Because the horizontal lines are parallel, we conclude that:
x = 105°.
How to find the value of x?
If you look at the image, you can see that the two horizontal lines are parallel.
From that, we can conclude that x and the top left angle (the one that measures 75°) are supplementary angles.
Where two supplementary angles are these that add up to 180°, then we have:
x + 75° = 180°
Now we can solve that for x:
x = 180° - 75° = 105°.
So we conclude that x measures 105°.
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Both numbers have three significant figures. How many significant figures should be recorded for the answer to the division problem below?
\(43.6 \div 21.2\)
= [?] significant figures
Answer:
8 significant figures should be provided.
Step-by-step explanation:
I believe I am correct, but check your answer anyways.
anyone that can explain this question to me and answer?
Answer:Compose a paragraph that identifies and describes each of the three Siberian regions.
Step-by-step explanation:
Explaining the Concept:
To get the perimeter of this square, we will first get the value of one side
Since all the sides of a square are equal, we will find the length of one of the side from the triangle EOF
Finding the length of one side of the triangle:
In triangle EOF:
Using the pythagoras's theorem
EO²+OF² = EF²
(5)² + (5)²= side² [since EF is a side of the square]
side²= 50
side = √50
side = 5√2 units
Perimeter of the Square:
We know that the perimeter of a square is 4 times its side
Perimeter = 4 * side
Perimeter = 4 * 5√2
Perimeter = 20√2 units
true or false a triangle with sides measure 35, 24 m, 16 m is a right triangle
If the triangle is right angled then the sides should form a Pythagorean triple.
That is the square of the biggest should be equal to the sum of the squares of the other two.
Otherwise it is not a right angled triangle.
So we test
\(35^2=1225\ne832=24^2+16^2\)Hence the answer is false
PLEASE I NEED THIS REALLY REALLY BAD
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
what is a quadratic function?When a polynomial function has one or more variables and the highest exponent of any one of the variables is two, the function is said to be quadratic. A "polynomial function of degree 2," then, is a quadratic function.
The definition of a quadratic function:A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. A parabola is the shape that makes up the graph of a quadratic function. The basic "U" shape of a parabola is the same whether it opens upward or downward, or with a different "width" or "steepness."
According to the given data:If we put the values of points in the above equation, then we get.
Putting point (0,6) we get
6 = 0 + 0 + c
=> c = 6
Putting point (2,8) we get
8 = 4a + 2b + 6
=> 2 = 4a + 2b
=> = 2a + b ......(1)
Putting point (3,-3) we get
-3 = 9a + 3b + 6
=> -9 = 9a + 3b
=> -3 = 3a + b ......(2)
From equation (1) b = 2a. Substitute the value of b in equation (2) we get
3 = 3a + 2a
=> a = 3/5
Now, b = 6/5
The quadratic function that includes the given points is given by y = 3/5x² + 6/5x + 6.
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with grams of a radioactive isotope, how much will be left after 4 half-lives?
After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:
Amount remaining = Initial amount × (1/2)^(number of half-lives)
In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.
So, the equation becomes:
Amount remaining = Initial amount × (1/2)^4
Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.
Simplifying the equation:
Amount remaining = Initial amount × (1/16)
Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.
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The state highway department is studying traffic patterns on one of the busiest highways in the state. As part of the study, the department needs to estimate the average number of vehicles that pass an intersection each day. A random sample of 64 days gives us a sample mean of 14,205 cars and a sample standard deviation of 1,010 cars. After calculating the confidence interval, the highway department officials decide that the precision is too low for their needs. They feel the precision should be 300 cars. Given this precision, and needing to be 99 percent confident, how many days do they need to sample
The required highway department needs to sample at least 77 days to achieve a precision of 300 cars with 99 percent confidence.
To calculate the required sample size given the desired precision and confidence level, we can use the formula for the confidence interval of a population mean:
CI = x ± Z * (σ/√n)
Where:
CI = Confidence interval width (desired precision)
x = Sample mean
Z = Z-score corresponding to the desired confidence level
σ = Population standard deviation (unknown, so we use the sample standard deviation as an estimate)
n = Sample size (unknown, what we want to find)
Since the desired confidence level is 99 percent, the Z-score corresponding to a 99 percent confidence level is approximately 2.576 (from the standard normal distribution table).
Given that the sample mean is 14,205 cars and the sample standard deviation is 1,010 cars, and the desired precision is 300 cars, we can plug in these values and solve for the required sample size (n):
300 = 2.576 * (1010/√n)
Now, solve for n:
√n = 2.576 * 1010 / 300
√n ≈ 8.732
n ≈ (8.732)^2 ≈ 76.27
Since the sample size must be a whole number (you can't have a fraction of a day), we round up to the nearest whole number. Therefore, the highway department needs to sample at least 77 days to achieve a precision of 300 cars with 99 percent confidence.
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AB+C=85
A+BC=86
What’s the break down tonthis
Answer:
A = 28
B = 2
C = 29
Step-by-step explanation:
28×2+29 = 85
28+2×29 = 86
Needa line segment has endpoints P(-8,7) and Q(6,-3). What is the midpoint of the segment?
Answer:
1/2(6-8), 1/2(-3+7)=-1,2
Answer: C - (-1, 2)
Step-by-step explanation:
1:prove that the tangent at the point (1,-2) to the circle x²+y²=5 also touches the circle x²+y²-8x+6y+20=0 .Also find the point of contact.
2:find the length of tangent to the circle
3x²+3y²-7x-6y=12 drawn from (6,-7)
Circle 1 has center at (0, 0)
The tangent passes through the center and point (1, -2).
Equation of tangent at (1, -2):
x*1 + y*(-2) = 5x - 2y = 5x = 2y + 5If the same line is tangent to circle 2 then they have one common point.
Solve the system:
x = 2y + 5x² + y² - 8x + 6y + 20 = 0Substitute x:
(2y + 5)² + y² - 8(2y + 5) + 6y + 20 = 04y² + 20y + 25 - 16y - 40 + 6y + 20 = 05y² + 10y + 5 = 0y² + 2y + 1 = 0(y + 1)² = 0y + 1 = 0y = -1 ⇒ x = 2(-1) + 5 = -2 + 5 = 3We see only one point of contact, (3, -1), this proves the line is tangent to circle 2 as well.
#2Given circle:
3x² + 3y² - 7x - 6y = 12 and external point (6, -7).Rewrite the equation of the circle as:
3x² + 3y² - 7x - 6y = 12x² + y² - 7/3x - 2y = 4x² - 2*7/6x + 49/36 + y² - 2y + 1 = 4 + 49/36 + 1(x - 7/6)² + (y - 1)² = 229/36The center is (7/6, 1) the radius is √229/36
The length of the tangent t is the leg of the right triangle with another leg r being the radius and the hypotenuse d being the distance between the center and the external point:
t² = d² - r²t² = (6 - 7/6)² + (-7 - 1)² - 229/36t² = 36 - 14 + 49/36 + 64 - 229/36t² = 86 - 180/36t² = 81t = 94x-k=17 solve for x
Answer:
k = -17 + 4x
Step-by-step explanation:
Simplifying
4x + -1k = 17
Reorder the terms:
-1k + 4x = 17
Solving
-1k + 4x = 17
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '-4x' to each side of the equation.
-1k + 4x + -4x = 17 + -4x
Combine like terms: 4x + -4x = 0
-1k + 0 = 17 + -4x
-1k = 17 + -4x
Divide each side by '-1'.
k = -17 + 4x
Find the measure of ∠GJK. (I need the answer as fast as possible)
Answer:
∠ GJK = 102°
Step-by-step explanation:
(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so
2x + 92 + 3x + 63 = 180
5x + 155 = 180 ( subtract 155 from both sides )
5x = 25 ( divide both sides by 5 )
x = 5
Then
∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°
find the value of x
Answer:
50
Step-by-step explanation:
140- 40=100
100÷2=50
x=50
Write an equation in slope-intercept form (-5,-7);y=-2x+4
Answer:
Step-by-step explanation:
First, let us substitute x and y values: -7 = -2(-5) + 4
Next, let us simplify using the substitution property of equality: 14 = -7 (SEE BELOW MORE INFO).
Now, this does not make sense yet because 14 cannot possibly equal -7. Therefore, we must add a b value, therefore leading us to the equation:
14 + b = -7
by simplifying, we can conclude that b = -21
Finally, we can plug in the b-value into our original equation:
y = -2x + 4 - 21
After simplifying, we get y = -2x - 17. When this is graphed, we can see that -2x - 17 intersects (-5, -7).
The results of a linear regression are shown below.
y= ax + b
a = -1.15785
b= 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship between x and y?
1)Strong Postive Correlation
2)Strong Negative Correlation
3)Weak Positive Correlation
4)Weak Negative Correlation
Answer:
2) Strong Negative Correlation
Step-by-step explanation:
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
Suppose a hospital tested the age and body fat data for 18 randomly selected adults with the following results:
age 23 23 27 27 39 41 47 49 50
%fat 9.5 26.5 7.8 17.8 31.4 25.9 27.4 27.2 31.2
age 52 54 54 56 57 58 58 60 61
%fat 34.6 42.5 28.8 33.4 30.2 34.1 32.9 41.2 35.7
Use R to answer the following questions. Include your R code with your submission, and plots (where applicable, you can take screenshots) and submit electronically.
(a) Calculate the mean, median and standard deviation of age and %fat.
(b) Draw the boxplots for age and %fat and interpret the results.
(c) Draw a scatter plot and interpret the results.
(d) Check the distribution of these two attributes.
(e) Calculate the correlation between these two attributes. Are these attributes positively or negatively correlated?
(f) Compute their covariance. Interpret the results.
We used R to analyze age and %fat data, including mean, median, correlation, boxplots, and scatter plot.
(a) To calculate the mean, median, and standard deviation of age and %fat, you can use the following R code:
# create age and %fat vectors
age <- c(23, 23, 27, 27, 39, 41, 47, 49, 50, 52, 54, 54, 56, 57, 58, 58, 60, 61)
fat <- c(9.5, 26.5, 7.8, 17.8, 31.4, 25.9, 27.4, 27.2, 31.2, 34.6, 42.5, 28.8, 33.4, 30.2, 34.1, 32.9, 41.2, 35.7)
# calculate mean
mean_age <- mean(age)
mean_fat <- mean(fat)
# calculate median
median_age <- median(age)
median_fat <- median(fat)
# calculate standard deviation
sd_age <- sd(age)
sd_fat <- sd(fat)
(b) To draw the boxplots for age and %fat, you can use the following R code:
# create boxplots
boxplot(age, main="Boxplot of Age")
boxplot(fat, main="Boxplot of Body Fat Percentage")
Interpretation: The boxplot for age shows that the median age is around 50, with the range of ages from 23 to 61. The boxplot for %fat shows that the median percentage of body fat is around 31%, with a range from around 8% to 42%.
(c) To draw a scatter plot, you can use the following R code:
# create scatter plot
plot(age, fat, xlab="Age", ylab="% Fat", main="Scatter plot of Age and Body Fat %")
Interpretation: The scatter plot shows that there is a positive correlation between age and %fat, with older adults generally having a higher percentage of body fat.
(d) To check the distribution of age and %fat, you can use the following R code:
# check distribution with histograms
hist(age, main="Histogram of Age", xlab="Age")
hist(fat, main="Histogram of Body Fat Percentage", xlab="% Fat")
(e) To calculate the correlation between age and %fat, you can use the following R code:
# calculate correlation
cor(age, fat)
(f) To compute the covariance between age and %fat, you can use the following R code:
# compute covariance
cov(age, fat)
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Which of the following pairs show(s) two congruent triangles?
O B only
OB and C only
O A, B, and C
O A and C only
Answer:
B only
Step-by-step explanation:
Triangles A and C are similar, but not congruent to each other. Similar triangles have proportional sides and congruent angles, while congruent triangles have congruent sides and congruent angles.
Therefore, only B is correct
The question is asking for pairs of congruent triangles but lacks key information needed to accurately answer this, such as lengths or angles. Congruent triangles are identified in geometry based on either side-lengths or angles.
Explanation:The question is about congruent triangles, which in mathematics means triangles that have the same size and shape. But to accurately answer which pairs show two congruent triangles, we need more information. The options provided include 'A', 'B', and 'C' but without knowing more about these elements (for example their lengths or angles), it is impossible to determine which are congruent. Congruent triangles are identified in geometry based on either side lengths (SSS: Side-Side-Side, SAS: Side-Angle-Side, ASA: Angle-Side-Angle) or angles (AAS: Angle-Angle-Side, HL: Hypotenuse-Leg for right triangles). Without this vital information, we cannot definitively answer the question. Be sure to verify all the properties required to prove two triangles congruent.
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Please help me with this quickly I don’t have much time leftWhich step has mistake?
Option E Step 2 has the fault as the simplification of x²-9=(x+3)(x-3) and the problem has (x-3)(x-3) as the simplification as a²−b²=(a+b)(a−b)
What is factorization?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics. Expanding brackets in reverse is a process known as factorising. Fully factorizing an expression entails putting it in brackets by eliminating the factors with the highest common denominator. Finding the highest common factor between all of the terms in the expression is the simplest way to factorize.
here,
the correct factorization of 4/(x²-9) will be
=4/(x+3)(x-3)
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Point (-8,4) and point (7,4) what is the distance between the points
Answer:
15 units
because the y-coordinates are the same, simply take the absolute difference of the x-coordinates. |-8 - 7| = |-15| = 15
(we take the absolute difference because distance can never be negative)
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The figure below is made up of two rectangular prisms.
3 m
7 m
10 m
4 m 1 m
Find the volume of the entire figure by adding the volumes of the separate figures.
Volume = 120 +
cubic meters
Answer:
Total Volume = 190 m³Step-by-step explanation:
Volume of the entire figure = L (Area 1 + Area 2)
where L = 10 m
Area 1 (blue prism) = 4 x 3 = 12 m²
Area 2 (brown prism = 1 x 7 = 7 m²
plugin values into the formula:
Volume of the entire figure = L (Area 1 + Area 2)
= 10 (12 + 7)
= 120 m³ + 70 m³
= 190 m³
Giving brainliest for CORRECT awnser.
Answer:
Option A
................
Use the model below to calculate 9÷1/3.
A green rectangle is divided into 9 equal parts arranged into 3 rows of 3 cells each.
A.
9/3
B.
3/9
C.
13 1/2
D.
27
Using thie model ,The answer is D. 27.
To calculate 9÷1/3 using the model below, we can imagine dividing the green rectangle into thirds vertically. Each third would contain 3 cells.
Then, we can see that there are a total of 9 cells in the rectangle. Since we are dividing by 1/3, we need to find out how many sets of 1/3 are in 9.
We can see that there are 3 sets of 1/3 in each row (since each row contains 3 cells, which are thirds). So, in total, there are 3 rows of 3 sets of 1/3, which gives us:
9÷1/3 = 3 rows x 3 sets of 1/3 = 9 sets of 1/3 = 27
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Wendy is making potato salad for a picnic. One sack of potatoes weighs 14 pounds.What is the weight of a sack of potatoes in ounces
Answer:
224 ounces
Step-by-step explanation:
1 pound is 16 ounces, 14 multiplied by 16 is 224
every pound equal 16 ounces so 14 × 16 = 224
The amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16 end quantity comma where d represents the distance that the object falls, in feet. If a bungee jumper free falls for 5 seconds, how far does the jumper fall? (5 points)
400 feet
160 feet
6,400 feet
80 feet
If the amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t equals the square root of the quantity d over 16. The distance the jumper fall is: A 400 feet.
How to find the distance?Using this formula to find the distance by solving for d
t=√d/q
Where:
t = Time = 5 seconds
d = Distance = ?
q = Quantity = 16
So,
5 seconds=√d/16
d=16x5²
d=16 × 25
d= 400 feet
Therefore we can conclude that the correct option is A.
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Tosh. Inc.'s bonds currently sell for $980 and have a par value of $1,000. They pay a $95 annual coupon and have a 12-year maturity, but they can be called in 3 years at $1,150. What is their yield to call (YTC)?
Answer:
14.24%
Step-by-step explanation:
We have found that the yield to call (YTC) formula is:
YTC = [C + (F-P) / N] / [(F + P) / 2]
Where:
C = Periodic coupon amount = 95
P = Current Price = 980
F = Redemption amount = 1150
N = time left to redemption = 3
We replace:
YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]
YTC = 0.1424
In other words, the yield to call (YTC) is equal to 14.24%
What is the equation of the line perpendicular to the line shown in the diagram that passes through the point (- 3, - 5) ?
Answer:
A X + 3y = 18
Step-by-step explanation:
Pamela's mother purchased five boxes of candy bars. If each box contains 20 bars, how many candy bars does Pamela's mother have? Explain your answer.
If each box contains 20 bars and Pamela's mother purchased 5 boxes
To get the number of candy bars Pamela's mother have, we will simply multiply the number of box by the number oc candy in each box
That is; 5 x 20bars = 100 candy bars
Hence Pamela's mother have 100 candy bars
Write the elements belonging to the set {x|x is a natural number less than 10
Answer:
The set A = { 1,2,3,4,5,6,7,8,9}
Step-by-step explanation:
Step(i):-
Given that the set
{ x/x/ is a natural number less than 10 }
Natural numbers :
The natural numbers are
{ 1,2,3,4,5,6,7,8,9,10,.........}
The set A = { x/x/ is a natural number less than 10 }
The set A = { 1,2,3,4,5,6,7,8,9}
The points L(0, 5), M (-7, 1), N(-9, -5), and O(-2, -1) form quadrilateral
LMNO. Plot the points then click the "Graph Quadrilateral" button
Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).
The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.
Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.
After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.
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13) The pet shop has 6,157 dog treats. They packed the treats into bags with 7 pieces in each bag. Any treats
that did not fit into a bag of 7 were given to the groomer to use to reward animals getting bathed. How many
bags of treats did they fill? How many treats were given to the groomer?
bags of treats and gave
left over treats to the groomer.
Answer: The pet shop filled___bags of treats and gave ____left over treats to the groomer.
The number of bags filled by the pet shop is 879 and the number of treats they gave to the groomer is 4.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the data given in the question,
Total number of dog treats in the shop = 6157
Number of treats per bag = 7
Extra treats will be given to the groomer.
Then, the number of bags will be,
6157/7 = 879.57
This means that a total of 879 bags are there, with 7 pieces of treats per bag.
So, the total number of treats in 879 bags will be,
879 × 7 = 6153
So, the amount of treats left for the groomer is,
6157 - 6153 = 4 treats.
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Find the range and standard deviation of the set of data.
11 8 5 11 25
Answer: The range is 20, Standard Deviation, σ: 6.8702256149271
Step-by-step explanation:
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