Since the ΔEFG is similar to ΔHIJ, so side HI is equivalent to the measure of length of segment [EF] divided by the scale factor [K].
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. TThe sum of all the angles of a triangle is 180 degrees. Mathematically - ∠x + ∠y + ∠z = 180°There are different types of triangles such as -equilateral triangle, scalene triangle, isosceles triangle etc.
We have triangle ΔEFG is similar to triangle ΔHIJ.
Since ΔEFG is similar to triangle ΔHIJ, then we can write -
EF/HI = FG/IJ = EG/HJ = K [constant]
Since the side lengths are not given, we can write -
EF/HI = K
HI = EF/K
Therefore, since the triangles ΔEFG is similar to ΔHIJ, the side HI is equivalent to HI = EF/K.
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If a scatter plot shows a linear association, which must be true of the data?
A.
There is a line that passes through all of the plotted data points.
B.
There is a line that passes through most of the plotted data points.
C.
There is a line that describes the relationship between the two measured quantities reasonably well.
D.
There is a tendency for relatively high values for one measured quantity to be paired with relatively high values for the other measured quantity.
Answer:
If a scatter plot shows a linear association, then there is a line that describes the relationship between the two measured quantities reasonably well. This means that there is a clear pattern in the data, and that the data points tend to follow a straight line when plotted on a graph. This does not necessarily mean that there is a line that passes through all of the plotted data points or that there is a tendency for relatively high values for one measured quantity to be paired with relatively high values for the other measured quantity.
Step-by-step explanation:
Answer:
A scatter plot shows a linear association.
Step-by-step explanation:
The booster club at NHS sells hot chocolate and coffee at high school football games. At the last game, they had sales of $182.50. They need to keep track of how many of each type drink was sold so that they can make predictions for future sales. Bruce knows that they used 275 cups that night. If the hot chocolate sells for 75 cents and coffee sells for 50 cents, how much of each type of drink was sold?
Answer:
180 cups of hot chocolate and 95 cups of coffee
Step-by-step explanation:
multiply the cups by the price and add them together and it adds up to the total sales they got
An employee started a new job and must enroll in a new family health insurance plan. One of the options involves prescription drug coverage.
The employee estimates that the entire family will fill 6 prescriptions per month, totaling $850. The monthly premium for the plan is $55, with 90% coverage for the first $600 in prescription costs, then 80% coverage for all prescription costs over $600. What is the total out-of-pocket
expense for one month?
A. $685
B $795
C $110
D $165
The monthly prescription of $850, and the 90% coverage for the first $600 and 80% coverage for the prescriptions over $600 indicates that the total out-of-pocket by the family for one month is $110.
The correct option is option C. $110
What is an out-of-pocket expense?An out-of-pocket expense is an health expense incurred by an insured person, for which the insured person is not reimbursed.
The monthly premium for the family's health insurance plan = $55
The coverage offered by the health insurance for the first $600 = 90%
The coverage for prescription above $600 = 80%
The expected number of prescriptions by the family per month = 6
The total cost of the family's monthly prescription = $850
Therefore, the out-of-pocket expense by the family for one month are;
Out-of-pocket prescription for the first $600 = $600 - 90% × $600 = $60
Amount of prescription over $600 = $850 - $600 = $250
Out-of-pocket for prescription above $600 = $250 - 80% × $250 = $50
The total out-of-pocket expense for one month = $60 + $50 = $110The correct option is therefore, option C $110
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Answer:
The correct answer is D: $165
Step-by-step explanation:
Find all real zeros of the function
The table below shows the number of students gaining certificates for outstanding achievements:
What is the modal number of certificates?
6
4
2
5
3
Examining the table showing number of students gaining certificates for outstanding achievements the modal number is 4
What is modal number in math?The most frequent number, or the one that appears the most frequently.
In a frequency table the frequency shows the number of times a the data measured appears
Looking at the table the number that has most frequency is 4. This means that the people that collected 4 certificates are more than any other set of people.
The next is two which have a frequency of two while the least the people that collected 6 certificates. they have a frequency of 2 which means they are only tow people
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when performing the steps of checking the abcs during the survey of the victim, the two most vital body systems are checked. which systems are those? (choose two.)
The two most vital body systems that are checked when performing the steps of checking the ABCs are the Circulatory and Respiratory Systems.
Blood veins in the circulatory system are responsible for moving blood away from and back toward the heart. Arteries carry blood out from the heart while veins carry it back. Oxygen, nutrients, and hormones are delivered to cells by the circulatory system, which also eliminates wastes like carbon dioxide.
The respiratory system refers to the network of tissues and organs in your body that facilitates breathing. It includes your lungs, blood vessels, and airways. The lungs' moving muscles are a part of the respiratory system. Together, these elements circulate oxygen throughout the body and remove waste gases like carbon dioxide.
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how many ways can the letters of the word mailbox be arranged in a row if m and a must remain together (in order) as a unit?
the number of arrangements if a and m come in a unit is 720.
What is the combination?
A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The number of k-combinations for a set with n components
The word is the mailbox.
So it contains 7 words and the total number of arrangements will be 7! = 5040.
And if a and m comes in a unit then: the number of the arrangements will be 6! = 720.
Hence the number of arrangements if a and m come in a unit is 720.
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a domino is a rectangular tile composed of two squares. an integer is represented on both squares, and each integer 0-9 is paired with every integer 0-9 exactly once to form a complete set. a double is a domino that has the same integer on both of its squares. what is the probability that a domino randomly selected from a set will be a double? express your answer as a common fraction.
The probability that a domino randomly selected from a set will be a double = 2 / 11
what is probability?
A thing's probability indicates how probable it is to happen. When we are uncertain about the result of a given event, we can talk about the probabilities of several outcomes—how likely they are. Statistics refers to the study of events that have a probability component.
When 'n' is the largest integer in the set, the total number of dominoes in the set is given by the following formula:
(n + 1) (n + 2) / 2
This means that (9 + 1) (9 + 2) / 2 =
(10)(11)/ 2 =
110/2 =55
10 of these dominoes will be "doubles"
So....the probability that a domino randomly selected from a set will be a double = 10 / 55 = 2 / 11
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circle $c$ has radius 10 cm. how many square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle $c$?
100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Base = 2r = 2*10 = 20 cm
Height = r= 10 cm
Area = 1/2 * base * height
= 1/2 * 20 * 10
= 100 square centimeters
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Determine the domain of the following graph
What is the meaning of the term splitting and why is it used?
The term splitting is one of the methods used in factoring the quadratic expression.
We know that the general form of quadratic equation is ax² + bx + c = 0
The term splitting is one of the methods used in factoring the quadratic equation. When we can not square the first and the last term of the quadratic expression then we can use the method of splitting of the middle term. In this method we have to rewrite the middle term of the quadratic expression as the sum or difference of the two terms (the first and the last term).
For example, to factor a quadratic expression 4x² + 8x - 5
first find the product of the first and last term: 4 x (-5) = -20
Now, find the factors of -20 in such way that addition or subtraction of that factors is the middle term (8x) (Splitting of middle term):
10 x (-2) = -20 and 10 - 2 = 8
Now we write the quadratic expression using the sum of the two new factors, including the proper signs.
4x² + 10x - 2x - 5
Now,factor each pair by finding common factors.
2x( 2x + 5) - 1(2x + 5)
Now, factor out the common binomials.
(2x - 1) ( 2x + 5)
Therefore, the quadratic factorization uses splitting of middle term wtere the middle term of quadratic expresseion is splitted in to two factors.
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What is the measure of angle D?​
If the angle C is 15 degree and angle D is complementary then the measure of angle D is 75 degree .
In the question ,
it is given that ,
the measure of angle C is = 15 degree ,
we have to find the measure of angle D in the question,
and the angle C and angle D are complementary ,
that means ; angle C + angle D = 90°
Substituting the values ,
we get ,
15° + ∠D = 90°
subtracting 15° from both the sides ,
we get ,
∠D = 90° - 15°
Simplifying further ,
we get,
∠D = 75°
Therefore , the measure of angle D is = 75° .
The given question is incomplete , the complete question is
If Angle C = 15 degrees and Angle D is complementary to Angle C, what is the measure of Angle D ?
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in a group of 700 people, must there be 2 who have matching first and last initials? why? (assume each person has a first and last name, and the initials are from the 26 letters of the roman alphabet.)
Answer: Yes
Step-by-step explanation:
There are 676 sets of unique first and last initials, there being 26 for the first and 26 for the last. With 700 people, there are not enough unique combinations for everyone to be different. Therefore, in a group of 700 people, there will always be two who have a matching first and last initial.
Complete the statement
Answer:
B
Step-by-step explanation:
Lines that are both perpendicular to a given line are parallel.
How do you find the scale factor of a dilation with coordinates?
To find the scale factor of dilation we need to know the coordinated and centre point of dilation
The scale factor of a dilation is a number that represents the relationship between the lengths of objects before and after the dilation. It is equal to the ratio of the lengths of corresponding sides after and before the dilation.
To find the scale factor of a dilation, it is required to know the coordinates of the two points that the dilation acts on. The scale factor is then given by the ratio of the distances between the two points after and before the dilation. We locate the centre of the dilatation, and then we measure the distances between this centre and various points on the preimage and the final image. Then the scale factor is determined by the ratio of these distances.
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the robinson family and the wong family each used their sprinklers last summer. the water output rate for the robinson family's sprinkler was per hour. the water output rate for the wong family's sprinkler was per hour. the families used their sprinklers for a combined total of hours, resulting in a total water output of . how long was each sprinkler used?
Robinson's time is 25 minutes and Wrong' time is 40 minutes.
Equation of Time:
x + y = 65 -------------------------- (1)
Total usage amount:
15x + 35y = 1775 -----------------------------(2)
There are several ways to answer this question. I will teach we how to create two equations from the given information. First we need to set some variables (or unknowns). we need to set up a sprinkler time variable for each household. Let's call the time of the Robinson family "x" and the time of the Wrong family "y". The total time used was 65, so the first formula is x + y = 65 ( Robinson's time plus Wrong's time gives total time).
Now,
We use the other hourly water information (remember we already have time variables for each family, x and y). We can set the following equation as 15x + 35y = 1775 (15 liters x the amount of time the Robinson's use water plus 35 liters x the amount of time the use water gives equal to total usage).
Now,
We can solve for one of the variables (x or y). It doesn't matter which one we start with. Also, it doesn't matter which formula you start with. I used
x + y=65 . On the other hand, subtracting x gives y = 65 - x.
Now,
Replace y in the other formula. 15x + 35y = 1775 turns into
15x + 35(65-x) = 1775.
Distribute 35 to each term in brackets. By isolating the x variable: x=25
Recall that x means how long the Robinson's have been using sprinklers.
Now,
We can plug x into the other equation: 25 + y = 65
Therefore,
Subtract 25 on the other side to isolate y: y= 40
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Given that about 25% of the mammalian genome is associated with genes, including introns and regulatory sequence, what would be the approximate average length of dna per gene if the genome contained 20,000 genes?
The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.
Average gene length: just 2.5% of the human genome codes for proteins. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements. "The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes".
A DNA region from which an mRNA is transcribed is the de facto definition of a "gene" in mammalian genome annotation. Because one cannot deduce function from a genome sequence alone, the correct functional genetic definition of a gene—a segment of DNA that can complement a mutant phenotype—is lost.
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Which is a graph of the following?
The graph of the function f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
How to determine the graph of the function?From the question, we have the following parameters that can be used in our computation:
f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
The above function is a piecewise function, and it can be split as follows:
f(x) = [x² if x ≤ 2]
f(x) = [x + 4 if x > 2]
The domain x ≤ 2 in f(x) = [x² if x ≤ 2] means that:
The x values stop at 2 (i.e. 2 inclusive)
The domain x > 2 in f(x) = [x + 4 if x > 2] means that:
The x values starts at a value greater than 2 (i.e. 2 exclusive)
This is represented by the graph (d) with the open and closed circles
Hence, the graph is graph d
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Triangle
X
Y
Z
XYZX, Y, Z is similar to triangle
P
Q
R
PQRP, Q, R.
35
35
30
30
X
X
Y
Y
Z
Z
Slice for n
Answer:
Step-by-step explanation:
arc ABC=___ for number 2 witch is actually labeled number 3
A tudent ketched ome art on a 8. 5 inch (X) 11 inch piece of paper. He want to reize it to fit an 8 inch (X) 10 inch frame. What percent of the original ketch wa till able to be included in the frame?
85.6% of original sketch could still be seen when it was cropped into the frame.
A percentage of what?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless connection between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimal. The symbol "%" is commonly written after the integer to indicate percentages.
Briefing:by using the area of rectangle which is lenght x width
The area of a sketch ( dimensions are 8.5 inch x 11 inch ) = 93.5 square inches
The area of a sketch ( dimensions are 8 inch x 10 inch ) = 80 square inches
Now, (80/93.5) 100 85.6% of original sketch would be contained in the frame.
85.6% of original sketch could still be seen when it was cropped into the frame.
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Prove: ABD is congruent to CBD
The Proof for ABD is congruent to CBD is shown below.
What is Congruence Rule?The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Two triangles are congruent by side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).
Given:
AB || CD, <CBD = <ADB
In ΔABD and ΔCDB
<CBD = <ADB {Given}
BD= BD {Common}
<ABD = <CDB {Alternate Interior Angle}
So, By ASA Congruence Rule ΔABD ≅ ΔCDB
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100 points crown if you answer all of these and explain your answer
The angles of a triangle are equal to 5x + 10, 8x − 20 and 3x + 30. Find the value of x
The acute angles of a right triangle measure (48 − x ) and (3x − 10). What is the value of
Triangle ABC is a right scalene triangle. If ∠ = 72°, what is the measure of ∠A?
An obtuse isosceles triangle contains an angle that measures 162°. What is the measure of another interior angle within this triangle?
The angles of a triangle are equal to 5x, 2x + 8, and 3x + 12. What is the measure of the smallest angle of the triangle?
The angles of a triangle are equal to x, x + 4 and 20. What is the measure of the largest angle of the triangle?
Answer:
Step-by-step explanation:
Answer: He will need 49 tiles.
Step-by-step explanation:
Given: The patio will measure 13.5 feet by 43 feet.
Area of patio = 13.5 feet x 43 feet [Area = length x width]
= 580.5 sq. feet
Since area of each concrete tile = 12 sq. inch
Number of concrete tiles required to cover patio = (Area of patio) ÷ (area of each concrete tile)
= 580.5 ÷ 12
= 48.375 sq. inch ≈49
A man starts walking north at 2 feet per second from a point p. A minute later a woman starts walking south at 1 foot per second from a point 800 feet due east of p. At what rate are the people moving apart 3 minutes after the woman starts walking?.
The required rate are the people moving apart 3 minutes after the woman starts walking is 2.36 ft/S.
Explain the rate of change of distance.The rate of change of distance is speed ( not uprooting). Similar distance in different headings is alluded to as a similar distance.
According to question:Let x and y be the distance of the man and woman respectively.
We have,
dx/dt = 2 ft/s, dy/dt = 1 ft/s
Then, x = 2×6×60 = 720 ft
y = 1×5×60 = 300 ft
And in triangle which make by the locus of man and woman.
(x +y)^2 + (800)^2 = z^2
z = √(1020)^2+(800)^2
z = 1296.3 ft
So, people are 1296.3 ft apart,
Rate change
[tex]\frac{d}{dt}[/tex](x+y)^2 = [tex]\frac{d}{dt}[/tex]z^2
2(x+y)(dx/dt+dy/dt) = (2z)dz/dt
(720+300)+(2+1) = (1296.3)dz/dt
dz/dt = 3060/1296.3 = 2.36 ft/s
Thus, their moving rate is 2.36 ft/s
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pleassee I need this as soooonnn as possible
At the grand opening of a store, the first 18 customers will randomly draw a gift certificate from a box which contains twelve $10 coupons, two $50 coupons, and four $20 coupons. How many $20 coupons would need to be added so that the probability of drawing a $20 coupon is 1/3 ????
Answer:
70
Step-by-step explanation:
20+20
Find the 64th tent of the arithmetic sequence -3, -14 -25.
The 64th term of the arithmetic sequence -3, -14 -25, will be - 696.
What is Arithmetic sequence?An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.
Given that;
The arithmetic sequence is,
⇒ -3, -14 -25.
Now,
Since, We know that;
⇒ nth term = a + (n - 1)d
Where, 'a' is first term, 'd' is common difference.
Here, The arithmetic sequence is,
⇒ -3, -14 -25.
First term (a) = - 3
Common difference (d) = - 14 - (-3)
= - 14 + 3
= - 11
So, We get;
⇒ 64th term = - 3 + (64 - 1) (-11)
= - 3 + 63 × - 11
= - 3 - 693
= - 696
Thus, 64th term = - 696
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a town has a population of 5000 and grows at 4% every year. what will be the population after 7 years, to the near test whole number?
which type of rigid transformation is the equivalent of two reflections across intersecting lines?
Rotation is the type of rigid transformation which is equivalent of two reflections across intersecting lines.
Define rigid transformation
A rigid transformation is a transformation that persists the original size or shape of a given figure. Examples of rigid transformations are rotation, reflection etc;
In mathematics a rigid transformation is also known as Euclidean Isometry or Euclidean transformation. Euclidean Isometry deals mainly with transformation of any figure. But, doesn't changes the length, shape or size of a given figure.
The concept of of two reflections across intersecting lines is equivalent to single rotation transformation of the original figure.
Therefore the rigid transformation or Euclidean isometry which is similar to two reflections across intersecting lines is rotation.
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A school gives every student a sandwich for a picnic on the last day of school. The school has 1,821 students. Each sandwich has 2 slices of bread, and there are 21 slices of bread in a loaf. How many loaves of bread are needed for all the sandwiches?
Answer:
86
Step-by-step explanation:
What is 3x+y=-3 and 3x+y=-4
Answer:
The equations 3x+y=-3 and 3x+y=-4 are both linear equations in the standard form. The standard form of a linear equation is ax+by=c, where a and b are coefficients, and c is the constant term.
Step-by-step explanation: