Given ∠CAT≈∠DOG, m∠C=25°, and m∠O=37°. What is the measurement of ∠G?
Answers
The measure of angle ∠G, found by using the definition of congruency and the angle sum property is 118°
What makes two triangles congruent?Two triangles are congruent if satisfy the following conditions
All three sides of one triangle are congruent to the three sides of the other triangle (SSS)Two sides and the included angle in one triangle are congruent to two sides and the included angle in the other triangle (SAS)Two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle (ASA)Two angles and the non included side of one triangle are congruent to two angles and a non included side of the other triangle (SAA)The hypotenuse side and a leg in a right triangle are congruent to the hypotenuse and a leg in the other triangle (HL)An acute angle and the hypotenuse side of a right triangle are congruent to an acute angle and the hypotenuse side the other triangle (HA)Parts of the question that appear missing includes;
ΔCAT ≅ ΔDOGm∠C = 25°m∠O = 37°The measure of angle ∠G is found as follows;
The order of the letters in the congruency statement indicates that angle ∠C is congruent to angle ∠D, angle ∠A is congruent to angle ∠O, and angle ∠T is congruent to angle ∠G, which from the definition of congruency, indicates that we have;
m∠C = m∠D = 25°
m∠A = m∠O = 37°
m∠T = m∠G
The measure of angle ∠G and angle ∠T can therefore, be found from the angle sum property of the interior angles of a triangle.
m∠C + m∠A + m∠T= 180° (angle sum property of a triangle)
m∠D + m∠O + m∠G= 180° (angle sum property of a triangle)
m∠G = 180° - (m∠D + m∠O) (subtraction property of equality)
m∠G = 180° - (25° + 37°) = 118°
The measure of angle ∠G, m∠G is 118°Learn more about the angle sum property of a triangle here:
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Related Questions
The average age of a college is 21.8 years. The average age of students of college is 24.2 years and average age of lecturers of college is 20.6 years. Find the ratio of the number of students to that of lecturers?
Answers
Answer:
22,2
Step-by-step explanation:
average also known as mean
so you find it by adding all the numbers together and dividing them by how many there are
so 21,8 + 24,2 + 20.6 = 66,6 divided by 3 equals 22,2
a T-shirt increased in price by 1/7 after the increase it was a priced at £56. what was the original price?
Answers
Explanation: divide £56 by 7. each of the seven parts is equal to £8. Subtract £8 from £56 and the original price is £48.
for a special fully discrete 20-year term insurance on (30): the death benefit is 1,000 during the first ten years and 2,000 during the next ten years.
Answers
The cost of the 20-year term insurance will be based on age, health, smoking, and other factors to determine the premium.
The cost of a special fully discrete 20-year term insurance on a 30-year-old would depend on a range of factors, including the insured's age, health, smoking status, and lifestyle. These factors would be used to calculate the risk of death during the 20-year term. The death benefit of 1,000 during the first ten years and 2,000 during the next ten years would also be taken into account when calculating the cost of the policy. Depending on the risk of death and the death benefits, the premium could vary significantly. For example, a 30-year-old in good health with no smoking history could pay less for the policy than a 30-year-old with a pre-existing condition and a smoking history. The premium could also be higher for individuals with riskier lifestyles. Ultimately, the cost of the 20-year term insurance will depend on the risk of death and the death benefit offered by the policy.
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A researcher wishes to estimate the proportion of all adults who own a cell phone. He takes a random sample of 2000 adults; 1650 of them own a cell phone. The population of interest to the researcher is:______
Answers
Answer:
All the adults
Step-by-step explanation:
The question says that the researcher wants to estimate all adults that own a cell phone.
So the population of interest is all the adults.
The statistic is the proportion p^ of the random sample of 2000 adults;
P^ = 1650/2000
= 0.825
The parameter of interest in the question is p, which is the proportion of those adults that own a cell phone.
What is the answer for this question ??
Answers
Answer:
1 236^2
Step-by-step explanation:
first find the area of the square field .
Side × side
100m×100m=10 000m^2
secondly find the area of the whole shape .
100m+3m+3m= 106m
side ×side
106m×106m=11 236m^2
lastly you subtract to get area of the path
11 236-10 000=1 236m^2
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
Answers
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
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It takes 10 3/4 inches of wood to make a frame for a small photo. Ms. Jones has 3 yards of wood. How many frames can she make? HELP PLS ANYONE
Answers
Explanation: First, find how many inches are in 3 yards. Since we know 1 yard = 36 inches, we do 36(3) and get 108. Next, we want to divide total inches of wood by inches of wood needed to make a frame. The equation is 108/10.75 and you will get 10 with a lot of decimals. Since she doesn't want to make part of a wood frame, we round down and get our final answer of 10 wood frames.
The grade distribution for a course is listed in the following table. If a student is randomly selected fro mly selected from this class, what is the probability that they received an A, B, or C? A B C D F 40 40 33 20 14
Answers
Answer:
the probability that a randomly selected student received an A, B, or C is approximately 0.769, or about 76.9%.
Step-by-step explanation:
To find the probability that a randomly selected student received an A, B, or C, we need to add up the number of students who received each of these grades and divide by the total number of students in the class.
The total number of students in the class is:
total = A + B + C + D + E = 40 + 40 + 33 + 20 + 14 = 147
The number of students who received an A, B, or C is:
A + B + C = 40 + 40 + 33 = 113
Therefore, the probability that a randomly selected student received an A, B, or C is:
P(A or B or C) = (A + B + C) / total = 113 / 147 ≈ 0.769
So the probability that a randomly selected student received an A, B, or C is approximately 0.769, or about 76.9%.
The concerns about the impact of technology on our lives are growing. There have been
recent research reports about the negative impact of digital technology usage on stress,
work productivity, happiness, and overall well-being. In light of these concerns, a polling
organization asked technology experts about their opinion on our digital life and found
that 29% of the experts believe that in the future our lives will be more harmed than
helped by their digital environment. In an effort to confirm these results, a local tech
company decides to ask 215 randomly selected customers their opinions about their
digital life. Answer parts a through c below.
A
a. What is the probability that 35 or more people from this sample are concerned about
the digital environment?
The probability is
(Round to four decimal places as needed.)
Answers
The probability that 35 or more people from the sample of 215 customers are concerned about the digital environment is 0.7043.
To calculate the probability that 35 or more people from the sample of 215 customers are concerned about the digital environment, we can use the binomial distribution formula.
The binomial distribution is applicable here because we have a fixed sample size (215 customers) and each customer can be categorized as either concerned or not concerned.
Let's denote p as the probability that a randomly selected customer is concerned about the digital environment.
From the given information, we know that 29% of technology experts believe our lives will be more harmed than helped, so p = 0.29.
The formula for the probability mass function of the binomial distribution is:
\(P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)\)
Where:
P(X = k) is the probability of k successes (in this case, customers concerned about the digital environment)
C(n, k) is the number of combinations of n items taken k at a time
\(p^k\) is the probability of k successes
\((1 - p)^{(n - k)\) is the probability of (n - k) failures
Now, let's calculate the probability of having 35 or more customers concerned:
P(X ≥ 35) = P(X = 35) + P(X = 36) + ... + P(X = 215)
Using this formula, we can calculate the probability using a cumulative approach:
P(X ≥ 35) = 1 - P(X ≤ 34)
Calculating this probability requires summing up a large number of individual probabilities, which can be time-consuming.
Therefore, it is more practical to use statistical software or calculators to obtain an accurate answer.
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Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answers
Answer:
Probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation:
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
The probability of 9 children selected from this school, at least 6 do not have cavities is 0.80.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Sixty percent of all children in a school do not have cavities.
The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities will be
n = 9
p = 0.60
Then we have
\(\rm P = 1 - P(less \ than \ or \ equal \ 6)\\\\P = 0.8\)
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Determine what type of model best fits the given situation: A 4% raise in salary each year.
Answers
the models aren't given..
Answer: no models given
Step-by-step explanation:
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Answers
Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
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Write an equation for the nth term of the arithmetic sequence 7,2,-3,-8,
Answers
Answer:
-5n+12
Step-by-step explanation:
find the difference which is -5
then find the difference from -5 to 7 which is 12
put it in the sequence
-5n+12
Answer:
-5n+12 that would be your equation
x
+
0
<
−
10
and
x
−
10
≥
−
10
Write the answer in interval notation.
Answers
The stem-and-leaf plots list the ages of the people in Lee’s study group and in Paul’s study group.
Which statement is NOT correct?
a. Paul’s group has a wider range of ages.
b. The data for Paul’s group has two modes.
c. The median age in both groups is 44 years.
d. The mean age in both groups is between 41 and 42 years.
Answers
The false statement from the stem-and-leaf plot is given as follows:
b. The data for Paul’s group has two modes.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
The mode of a data-set is the data-set that appears the most times in a data-set.
Hence, for Paul's group, the mode is given as follows:
44.
As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.
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Q2 Which statement is true?
All squares are rhombi.
All rectangles are rhombi.
All parallelograms are rectangles.
All trapezoids are parallelograms.
Answers
Answer:
All parallelograms are rectangles.
In the figure below, S is the center of the circle. Suppose that JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5. Find the
following.
Answers
The measure for NS is 3.5 cm and the value of x is 2.
We have,
JK = 16, MP= 8, LP = 2x + 4, and PS= 3.5.
Since PS is perpendicular to ML then
MP = LP
So, 8 = 2x+ 4
2x = 8-4
2x= 4
x= 4/2
x= 2
Now, ML = MP + PL = 16
and, JK = ML= 16
Then, NS = PS
NS = PS = 3.5 cm
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A cellular phone company charges $67.95 per month for a service plan that includes 6 GB of data. In addition to the basic monthly rate, the company charges $8.95 for each additional GB of data over 6 GB. A customer on this plan receives a bill for $148.50. How much data did this customer send and receive during the month?
Answers
Answer:
The customer send and receive 15 GB of data during the month.
Step-by-step explanation:
Given;
Monthly charge for 6 GB of data = $67.95
Additional charge for each additional GB of data over 6 GB = $8.95
Bill received by the customer = $148.50
Therefore, we have:
Total amount paid for additional GB of data over 6 GB = Bill received by the customer - Monthly charge for 6 GB of data = $148.50 - $67.95 = $80.55
Additional GB of data over 6 GB = Total amount paid for additional GB of data over 6 GB / Additional charge for each additional GB of data over 6 GB = $80.55 / $8.95 = 9 GB
Total data customer send and receive during the month = 6 GB + Additional GB of data over 6 GB = 6 GB + 9 GB = 15 GB
Therefore, the customer send and receive 15 GB of data during the month.
Mary and Jeff both have jobs at a baseball stadium selling bags of peanuts. They each get paid $12 per game
and $1.75 for each bag of peanuts they sell. (A-CED.1)
a.) How many bags of peanuts does Jeff need to sell to earn $54?
b.) How much will Mary earn if she sells 70 bags of peanuts at a game?
Please please help me please please I will give you brainless
Answers
1.75p = 42
p = 24 bags
b) 1.75(70) + 12 = b
122.5 + 12 = b
b = $134.50
how to find rations in triangles
Answers
Answer:
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
Step-by-step explanation:
Can someone help me
Answers
The scale factor that was used to convert triangle ABC into the image in A ' B ' C ' is 1 / 2.
How to find the scale factor ?To find the scale factor, you need to find the length of a side of triangle ABC and then the length of the corresponding side in A ' B ' C '.
The side length we will pick is AB which is:
= 6 - 2
= 4 units
The side length of the other triangle is A' B' :
= 3 - 1
= 2 units
The scale factor is:
= 2 / 4
= 1 / 2
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Dana is making bean soup. The recipe she has makes 10 servings and uses
3/4
of a pound of beans. How many total pounds of beans does she need to make 5 servings of soup?
She has
1/16
of a pound of beans in one container and
1/4
of a pound of beans in another container. How many more pounds of beans does Dana need to make the 5 servings of soup? Show your work or explain your answer.
Answers
Helpp guyss left with this one onlyy!!!!
Answers
Answer:
\(m=\frac{2}{5}\)
Step-by-step explanation:
1. To find the slope we need to use the slope formula, \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
2. The points that were given were (0,0) and (5,2). Let's plug those into the formula.
\(\frac{2-0}{5-0}\)
\(\frac{2}{5}\)
So, your slope would be \(m=\frac{2}{5}\)
Hope this helped! C:
7 1/6 - 62/5 = ?
O A. 45
O B. 145
O C. 1/5
O D. 1335
Answers
Answer:
-17/32
this is the answer I got
Find the area of the parallelogram
Answers
Answer:
1191 cm²
Step-by-step explanation:
Area of parallelogram = base X vertical height.
Call the vertical line h.
h/ sin 80 = 7/ sin 10
h = (7 sin 80) / sin 10
= 39.7.
Area of parallelogram = 30 X 39.7
= 1191 cm²
The Area of Parallelogram whose side length is 30 cm is 1,190.952 square cm.
Given:
Side length = 30 cm
Using Trigonometry
tan 80 = P / Base
5.6712 = P / 7
P = 39.6984 cm
Using the formula for Area of parallelogram
= Base x height
= 30 x 39.6984
= 1,190.952 square cm.
Therefore, the area is 1,190.952 square cm.
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The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 8 t + 1.7 , where t is the time in hours. Find the composite function N ( T ( t ) ) : N ( T ( t ) ) = Find the time when the bacteria count reaches 8019. Time Needed = hours
Answers
Answer:
\(N(T(t)) = 1408t^2 - 385.6t - 105.52\)
Time for bacteria count reaching 8019: t = 2.543 hours
Step-by-step explanation:
To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:
\(N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40\)
\(N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40\)
\(N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1\)
\(N(T(t)) = 1408t^2 - 385.6t - 105.52\)
Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:
\(8019 = 1408t^2 - 385.6t - 105.52\)
\(1408t^2 - 385.6t - 8124.52 = 0\)
Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.
Name a linear pair.
Answers
Answer:
It is C. Linear pairs make a 180 degree turn. Hope this helps!
Step-by-step explanation:
Answer:
C. ∠GQI, ∠IQM
Step-by-step explanation:
linear pairs must add up to 180°
∠GQI and ∠IQM make a straight line which is 180°
a + b=c make (a) the subject with working
Answers
Step-by-step explanation:
a= c-b pls let me know if it is correct or not
Between x = 0 and x = 1, which function has a greater average rate of change than y = 3x
?
Answers
Answer:
x=1
Step-by-step explanation:
y=3x so just add 1+3=4 then add veriable y=4x
Eight committee members are meeting in a room that has twelve chairs. In how many ways can they sit in the chairs
Answers
Answer:
495 different waysStep-by-step explanation:
We will use the combination rule to solve this questions since it bothers selection. Combination has to do with selection.
If r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
If there are Eight committee members meeting in a room that has twelve chairs, the number of ways they can sit in the chair can be done in 12C8 number of ways.
12C8 = 12!/(12-8)!8!
12C8 = 12!/4!8!
12C8 = 12*11*10*9*8!/4*3*2*8!
12C8 = 12*11*10*9/4*3*2
12C8 = 11*10*9/2
12C8 = 11*5*9
12C8 = 495
Hence the committee can sit in the chairs in 495 different ways