HERE IS A HARD QUESTION , COULD U PLEASE ANSWER B PLEASE? I DID A ! 1ST ANSWER WOULD BE MARKED BRAINLIEST AND GET 5/5 WITH A THANKS! ILL ALSO COMMENT ON YOUR ANSWER ! BUT IF IT ISNT CORRECT , I WONT MARK BRAINLIEST! Thank you for your answers!!!!
Answers
Step-by-step explanation:
The coordinates of point B: (0,6)
Coordinates of point C: (3,8)
A kite has 4 sides, of which we have 2 equal pairs, thus the coordinates of point D must be (6,6)
Answer:
(6,6)
Step-by-step explanation:
The question is asking us to complete the half figure, and make it a kite. We can see that the 2 lines AB and BC are half of the shape. In the attachment, I drew a line of symmetry down the middle of the shape.
I also created a point, Y, down the red line, AC, to represent the perpendicular bisector of the 2 diagonals. We can see that line segment BY is the radius of the entire line BD.
This radius is 3 units, so we now know that the diameter horizontally is 6 units. We can draw this on the other side to create point D.
This means that point D is at (6,6).
See attachment for more information, hope this helps!
Related Questions
An isosceles triangle has legs measuring 9 feet and a base of 12 feet. Find the measure of the base angle, x, to the nearest degree
Answers
The measure of the base angle x is approximately 81.54 degrees.
To get the measure of the base angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since this is an isosceles triangle, we know that the two base angles are congruent (they have the same measure).
Let's call the measure of each base angle y. Then we can set up an equation:
y + y + x = 180
Simplifying, we get:
2y + x = 180
Now we can use the fact that the legs of the triangle are congruent to find the measure of y. Since this is an isosceles triangle, we know that the two legs are congruent. This means we can use the Pythagorean theorem to find the length of the height, h, of the triangle: h^2 = 9^2 - (12/2)^2
h^2 = 81 - 36
h^2 = 45
h = sqrt(45)
h = 6.71 (rounded to two decimal places)
Now we can use the definition of the tangent function to find y:
tan(y) = h / (12/2)
tan(y) = 6.71 / 6
tan(y) = 1.1183 y = tan^-1(1.1183)
y = 49.23 degrees (rounded to two decimal places)
Finally, we can substitute this value of y into our equation to find x:
2y + x = 180
2(49.23) + x = 180
98.46 + x = 180
x = 81.54 degrees (rounded to two decimal places)
Therefore, the measure of the base angle x is approximately 81.54 degrees.
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Select the proper inverse operation to check the answer to 25
-13=12
Answers
12+13 = 25, therefor the answer is correct
During a senate campaign, a volunteer passed out a "vote for roth" button. according to the catalog from which the button was ordered, it has a circumference of 25.12 centimeters. what is the button's area?
Answers
The button's area is approximately 50.27 square centimeters.
How to find the Area?To find the area of the button, we need to know the diameter of the button. We can find this by using the formula for circumference of a circle:
C = πd
where C is the circumference and d is the diameter.
Substituting the given value for C:
25.12 cm = πd
Solving for d:
d = 25.12 cm / π
d ≈ 8 cm
Now that we know the diameter, we can use the formula for area of a circle:
A = πr^2
where r is the radius (half the diameter).
Substituting the value for d:
r = d/2 = 4 cm
Substituting this value into the formula:
A = π(4 cm)^2
A ≈ 50.27 cm^2
Therefore, the button's area is approximately 50.27 square centimeters.
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A researcher would like to examine how the chemical tryptophan, contained in foods such as turkey, can reduce mental alertness. a sample of n = 9 college students is obtained, and each student’s performance on a familiar video game is measured before and after eating a traditional thanksgiving dinner including roasted turkey. the average mental alertness score dropped by md= 14 points after the meal with ss= 1152 for the difference scores.
a. is there is significant reduction in mental alertness after consuming tryptophan versus before? use a one-tailed test with α = .05.
b. compute r2 to measure the size of the effect.
Answers
r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.
a. To test whether there is a significant reduction in mental alertness after consuming tryptophan versus before, we can use a paired samples t-test. The null hypothesis is that there is no difference in mental alertness scores before and after the meal, and the alternative hypothesis is that the scores are lower after the meal:
H0: μd = 0 (no difference)
Ha: μd < 0 (lower scores after the meal)
Here, μd is the mean difference score in mental alertness before and after the meal. We will use a one-tailed test with α = .05, since we are only interested in the possibility of lower scores after the meal.
The t-statistic for a paired samples t-test is calculated as:
t = (Md - μd) / (sd / sqrt(n))
Where Md is the mean difference score, μd is the hypothesized mean difference (in this case, 0), sd is the standard deviation of the difference scores, and n is the sample size.
We are given that Md = 14, and the standard deviation of the difference scores (sd) is:
sd = sqrt(SSd / (n - 1)) = sqrt(1152 / 8) = 12
Substituting these values, we get:
t = (14 - 0) / (12 / sqrt(9)) = 3.5
Using a one-tailed t-distribution table with 8 degrees of freedom and α = .05, the critical value is -1.86. Since our calculated t-value (3.5) is greater than the critical value, we reject the null hypothesis and conclude that there is a significant reduction in mental alertness after consuming tryptophan versus before.
b. To compute r2 to measure the size of the effect, we can use the formula:
r2 = t2 / (t2 + df)
Where t is the calculated t-value for the test, and df is the degrees of freedom, which is n-1 in this case.
Substituting the values , we get:
r2 = (3.5)2 / ((3.5)2 + 8) = 0.523
Therefore, r2 = 0.523, which means that approximately 52.3% of the variance in the difference scores can be accounted for by the reduction in mental alertness after consuming tryptophan.
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The sum of the numerator and denominator of the fraction is 12. If the denominator is increased by 3, the fraction becomes 12. Find the fraction.
Answers
Let the fraction be x/y.
We know that x + y = 12, and that (x) / (y + 3) = 12.
Multiplying both sides of the second equation by (y + 3), we get:
x = 12(y + 3)
Substituting this into the first equation, we get:
12(y + 3) + y = 12
Expanding and simplifying, we get:
13y + 36 = 12
Subtracting 36 from both sides, we get:
13y = -24
Dividing both sides by 13, we get:
y = -24/13
Substituting this value of y into the equation x + y = 12, we get:
x - 24/13 = 12
Multiplying both sides by 13, we get:
13x - 24 = 156
Adding 24 to both sides, we get:
13x = 180
Dividing both sides by 13, we get:
x = 180/13
Therefore, the fraction is 180/13 divided by -24/13, which simplifies to -15/2.
Are the events "having a dog" and "having a cat" independent from each other?
a) Cannot tell with the given information
b) Yes, because P(cat) = P(cat | dog) and P(dog) = P(dog | cat)
c) The events are disjoint
d) No, because P(cat) is not equal to P(cat | dog) and P(dog) is not equal to P(dog | cat)
Answers
Option A) Cannot tell with the given information as the question doesn't provide any information about the relationship between having a dog and having a cat.
Without additional information, we cannot determine if these events are independent, dependent, disjoint, or have any other relationship. Independent events are events in which the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other event.
In other words, the probability of one event happening does not depend on whether or not the other event happens.
Formally, events A and B are independent if and only if:
P(A ∩ B) = P(A) * P(B)
Where P(A) is the probability of event A occurring, P(B) is the probability of event B occurring, and P(A ∩ B) is the probability of both events A and B occurring simultaneously.
If the above equation holds true, then we can say that events A and B are independent. If not, then events A and B are dependent.
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After some not so high practice dives by the circus owner, the circus performers decide to do a practice run of the show with the diver himself. but they decide to set it up so they will not have to worry about a moving cart. instead, the cart containing the tub of water is placed directly under the ferris wheel’s 11o’clock position. as usual, the platform passes the 3o’clock position at t=0
how many seconds will it take for the platform to reach the 11 o’clock position?
what is the diver’s height off the ground when he is at the 11 o’clock position?
radius = 50 ft
center of wheel is 65 feet off ground
turns counterclockwise at a constant speed, with a period of 40 seconds.
platform is at 3 o’clock position when it starts moving
Answers
The ferris wheel will take a total time of 10 seconds for the platform to reach the 11 o'clock position and the diver's height off the ground when he is at the 11 o'clock position is 50 feet.
To determine the time it takes for the platform to reach the 11 o'clock position and the diver's height off the ground, we will use the given information about the ferris wheel.
1. The ferris wheel has a radius of 50 ft and turns counterclockwise at a constant speed with a period of 40 seconds.
2. The center of the wheel is 65 ft off the ground.
3. The platform is at the 3 o'clock position when it starts moving (t=0).
The ferris wheel has a period of 40 seconds, which means it takes 40 seconds for it to make a full rotation. The distance between the 3 o'clock position and the 11 o'clock position is 90 degrees out of 360, which is one-fourth of the total distance around the circle.
Therefore, it will take 1/4 of the total time for the platform to reach the 11 o'clock position, which is 40/4 = 10 seconds.
To find the diver's height off the ground at the 11 o'clock position, we can use the sine function. Let's call the angle formed by the radius from the center of the ferris wheel to the diver and the radius from the center of the ferris wheel to the 3 o'clock position θ.
Since the platform starts at the 3 o'clock position and rotates counterclockwise, θ will increase as time passes. At the 11 o'clock position, θ will be 90 degrees.
We know that the radius of the ferris wheel is 50 feet and the center of the ferris wheel is 65 feet off the ground. Let's call the height of the diver off the ground h. Then we have:
sin θ = h / (50 ft)
h = (50 ft) * sin θ
At the 11 o'clock position, θ = 90 degrees, so we have:
h = (50 ft) * sin 90°
h = 50 ft
Therefore, the diver's height off the ground when he is at the 11 o'clock position is 50 feet.
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The city is 30 miles long and two-thirds as wide, and 555,000 citizens currently live there. The mayor calculates that the minimum number of people who would have to move outside the city for adequate services to be maintained is 75,000. Enter the maximum population density , in citizens per square mile , that is assumed in the mayor's calculation
Answers
The maximum population density evaluated is 1200 citizens per square mile, under the condition that the city is 30 miles long and two-thirds as wide, and 555,000 citizens currently live there.
Now to evaluate the maximum population density that is considered in the mayor's calculation is
Let us first calculate the area of the city which is (2/3) × (30 miles)
= 20 miles.
So, now we can calculate the current population density which is
555,000 / (20 × 20)
= 1387.5 citizens per square mile.
Hence the mayor evaluates that at least 75,000 people must transfer out of the city for adequate services to be exercised, we can find the new population as
555,000 - 75,000
= 480,000 citizens.
Therefore, the new population density would be 480,000 / (20 × 20)
= 1200 citizens per square mile
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i need help fast!!!!
Answers
Answer:
1st choice: 1/4(y - 10) = 2/3
Step-by-step explanation:
the "variable" is y
"is" means "=" (equals sign)
one fourth = 1/4
"difference of" means subtract
Answer: 1/4(y - 10) = 2/3
Solve the inequalities 1/3(2x-1)≤1-2/5(2-3x)
Answers
The solution to the inequality is x ≥ -1.
We solve the inequality 1/3(2x-1)≤1-2/5(2-3x).
Let's go step by step:
Begin by distributing the fractions to the terms inside the parentheses:
(1/3 * 2x) - (1/3 * 1) ≤ 1 - (2/5 * 2) + (2/5 * 3x)
(2x/3) - (1/3) ≤ 1 - (4/5) + (6x/5)
Combine like terms on each side of the inequality:
(2x - 1)/3 ≤ (1 - 4/5) + 6x/5
(2x - 1)/3 ≤ (1/5) + 6x/5.
To eliminate the fractions, find a common denominator, which in this case is 15.
Multiply each term by 15:
15 * (2x - 1)/3 ≤ 15 * (1/5) + 15 * 6x/5
5(2x - 1) ≤ 3 + 18x
Distribute and simplify:
10x - 5 ≤ 3 + 18x
Move the variables to one side and constants to the other side:
10x - 18x ≤ 3 + 5
-8x ≤ 8
Divide both sides by -8 (remember to flip the inequality sign since we are dividing by a negative number):
x ≥ -1.
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Help with geometry on equations of circles. Point C is a point of tangency. How would I solve this to get DA and DE?
Answers
Answer:
DA = 17DE = 9Step-by-step explanation:
You want the segment lengths DA and DE of the hypotenuse in the triangle shown in the figure.
Right triangleThe radius to a point of tangency always makes a right angle with the tangent. This is a right triangle with legs 8 and 15, so you know from your knowledge of Pythagorean triples that the hypotenuse is 17.
DA = 17
DE = 17 -8 = 9
__
Additional comment
In case you haven't memorized a few of the useful Pythagorean triples, {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, you can always figure the missing side length of a right triangle using the Pythagorean theorem.
It tells you the sum of the squares of the legs is the square of the hypotenuse:
AC² +CD² = DA²
8² +15² = DA²
64 +225 = 289 = DA²
DA = √289 = 17
Of course, AE is the radius of the circe, 8, so ...
AE + DE = DA
8 +DE = 17
DE = 17 -8 = 9
Alternatively, you can solve this using the relation between tangents and secants. If the line DA is extended across the circle to intersect it again at X, then ...
DC² = DE·DX
15² = DE·DX = DE(DE +16) . . . . . . . EX is the diameter, twice the radius of 8
DE² +16DE -225 = 0
(DE +25)(DE -9) = 0 . . . . factor
DE = 9 . . . . the positive solution
DA = 9 +8 = 17
We like the Pythagorean theorem solution better, as the factors of the quadratic may not be obvious.
Let functions f and g be defined over the real numbers as f(x)=x+3 and g(x) = 4x. It follows that f(g(x)) = ?
F. 12x
G. 4x+3
H. 5x+3
J. 4x² +3
K. 4x² + 12x
Answers
Answer:
I think it is k
Step-by-step explanation:
x+3(4x)
4x^2 + 12x
I am sorry if this is wrong
A lean-to is a shelter where the roof slants down to the ground. The length of the roof of one lean-to is 17 feet. The width of the lean-to is 15 feet. How high is the lean-to on its vertical side?
Answers
The height of the lean-to on its vertical side is 8 feet.
What is the height of a lean-to on its vertical side?
To find the height of the lean-to on its vertical side, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the vertical side is the hypotenuse, and the length and width are the other two sides.
So, we have:
[tex]height^2 = hypotenuse^2 - width^2[/tex]
We know the length of the roof (the hypotenuse) is 17 feet, and the width is 15 feet. So we can plug these values into the equation and solve for the height:
[tex]height^2 = 17^2 - 15^2\\height^2 = 289 - 225\\height^2 = 64\\height = 8[/tex]
Therefore, the height of the lean-to on its vertical side is 8 feet.
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In which type of statistical study is the population influenced by researchers?
Answers
The type of statistical study in which the population is influenced by researchers is known as an experimental study.
In an experimental study, researchers manipulate one or more variables to observe the effect on another variable. The population in an experimental study is usually a sample that is randomly selected to represent the larger population.
The researchers intentionally intervene in the study, which can impact the behavior or responses of the participants. This can be seen as a form of bias since the researchers are influencing the population. However, in some cases, this is necessary to determine causality or to test a hypothesis.
To minimize bias, experimental studies often use control groups. The control group is used to provide a baseline for comparison with the group that is exposed to the manipulated variable. This helps to determine if any observed effects are due to the intervention or if they are due to other factors.
In summary, an experimental study is the type of statistical study in which the population is influenced by researchers. While this can introduce bias, the use of control groups and other measures can help to minimize the impact of this bias on the results.
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without using a protractor, you can determine whether the angles are right angles by measuring the length of the diagonal and applying the converse of the pythagorean theorem. 12 cm 13 cm 5 cm 5 cm 12 cm the length of both diagonals for each lateral side is 13 centimeters. from this, can you prove that the lateral sides are rectangles? why or why not?
Answers
Since we have shown that all four angles formed by the lateral sides are right angles, and the opposite sides are parallel and congruent, we can conclude that the lateral sides are rectangles.
How to prove that angles between the 5 cm and 12 cm sides are right angles?Yes, we can prove that the lateral sides are rectangles based on the given information.
Firstly, we can see that the two diagonals of the lateral sides are congruent (both measure 13 cm), which means that the opposite sides of the figure are parallel. This is because, in a rectangle, opposite sides are parallel and congruent.
Next, we can use the converse of the Pythagorean theorem to determine if the angles are right angles. The converse of the Pythagorean theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
For each of the lateral sides of the figure, we can consider the two triangles formed by one of the diagonals and the adjacent sides. Applying the Pythagorean theorem, we can see that:
For the first lateral side, we have:
(5 cm)^2 + (12 cm)^2 = (13 cm)^2
Therefore, the angles between the 5 cm and 12 cm sides are right angles.
For the second lateral side, we have:
(5 cm)^2 + (12 cm)^2 = (13 cm)^2
Therefore, the angles between the 5 cm and 12 cm sides are also right angles.
Since we have shown that all four angles formed by the lateral sides are right angles, and the opposite sides are parallel and congruent, we can conclude that the lateral sides are rectangles.
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Evaluate the integral dy (tan-'[y/8)) (64+y?) ( 1 + dy (tan-'(4/8)) (64+y?) =
Answers
Answer: ln|y/8| + C
Explanation:
First, we need to recognize that the derivative of arctan(x) is 1/(1+x^2). Therefore, the derivative of arctan(y/8) is 8/(64+y^2).
Now, using the substitution u = y/8, we can rewrite the integral as:
∫(1/u)(64+64u^2)(8/(64+64u^2))du
Simplifying, we get:
∫(1/u)du = ln|u| = ln|y/8|
Therefore, the final answer is:
ln|y/8| + C
where C is the constant of integration.
Kimberly rolls two six-sided number cubes numbered 1 through 6 and adds up the two numbers construct a tree diagram to determine all the possible outcomes list the sum at the end of each branch of the tree
Answers
When Kimberly rolls two six-sided number cubes numbered 1 through 6, it creates 36 possible outcomes which is represent in the tree diagram below
What is a tree diagram?A tree diagram is a visual representation of outcomes. It consists of branches that represent the possible outcomes of each step.
When it comes to Kimberly rolling two six-sided number cubes, we can start by rolling the first cube, and then rolling the second cube.
For each roll of the first cube, there are six possible outcomes (1 to 6). For each outcome of the first cube, there are six possible outcomes for the second cube.
This results in a total of 6 x 6 = 36 possible outcomes.
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High school competency test a mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. the top 3% of students receive $500. what is the minimum score you would need to receive this award? the bottom 1.5% of students must go to summer school. what is the minimum score you would need to stay out of this group?
Answers
A score of at least 183 is required to stay out of the bottom 1.5%. To find the minimum score required to receive the award, we need to determine the z-score corresponding to the top 3% of students.
Since the distribution is normal, we can use the standard normal distribution table to find the z-score. From the table, we find that the z-score corresponding to the top 3% is approximately 1.88.
Therefore, we can use the formula z = (x - μ) / σ, where μ = 400 and σ = 100, to find the minimum score required: 1.88 = (x - 400) / 100
Solving for x, we get: x = 1.88(100) + 400 = 488. Therefore, a score of at least 488 is required to receive the award.
To find the minimum score required to stay out of the bottom 1.5%, we need to determine the z-score corresponding to the bottom 1.5%.
From the standard normal distribution table, we find that the z-score corresponding to the bottom 1.5% is approximately -2.17. Therefore, we can use the same formula as before to find the minimum score required: -2.17 = (x - 400) / 100.
Solving for x, we get: x = -2.17(100) + 400 = 183. Therefore, a score of at least 183 is required to stay out of the bottom 1.5%.
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CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
Answers
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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What is the average rate of change for the number of shares from 2 minutes to 4 minutes?
Answers
The average rate of change for the number of shares from 2 minutes to 4 minutes is 25 shares per minute.
To find the average rate of change for the number of shares from 2 minutes to 4 minutes, we need to know the initial number of shares at 2 minutes and the final number of shares at 4 minutes. Once we have those values, we can use the formula:
average rate of change = (final value - initial value) / (time elapsed)
Let's say the initial number of shares at 2 minutes was 100 and the final number of shares at 4 minutes was 150. The time elapsed between 2 minutes and 4 minutes is 2 minutes. Plugging these values into the formula, we get:
average rate of change = (150 - 100) / 2
average rate of change = 50 / 2
average rate of change = 25
Therefore, the average rate of change is 25 shares per minute.
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i need this answer in by 6:00.. i have tutoring at that time
Answers
Answer:
80
Step-by-step explanation:
v=bxh
v=10x8
v=80
Jocelyn's car tires are spinning at a rate of 120 revolutions per
minute. If her car's tires are 28 inches in diameter, how many
miles does she travel in 5 minutes? Round to the nearest
hundredth. 63360 inches = 1 mile.
Answers
The required answer is Jocelyn travels approximately 0.83 miles in 5 minutes.
Jocelyn's car tires are spinning at a rate of 120 revolutions per minute. If her car's tires are 28 inches in diameter, we can calculate the distance traveled in one revolution by finding the circumference of the tire:
Circumference = π x diameter
Circumference = 3.14 x 28 inches
Circumference ≈ 87.92 inches
So in one revolution, the car travels approximately 87.92 inches. To find out how many miles Jocelyn travels in 5 minutes, we need to multiply the number of revolutions in 5 minutes (which is 120 revolutions per minute x 5 minutes = 600 revolutions) by the distance traveled in one revolution (87.92 inches).
Distance traveled in 5 minutes = 600 revolutions x 87.92 inches/revolution
Distance traveled in 5 minutes = 52,752 inches
To convert inches to miles, we can use the conversion factor given: 1 mile = 63,360 inches.
Distance traveled in 5 minutes = 52,752 inches ÷ 63,360 inches/mile
Distance traveled in 5 minutes ≈ 0.83 miles
Therefore, Jocelyn travels approximately 0.83 miles in 5 minutes with her car tires spinning at a rate of 120 revolutions per minute. Rounded to the nearest hundredth, the answer is 0.83 miles.
To find out how many miles Jocelyn travels in 5 minutes, follow these steps:
1. Calculate the circumference of one tire: Circumference = Diameter × π.
Circumference = 28 inches × π ≈ 87.96 inches.
2. Determine the distance traveled in one revolution: One revolution covers the circumference of the tire, which is 87.96 inches.
3. Calculate the distance traveled in one minute: 120 revolutions per minute × 87.96 inches per revolution ≈ 10,555.2 inches per minute.
4. Determine the distance traveled in 5 minutes: 10,555.2 inches per minute × 5 minutes = 52,776 inches.
5. Convert the distance from inches to miles: 52,776 inches ÷ 63,360 inches per mile ≈ 0.83 miles.
So, Jocelyn travels approximately 0.83 miles in 5 minutes.
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Question 13
"s
the measure of one of the small angles of a right triangle is 30 less than 7 times
small angle. find the measure of both angles.
smallest angle:
other non-right angle:
add work
> next question
Answers
The smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.
To find the measure of both angles in a right triangle with the given conditions, we will use the information provided:
Let x be the measure of the smallest angle. The problem states that the measure of one of the small angles is 30 less than 7 times the smallest angle, which can be written as:
Other non-right angle = 7x - 30
Since this is a right triangle, the sum of the two small angles must be 90 degrees (because the other angle is 90 degrees, and the sum of angles in a triangle is 180 degrees). So, we can set up the following equation:
x + (7x - 30) = 90
Now, solve for x:
8x - 30 = 90
8x = 120
x = 15
So, the smallest angle is 15 degrees. Now, we can find the measure of the other non-right angle:
Other non-right angle = 7x - 30 = 7(15) - 30 = 105 - 30 = 75 degrees
In summary, the smallest angle measures 15 degrees and the other non-right angle measures 75 degrees.
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How is the quotient 7^18/7^-9 expressed as a power of 7
Answers
The quotient of the expression (7¹⁸/7⁻⁹) expressed as a power of 7 is 7 ²⁷.
What is the quotient of the expression?The quotient of the expression is calculated as follows;
When you divide two numbers with the same base, you subtract the exponents of the base. Using this rule, we can simplify the expression as follows;
7¹⁸ / 7⁻⁹
= 7 ⁽¹⁸ ⁻ ⁻⁹⁾
= 7 ⁽¹⁸ ⁺ ⁹⁾
= 7 ²⁷
Therefore, the quotient of the expression (7¹⁸/7⁻⁹) is 7 ²⁷.
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The graph represents the distance the Pennsylvania Train traveled over 8 hours.
The Baltimore Train traveled 1,020 miles in 12 hours. Both trains traveled at a constant rate. Which sentence is true?
A. The Baltimore Train was faster by 10 miles per hour.
B. The Baltimore Train was faster by 15 miles per hour.
C. The Pennsylvania Train was faster by 10 miles per hour.
D. The Pennsylvania Train was faster by 15 miles per hour.
Answers
Answer:
Baltimore Train: 1,020 mi/12 hr = 85 mph
Pennsylvania Train: 75 mph
So the correct answer is A.
Use the rules to find derivatives of the following functions at the specified values
h(x) = 8x at x = 4
h'(4) = _____
Answers
To find the derivative of h(x) = 8x, we use the power rule, which states that the derivative of x^n is nx^(n-1). Applying this rule to h(x), we get h'(x) = 8.
To find the value of h'(4), we simply plug in x = 4 into our derivative expression: h'(4) = 8.
Therefore, the derivative of h(x) = 8x at x = 4 is h'(4) = 8.
To find the derivative of the function h(x) = 8x at x = 4, you can use the power rule for differentiation. The power rule states that if h(x) = x^n, then h'(x) = n * x^(n-1).
For h(x) = 8x, n = 1, so:
h'(x) = 1 * 8x^(1-1) = 8
Now, to find h'(4), just plug in x = 4:
h'(4) = 8
So, h'(4) = 8.
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A prism 5 feet tall whose base is a right triangle with leg lengths 6 feet and 7 feet
what is the volume in cubic feet?
Answers
The volume of the prism is 21 * 5 = 105 cubic feet.
To find the volume of a prism with a triangular base, you need to follow these steps:
1. Determine the area of the triangular base: Since the base is a right triangle with leg lengths of 6 feet and 7 feet, you can use the formula for the area of a right triangle: (1/2) * base * height. In this case, the area would be (1/2) * 6 * 7 = 21 square feet.
2. Multiply the area of the triangular base by the height of the prism: The prism is 5 feet tall, so the volume can be calculated by multiplying the area of the base (21 square feet) by the height (5 feet).
Thus, the volume of the prism is 21 * 5 = 105 cubic feet.
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Define a useful quantity for our expectation about the amount of a time an
in-control process will remain ostensibly in-control, the average run length (ARL), to be the number of samples that will be observed, on average, before a point falls outside control limits. If p is the probability that any given point falls outside the control limits, then:
ARL = 1/p
(Estimating the true ARL may be useful for detecting an out-of-control process, but not
necessarily doing so quickly.) A process is Gaussian with mean 8 and standard deviation 2. The process is monitored by taking samples of size 4 at regular intervals. The process is declared to be out of control if a point plots outside the 3σ control limits on an X-chart. If the process mean shifts to 9, what is the average number of samples that will be drawn before the shift is detected on an X-chart?
Answers
Answer:
First, we need to calculate the control limits for the X-chart. Since the sample size is 4, the standard deviation of the sample mean is:
σ/√n = 2/√4 = 1
The 3σ control limits for the X-chart are:
Upper Control Limit (UCL) = 8 + 3(1) = 11
Lower Control Limit (LCL) = 8 - 3(1) = 5
Next, we need to find the probability that a point falls outside the control limits when the process mean shifts to 9. This can be calculated using the Gaussian distribution:
P(X < 5 or X > 11) = P(Z < (5-9)/2) + P(Z > (11-9)/2) = 0.00135 + 0.00135 = 0.0027
where Z is the standard normal distribution.
Therefore, the average run length (ARL) is:
ARL = 1/p = 1/0.0027 = 370.37
So on average, it will take 370.37 samples before the process mean shift is detected on an X-chart.
2. A social media company claims that over 1 million people log onto their app daily. To test this claim, you record the number of people who log onto the app for 65 days. The mean number of people to log in and use the social media app was discovered to be 998,946 users a day, with a standard deviation of 23,876. 23. Test the hypothesis using a 1% level of significance.
Answers
The hypothesis test suggests that there is not enough evidence to reject the claim made by the social media company that over 1 million people log onto their app daily, as the t-value (-1.732) is less than the critical value (-2.429).
Null hypothesis, The true mean number of people who log onto the app daily is equal to or less than 1 million.
Alternative hypothesis, The true mean number of people who log onto the app daily is greater than 1 million.
Level of significance = 1%
We can use a one-sample t-test to test the hypothesis.
t = (X - μ) / (s / √n)
where X is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values, we get
t = (998,946 - 1,000,000) / (23,876 / √65)
t = -1.732
Using a t-distribution table with 64 degrees of freedom and a one-tailed test at a 1% level of significance, the critical value is 2.429.
Since the calculated t-value (-1.732) is less than the critical value (-2.429), we fail to reject the null hypothesis. There is not enough evidence to support the claim that more than 1 million people log onto the app daily.
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The solution of a quadratic equation are x=-7 and 5. Which could represent the quadratic equation, and why?
Answers
An answer option that could represent the quadratic equation, and why is: B. x² + 2x - 35 = 0, the factors are (x + 7) and (x - 5) and (x + 7)(x - 5) = x² + 2x - 35.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factors (zeros or roots) provided as follows;
y = (x + 7)(x - 5)
y = x² + 2x - 35
x² + 2x - 35 = 0
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.