing all three parts of the inequality by 1400, we get:

6 ≤ x ≤ 25

Therefore, Gerald needs to visit his parents at least 6 times a year, but no more than 25 times a year to attain Gold status. In interval notation, we can express this as:

[6, 25]

This cathedral's ceiling features a standard octagon with a 64-foot diameter and a 10.5-foot radius. The apothem is roughly 9.7 feet long, while the normal octagon is roughly 310.8 square feet in size.

The perimeter of the octagon is the sum of the lengths of its sides, so each side has a length of 64/8 = 8 feet.

Draw a line from the centre of the octagon to the midpoint of one of its sides. This line segment is the apothem, which is also the radius of a triangle formed by two consecutive vertices and the centre of the octagon. This triangle is an isosceles triangle, with a base length of 8 and apothem 10.5. We may get the triangle's height using the Pythagorean theorem:

[tex]height^2 = \frac{apothem^2 - base^2}{4}[/tex]

[tex]height^2 = \frac{10.5^2 - 8^2}{4}[/tex]

[tex]height^2[/tex] = [tex]\frac{110.25 - 64}{4}[/tex]

[tex]height^2[/tex] ≈ [tex]\frac{46.25}{4}[/tex]

[tex]height[/tex] ≈ 9.7

So the length of the apothem is approximately 9.7 feet.

The area of the octagon is given by the formula A = (1/2)ap, where a is the apothem and p is the perimeter. With our current values substituted, we obtain:

A =(1/2)×9.7×64

A ≈310.8

A ≈310.8 [tex]ft^2[/tex]

So the area of the regular octagon is approximately 310.8 square feet.

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If 4/10 of Lake Okeechobee is covered in a harmful algal bloom in the first month, then 6/10 of the lake is not covered in the bloom.

In the second month, if 90% of the lake is covered in the bloom, then 10% of the lake is not covered in the bloom.

Since the amount of the lake that is covered by the bloom increased from 4/10 to 9/10, this is an increase of:

(9/10) / (4/10) = (9/10) x (10/4) = 2.25 times

Therefore, the algal bloom increased by 2.25 times.

The distance between the base of the second ladder and the wall is 1.6 meters.

So we know that the two ladders are parallel, then the triangles that we are forming (between the ladder, the floor, and the wall) are two similar triangles.

We know that the length of the first ladder is 4.2m

The length of the second ladder is 5.6 m

Then the scale between these sides is:

4.2m*k = 5.6m

k = 5.6m/4.2m =  4/3

Then the distances of the bases are related by tha same scale, the distance between the base and the wall of the second base is:

(4/3)*1.2 m= 1.6m

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Answer:

Step-by-step explanation:

You want a graph and the x-intercept of the line through (-3, 4) with y-intercept 1.

The slope formula gives you the slope you can use with the slope-intercept equation.

  m = (y2 -y1)/(x2 -x1)

One point is given as (-3, 4). The y-intercept is (0, 1), so the slope is ...

  m = (1 -4)/(0 -(-3)) = -3/3 = -1

Then the equation for the line is ...

  y = mx +b

  y = -1x +1

  y = -x +1 . . . . simplify

The x-intercept is the point that has y-coordinate 0:

  0 = -x +1

  x = 1 . . . . . . add x

The line crosses the x-axis at x

Answer:

[tex]2x-5\leq 24[/tex]

Step-by-step explanation:

You figure this out you need to look for keywords. The difference means subtracting and less than or equal to creates [tex]\leq[/tex]. So twice a number, we will call x can be represented by [tex]2x[/tex]. The word difference can be represented by [tex]-[/tex] and less than or equal to 24 can be represented by [tex]\leq 24[/tex]. Combine all these hints into an equation and you get [tex]2x-5\leq 24[/tex]

Answer: The best measure of center for skewed data is the median, which is not affected by extreme values. From the given box plot, we can see that the line in the box is at 10, which is also the center of the box. Therefore, the median is the best measure of center, and its value is 10. So the correct answer is:

The median is the best measure of center and equals 10.

Step-by-step explanation:

Answer:

The answer is option D.

The median is the best measure of center and equals 10.

Step-by-step explanation:

Your welcome :) :)

Answer:

  3.00%

Step-by-step explanation:

You want the interest rate that will make an $8000 deposit achieve a value of $9571.31 in 6 years when interest is compounded quarterly.

The compound interest formula can be solved for the interest rate when other values are known:

  A = P(1 +r/n)^(nt) . . . . . . . interest at rate r compounded n times per year

  9571.31 = 8000(1 +r/4)^(4·6) . . . . fill in known values

  (9571.31/8000)^(1/24) = 1 +r/4

  1 +r/4 ≈ 1.0075000

  r ≈ 0.0075000 × 4 ≈ 3.00%

The interest rate is 3.00%.

__

Additional comment

A financial calculator, app, or spreadsheet can find this for you.

Answer:

(7,18)

Step-by-step explanation:

I think that you are asking for a solution to both equations

-2x + y = 4       → x -2  →   4x -2y = -8

-5x + 2y = 1            → (+)   -5x + 2y = 1  

                                          -x         = -7

x = 7

Substitute 7 for x in either of the two equations and solve for y.

-2(7) + y = 4

-14 + y = 4  Add 14 to both sides

y = 18

The solution is (7,18).

Check:

-2x + y = 4

-2(7) + 18 = 4

-14 + 18 = 4

4=4 Checks.

-5x + 2y = 1

-5(7) + 2(18) = 1

-35 + 36 = 1

1 = 1 checks

Helping in the name of Jesus.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount of money at the end of the investment period, P is the principal (initial investment), r is the interest rate (expressed as a decimal), n is the number of times the interest is compounded per year, and t is the number of years of the investment period.

For Brandon's account:

P = $9,200

r = 3.25% = 0.0325

n = 4 (compounded quarterly)

t = 19 years

A = 9200(1 + 0.0325/4)^(4*19) = $17,631.51

For Lamonte's account:

P = $9,200

r = 2.875% = 0.02875

n = 12 (compounded monthly)

t = 19 years

A = 9200(1 + 0.02875/12)^(12*19) = $16,031.63

The difference in the amount of money between Brandon's and Lamonte's accounts after 19 years is:

$17,631.51 - $16,031.63 = $1,599.88

Therefore, Brandon would have approximately $1,599 more in his account than Lamonte after 19 years, to the nearest dollar.

Answer:1141

Step-by-step explanation:

Answer:

I assume you mean pi (π) squared, which is π^2. Calculating with π^2 is similar to calculating with any other number, except that you use π^2 instead of a regular number. Here are a few examples:

Example 1: Find the circumference of a circle with radius 5π.

The formula for the circumference of a circle is C = 2πr, where r is the radius. Substituting 5π for r, we get:

C = 2π(5π) = 10π^2

Therefore, the circumference of the circle is 10π^2.

Example 2: Find the area of a circle with diameter 3π.

The formula for the area of a circle is A = πr^2, where r is the radius. Since the diameter is 3 times the radius, we have:

r = (1/2)(3π) = (3/2)π

Substituting this into the formula, we get:

A = π((3/2)π)^2 = (9/4)π^3

Therefore, the area of the circle is (9/4)π^3.

In general, whenever you see π^2 in a formula, you can just substitute it for the regular number. Keep in mind that π is an irrational number (it goes on forever without repeating), so you may need to use an approximation like 3.14 or 22/7 depending on the level of accuracy required in your calculations.

Step-by-step explanation:

explanation included above with examples.

Consequently, 1.11 milliliters of Kefzol solution must be administered in order to provide 250 milligrams of the medication.

A solution in mathematics is the response to a question or equation. For instance, the answer to the equation x + 2 = 5 would be 3, as it is the value of x that the equation requires. Similar to the last example, the answer to the question, "What is the area of a square with side length 4?" is 16, as the square's area is 16. Depending on the issue or equation, a solution can be represented in a variety of ways.

given

To address this issue, we must figure out how much Kefzol solution must be used to deliver 250 milligrams of the medication.

We can start by converting the dose from milligrams to milliliters using the provided data. We can establish a ratio because we know that the Kefzol solution has a concentration of 225 milligrams per milliliter:

250 mg/x ml equals 225 mg/1 ml.

If we cross-multiply, we obtain:

225 milligrams per 1 milliliter divided by 250

If we simplify, we get:

x = 225 mg/ml and 250 mg

x = 1.11 ml

Consequently, 1.11 milliliters of Kefzol solution must be administered in order to provide 250 milligrams of the medication.

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Answer: Dallas

Step-by-step explanation:

To get the amount after taxes, you have to multiply your earnings by the tax rate and subtract that amount.

Boston:

70,000 * 0.28 = 19,600

70,000 - 19,600 = $50,400

Dallas:

63,000 * 0.19 = 11,970

63,000 - 11,970 = $51,030

Since Dallas gives you more money, it would be the correct option.

Using similar triangles, we can set up the following proportion:

(tree height + Donna's height) / (distance from Donna to mirror) = Donna's height / (distance from mirror to top of tree)

Let h be the height of the tree.

Then we have:

(h + 6) / 6.6 = 6 / (37 + h)

Multiplying both sides by (37 + h) and simplifying, we get:

h + 6 = 222 / 6.6 - h / 6.6

Multiplying both sides by 6.6 and simplifying, we get:

6.6h + 39.6 = 222 - h

Solving for h, we get:

7.6h = 182.4

h = 24

Therefore, the height of the tree is approximately 24 feet.