Consider parallelogram VWXY below.Use the information given in the figure to find m ZZVW, x, and m ZZWV.3x + 3m ZZVm ZZW42064°X
Answers
Given :
\(\begin{gathered} \angle ZYX=42^0 \\ \angle ZXY=64^0 \\ YZ\text{ = 6} \\ ZW\text{ = 3x + 3} \end{gathered}\)Required :
\(\angle\text{ ZVW , x, }\angle\text{ ZWV}\)From the properties of a parallelogram,
The diagonals separate it into two congruent triangles. Hence,
\(\Delta\text{ VYX }\cong\text{ }\Delta\text{ }VWX\)Remember that congruent triangles have the same three sides and exactly the same three angles
\(\begin{gathered} \text{Hence ZY = ZW } \\ 6\text{ = 3x + 3} \\ \text{collect like terms} \\ 3x\text{ = 3} \\ x\text{ = 1} \end{gathered}\)Similarly,
\(\begin{gathered} \angle ZVW=64^0 \\ \angle ZWV=42^0 \end{gathered}\)Note: The congruent triangles are flipped along the diagonal
Related Questions
Identify the type of data (qualitative/quantitative) and the level of measurement for the following variable. Explain. The average mass (in grams )of a sample of rocks collected in the waters of a region.
1. Are the data qualitative or quantitative?
A. Qualitative, because descriptive terms are used to measure or classify the data.
B. Quantitative, because descriptive terms are used to measure or classify the data.
C. Qualitative, because numerical values, found by either measuring or counting, are used to describe the data.
D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.
2. What is the data set's level of measurement?
A. Ratio, because the differences in the data can be meaningfully measured, and the data have a true zero point.
B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zoro point.
C. Nominal, because the data are categories or labels that cannot be ranked.
D. Ordinal, because the data are categories or labels that can be ranked.
3. What is the probability of randomly selecting a diamond from a standard 52-card deck?The probability of selecting a diamond is 0.25.
4. Use the contingency table to complete parts a) through d) below.
Event A Event B
Event C 10 11
Event D 3 4
Event E 14 8
A) Determine the probability of P(AIC).
B) Determine the probability of P(CIA).
C) Determine the probability of P(BE).
5. Use the contingency table to complete parts a) through d) below.
Event A Event B
Event C 10 11
Event D 3 4
Event E 14 8
A) Determine the probability of P(CIA).
B) Determine the probability of P(BE).
C( Determine the probability of P(EB).
Answers
Answer:
Step-by-step explanation:
Hello!
The variable is
X: average mass of a sample of rocks collected in the waters of a region. (measured in grams)
Variables can be:
Quantitative: they represent number, any characteristic that can be "counted" is a quantitative variable, the most common examples are weight, volume, temperature, height, etc...
There are two types of quantitative variables:
⇒ Discrete variables: The only take certain values within the interval of definition of the variable, for example "number of sales" or "money in a wallet"
⇒ Continuous variables: They can take any value within an interval, in this example that you are working with mass, depending on the precision of the scale the mass can have infinite decimal values.
Qualitative: they represent characteristics that cannot be counted, meaning, they are not represented by numbers. There are many attributes that are qualitative variables, for example: colors, race of an animal, phenotypes, types of business, etc...
1)
The variable in this example is Quantitative, it takes numerical values, and the correct option is:
D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.
2)
The values of mass of the rocks can take any value within the range of definition of the variable, they only depend on the precision of the scale used to weight the rocks.
B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zero point.
3)
A standard 52-card deck contains 13 cards for each suit (clubs, diamonds, hearts and spades)
To calculate the probability of choosing a card at random and it being a Diamond, supposing that all cards are equally probable, you have to divide the total number of diamonds by the total number of cards in the deck:
P(diamond)= 13/52= 0.25
For items 4) and 5) the contingency tables are attached.
4)
a. and b. are conditional probabilities, to calculate them you have to apply the following formula: \(P(A|B)= \frac{P(AnB)}{P(B)}\)
This means that the probability of the event "A" given that event "B" has occurred is equal to the probability of the intersection between events "A" and "B" divided by the probability of event "B"
a. P(A|C)= \(\frac{P(AnC)}{P(C)}\)
To calculate the probability of the intersection P(A∩C) you have to divide the observations where both events cross by the total of observations on the table:
P(A∩C)= 10/50= 0.20
The probability of C is found in the margins of the table, in this case you have to divide the total of observations for event C by the total of observations of the table:
P(C)= 21/50= 0.42
Now you can calculate the asked probability:
\(P(A|C)= \frac{0.2}{0.42}= 0.48\)
b. P(C|A)= \(\frac{P(AnC)}{P(A)}\)
From item a. we already know that P(A∩C)= 10/50= 0.20
The probability of event A is in the margin of the table and you calculate it as:
P(A)= 27/50= 0.54
Then:
\(P(C|A)= \frac{0.20}{0.54} = 0.37\)
c. P(BE)
This symbolized the probability of the events "B" and "E" occurring at the same time, you can also symbolize it as P(B∩E)
To calculate the probability of B and E happening you have to do as follows:
P(B∩E)= 8/50= 0.16
5)
a. P(C|A)= 0.37 (As calculated in 4b.)
b. P(BE) and c. P(EB) ⇒ Both expressions symbolize the intersection between events "B" and "E", P(B∩E)= P(E∩B)= 0.16 (As calculated in 4c.)
I hope this helps!
A rectangular field is 5cm wide and 4cm long requires 260m of fencing. find y
Answers
Answer:
50 + x + 50 + x = 260, or
100 + 2x = 260, or
50 + x = 130,
Step-by-step explanation:
A company refinishes wood floors for $1.50 per square foot. Makayla hires the company to refinish 1,000 square feet
in her home. How much does she pay for the refinishing work?
$500
$1,000
$1,500
$5,000
Answers
Answer:
The correct answer is $1,500
Step-by-step explanation:
hope this helps
Solve for x
-22.3=x/3 -3.1
Answers
Answer:
-57.6=x
Step-by-step explanation:
-22.3= x/3-3.1
-19.2=x/3
-57.6=x
What would the height need to be for this curve to be a density curve?
1/5
1/4
1/2
1
Answers
For a curve to be a density curve, it must meet certain conditions such as it should be non-negative, and the area under the curve should equal 1. Furthermore, the curve should be continuous and smooth, and there should be no values outside the range of the data.
Let's see how the height would need to be for this curve to be a density curve.A density curve is a statistical representation of the distribution of a dataset or population. Density curves are used to describe the distribution of continuous data and provide a visual representation of the likelihood of an event occurring within a specific range of values. It helps to determine the proportion of data that falls within a given range of values. A density curve is used to provide a graphical representation of data without showing the individual data points.To be a density curve, a curve must have the following properties:The curve should be non-negative.The area under the curve should be equal to 1.The curve should be smooth and continuous.There should be no values outside the range of the data.From the above properties, we can conclude that the height required for a curve to be a density curve depends on the data that the curve represents. As long as the curve meets the above conditions, it can be considered a density curve. So, there is no specific height required for a curve to be a density curve. The height of the curve can vary depending on the range of the data and the distribution of the data.For such more question on properties
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A decorative vase is on sale from $80 to $50. What is the
percent change of the price of the vase. Be sure to indicate
if it was a decrease or increase. Show the formula you use to
solve. Round to a whole number.
Answers
Since the result is negative, we can say that the price of the vase decreased by 37.5%. Rounding to a whole number, the percent change is 38% (since a 37.5% decrease is approximately equal to a 38% decrease).
What is percent?Percent (often symbolized as "%") is a way of expressing a fraction or a portion of something in terms of hundredths. It is used to describe the relationship between a part and a whole, with the whole being represented by 100%. Percentages are commonly used in many areas of life, such as finance, business, and statistics. They can be used to describe changes in values over time, to compare different quantities or amounts, or to express probabilities or frequencies.
Here,
The percent change in the price of the vase can be calculated using the formula:
percent change = (new price - old price) / old price x 100%
In this case, the old price of the vase was $80 and the new price is $50. Substituting these values into the formula, we get:
percent change = ($50 - $80) / $80 x 100%
percent change = -0.375 x 100%
percent change = -37.5%
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Triangle 1: A(6,6), B(12,9), C(9,6)
Triangle 2. A' (22), B’ (4,3), C (3,2)
What scale factor was used to transform triangle 1 to triangle 22
To transform Triangle 1 to Triangle 2, a scale factor of
was used
Answers
9514 1404 393
Answer:
1/3
Step-by-step explanation:
All of the coordinates of the points of Triangle 2 are 2/6 = 1/3 of those of Triangle 1. The scale factor is 1/3.
bella answered 33 questions on her math test. she earned a 92% on the test. how many questions did she answer correct
Answers
Answer: 30.36
Step-by-step explanation:
92% of 33 is 30.36. I don't know how Bella got 30.36 questions correct, but that is what I got.
if 1 pound of chacolate creams at Philadelphia candies cost $7.52 how much does that cand cost by the ounce
.
Answers
we can divide our cost of chocolate (7.52) by the weight of the chocolate (16 oz) 7.52/16=
$0.47 per ounce of candy
Adriana sold 50 shares of a company’s stock through a broker. The price per share on that day was $22.98. The broker charged her a 0.75% commission. What was Adriana’s real return after deducting the broker’s commission?
A.
$8.62
B.
$229.80
C.
$1,140.38
D.
$1,149.00
Answers
C $1,140.38
Step-by-step explanation:
We are given that Adriana sold 50 shares and that the price per share was $22.98
This means that:
Total value = 50 * 22.98 = $1149
Now, we know that the broker charged 0.75% commission on the total value
This means that:
Broker's charge = 0.75% * 1149 = 0.0075 * 1149 = $8.6175
Therefore,
Adriana's return = Total value - broker's charge
Adriana's return = 1149 – 8.6175 = $1,140.38
If m23 = 111, what is mZ14?
10
9
2
1
>
11
12
3
4
14 13
6
5
15 16
8
7
(not drawn to scale)
A 69
B 111
Answers
Answer:
a will be the correct answer plzz tick that and win 1 lakh
Jerry has $5 and $10 bills in his wallet. He has a total of 7 bills in his wallet for a total of $50. How many bills does he have of each?
Answers
Answer:
Step-by-step explanation:
The area of a rectangle is 4y+10.A.Represent the area of the rectangle in factored form.B.Use the factored form to give one possible set of dimensions for this rectangle
Answers
Answer:
2 ( 2y + 5 )
Step-by-step explanation:
→ Take out 2 as a factor
2 ( 2y + 5 )
Answer:
A = 2(2y + 5)2 and 11 (when y = 3)Step-by-step explanation:
The area equation is:
A = lwGiven:
A = 4y + 10This can be factored as:
A = 2(2y + 5)Let y = 3, then the dimensions are:
2 and 2*3 + 5 = 11what is the meaning of sequence in mathematic and
Answers
Answer:
A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
Step-by-step explanation:
Write an equation of the vertical line that passes through the point (x, y) = (-2,3).
Answers
Answer:
x = -2
Step-by-step explanation:
60% of the books in a library are for adults, 5% are for young people and the rest are for children. If there are 280 books for children, how many books are there altogether?
Answers
Answer:
800 books
problem solving steps：
adults:60%
young people:5%
children=100%-60%-5%
=35%
35%=280 books
1%=280÷35
=8
100%=800
so,there are 800 books
The diameter of Jacob's circular tabletop is 6 feet. What is the area, in square feet, of Jacob's tabletop?
Answers
Answer:
approximately 28.26 square feet
Step-by-step explanation:
The formula for the area of a circle is A = pi(r)^2. So, the radius is half of the diameter, meaning it's 3 feet. Then we square it to get 9, and multiply by pi, or 3.14. This leads us to the approximated answer of 28.26 square feet.
The area is:
28.27 square feet
Work/explanation:
Since the tabletop is circular, we use the formula for a circle's area, which is: \(\bf{A=\pi r^2}\).
We have the diameter, and to find the radius, we divide the diameter by 2, which gives us 6 ÷ 2 = 3 feet, so the radius of the tabletop is 3 feet.
Now, here's a diagram for you;
\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 3\ ft}\end{picture}\)
Plug in the data:
\(\sf{A=\pi\times3^2}\)
\(\sf{A=\pi\times9}\)
\(\sf{A=28.27\:ft^2}\)
Hence, the area is 28.27 square feet.Write your slopes for the equation as a fraction. Leave no spaces. Use the / in your fractions.
a. Write a second equation for the system so it has infinitely many solutions.
b. Write a second equation whose graph goes through (0, 2) so that the system has no solutions.
c. Write a second equation whose graph goes through (2, 2) so that the system has one solution at (4, 3)
Answers
Answer:
Equation of given line: y = (3/2)x - 3
a) 2y = 3x - 6
-3x + 2y = -6
3x - 2y = 6
6x - 4y = 12
b) y = (3/2)x + 2
c) m = (3 - 2)/(4 - 2) = 1/2
2 = (1/2)(2) + b
2 = 1 + b, so b = 1
y = (1/2)x + 1
Mr. Santos plants beans and squash in the areas shown in the model below.
Beans:
Squash:
21 acres
12 acres
Which expression is equivalent to the sum of the two areas?
3/4 + 7) acres
7(3+4) acres
4(3+ 7) acres
3(3+ 7) acres
Plz answer!
Answers
Answer:
it is A hope this helps
Step-by-step explanation:
I just took the test
Answer: its a
Step-by-step explanation:
itook the test
Marcel plugged in his work tablet and phone. The phone had a battery charge of 13% and started increasing by 2 percentage points every 3 minutes. The tablet had charge of 25% and started increasing by l percentage point every 3 minutes. Let t represent the time, in minutes, since Marcel plugged in the phone and tablet. Complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.
Answers
An inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36 minutes.
How to complete the inequality?From the information provided, we have the following parameters about Marcel's work tablet and phone:
Initial battery charge of phone = 13%.
Rate of charging phone = 2 percentage points every 3 minutes = 2/3 % in 1 minute.
Therefore, the total quantity of charge on the phone after t minutes is given by 13% + t(2/3)%.
For his tablet, we have the following information:
Initial battery charge of tablet = 25%.
Rate of charging tablet = 1 percentage point every 3 minutes = 1/3 % in 1 minute.
Therefore, the total quantity of charge on the tablet after t minutes is given by 25% + t(1/3)%.
Since the the total quantity of charge on the phone after t minutes is greater than the total quantity of charge on the tablet after t minutes, we have the following mathematical expression (inequality):
13% + t(2/3)% ≥ 25% + t(1/3)%
t(2/3) - t(1/3) ≥ 25 - 13
t(1/3) ≥ 12
t/3 ≥ 12
t ≥ 12 × 3
t ≥ 36 minutes.
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if m<xyz = 58 and m<wxz = 51 find m<wzx
Answers
Answer:
m<wzx = 71
Step-by-step explanation:
Assuming these are interior angles of a triangle.
The sum of all three interior angles of a triangle is always 180 degrees, therefore:
m<xyz + m<wxz + m<wzx = 180
Substitute our values:
58 + 51 + m<wzx = 180
m<wzx = 180 - 58 - 51
m<wzx = 71
Please answer ASAP need steps.
Answers
Answer:
The ANSWER is 1/2 x (3/5) : (9/15) (-6/4) : (4/1) = -3/16 = -0.1875
Step-by-step explanation:
Multiple: 1/2 * 3/5 = 1 · 3/2 · 5 = 3/10
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 10) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half multiplied by three fifths is three tenths.
Divide: the result of step No. 1 : 9/15 = 3/10 : 9/15 = 3/10 · 15/9 = 3 · 15/10 · 9 = 45/90 = 45 · 1/45 · 2 = 1/2
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 9/
15 is 15/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 45 gives 1/2.
In other words - three tenths divided by nine fifteenths is one half.
the result of step No. 2 * (-6/4) = 1/2* (-6/4) = 1 · (-6)/2 · 4 = -6/8 = -3 · 2/4 · 2= -3/4
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-6, 8) = 2. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one half multiplied by minus six quarters is minus three quarters.
Divide: the result of step No. 3 : 4 = -3/
4 : 4 = -3/4 · 1/4 = -3 · 1/4 · 4 = -3/16
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/
1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - minus three quarters divided by four is minus three sixteenths.
Suppose that a volcano is erupting and readings of the rate r(t) at which solid materials are spewed into the atmosphere are given in the table. The time t is measured in seconds and the units for r(t) are measured in tonnes (metric tons) per second. Note that r(t) is increasing over the interval [0, 6]. t 0 1 2 3 4 5 6 r(t) 28 18 34 48 54 60 (a) Give upper and lower estimates (in tons) for the total quantity Q(6) of erupted materials after six seconds. (Use six equal subintervals.) lower estimate Q(6) tons upper estimate tons = 016) (b) Use the midpoint rule to estimate Q(6) (in tons). (Use three equal subintervals.) Q(6) = tons Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table. t(h) 0 2 4 6 8 10 r(t) (L/h) 8.6 7.5 6.7 6.4 5.7 5.1 Find lower and upper estimates for the total amount of oil in liters) that leaked from the tank over the interval [0, 10]. (Use five equal subintervals.) lower estimate upper estimate
Answers
Lower estimate obtained would be = 35.4 liters
Upper estimate obtained would be = 35.4 liters
What is Estimate?
Estimation finds an estimate or approximation.
An approximation is a value, amount, or size closest to the true value found by rounding off.
To find upper and lower estimates for the total quantity of erupted materials after six seconds using six equal subintervals, we can use the left endpoints and the right endpoints of the subintervals to find the estimates.
The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. Since there are six subintervals, we have:
lower estimate = (28 + 18 + 34 + 48 + 54 + 60) * (6/6) = 324 tons
The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval. We have:
upper estimate = (18 + 34 + 48 + 54 + 60 + 60) * (6/6) = 324 tons
To use the midpoint rule to estimate Q(6) using three equal subintervals, we need to find the midpoints of the subintervals. The subintervals are [0,2], [2,4], and [4,6]. The midpoints are 1, 3, and 5. The value of r(t) at these points is 18, 48, and 54 respectively. The midpoint rule estimate is given by:
Q(6) = (18 + 48 + 54) * (6/3) = 180 tons
To find lower and upper estimates for the total amount of oil leaked over the interval [0, 10] using five equal subintervals, we can again use the left endpoints and the right endpoints of the subintervals to find the estimates. The lower estimate is obtained by using the left endpoints of the subintervals to estimate the value of r(t) at each subinterval. The upper estimate is obtained by using the right endpoints of the subintervals to estimate the value of r(t) at each subinterval.
The subintervals are [0,2], [2,4], [4,6], [6,8], and [8,10]. The left endpoints are 0, 2, 4, 6, and 8, and the right endpoints are 2, 4, 6, 8, and 10. The lower estimate is obtained by using the left endpoints:
lower estimate = (8.6 + 7.5 + 6.7 + 6.4 + 5.7) * (10/5) = 35.4 liters
The upper estimate is obtained by using the right endpoints:
upper estimate = (7.5 + 6.7 + 6.4 + 5.7 + 5.1) * (10/5) = 35.4 liters
Hence, The Lower estimate obtained would be = 35.4 liters and
Upper estimate obtained would be = 35.4 liters
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A $17,000 deposit in an account with an APR of 3.5%. The balance in the account after 20 year is approximately
Answers
Answer:
it will be 11900 in 20 years.
For the arithmetic sequence beginning with the terms {-1, 2, 5, 8, 11, 14...}, what is the sum of the first 16 terms?
Answers
Answer:
S₁₆ = 344
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then
S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]
= 8 (- 2 + 45)
= 8 × 43
= 344
20 points !!
Alexis has the following grades in his math class:
Homework grades: 76, 82, 85
Quiz grades: 74, 80, 80
Test Grades: 60, 68
If the teacher weights homework at 10%, Quizzes at 20%, Tests at 60%, what is her current class average? Please be careful with this one the categories don’t sum to 100% because she hasn’t taken her final exam yet.
Question 5 options:
a) 81
b) 76
c) 69
d) 72
Answers
Answer:
C
Step-by-step explanation:
First we need to find the average in every section, such as the Hw, quiz and tests.
(76+82+85)/3=81 Hw
(74+80+80)/3=78 quiz
(60+68)/2=64 test
Hw is weighted at 10% so it is 81×1=81.
Quizzes are weighted at 20% so 78×2=156
Tests are weighted at 60% so 64×6=384.
Add them all up then divide them by 9,
(81+156+384)/9= 69%
Name this triangle by its sides and angles. This is a(n) ____________________ triangle.
A.obtuse, isosceles
B.right, scalene
C.obtuse, scalene
D.right, isosceles
Answers
Answer:
right scalene
Step-by-step explanation:
Since all three sides have different lengths , this is a scalene triangle
(isosceles means two sides have the same lengths and equilateral means all three sides have the same length)
We have a right angle indicated by the box in the corner
A large soda bottle cap has a radius of 1+2 /2 centimeters. What is the area of the bottle cap? (R the area of a circle is no where r is the radius). 1 + 2v2 A. (5-12 - square IT square centimeters
Answers
Answer:
bottle top
Step-by-step explanation:
How many fluid ounces are there in 3 pints and 12 fluid ounces?
Answers
Answer:
60 fluid ounces
Mark my as brainliest please
Need help on this please
Answers
Area of the sector = 90/360 ×πr^2
=1/4 ×3.142×6×6
=1/4×113.112
=28.278kilometers square
Approximately 28kilometers square