Answer:
Step-by-step explanation:
The experimental probability of getting a Twix is 3/5 or 60%.
Mr. Argo went to dinner with a friend at Outfront Steakhouse. His dinner cost $40, and he left a 20% tip. What was his total cost?
Answer: 48$
Step-by-step explanation: well 20% of 40$ is 8$ so the total cost is 48$ that he payed
Answer:
$48.00
Step-by-step explanation:
Question 4(Multiple Choice Worth 2 points)
(Ratios MC)
In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting
average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far,
Jana has hit the ball 7 times out of 10 attempts. Tasha has hit the ball 10 times out of 16 attempts. Which player has a ratio that
means they have a better batting average?
O Tasha, because she has the lowest ratio since 0.7 < 0.625
O Tasha, because she has the highest ratio since
56 50
80 80
O Jana, because she has the highest ratio since 5650
80 80
O Jana, because she has the lowest ratio since 0.7 < 0.625
The correct answer is Tasha, because she has the highest ratio since 0.625 > 0.7.
What is ratio?Receive is a comparison between two or more quantities expressed as a fraction or a set of relative quantities it is used to compare the size of one number to another or the compare changes overtime ratio can be expressed in word as fraction or decimal receiver in important concept in mathematics used to analyse data and solve problem.
Tasha has hit the ball 10 times out of 16 attempts, which means her batting average is 0.625. Jana has hit the ball 7 times out of 10 attempts, which gives her a batting average of 0.7. Therefore, Tasha has the better batting average.
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Which of these is NOT a way to show that two figures are congruent?
If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.
What is Triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
What is the condition to be congruent?If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
here, we have,
Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.
In Δ PQR and ΔXYZ, as shown in figure,
we can identify that PQ = XY, PR = XZ,
and QR = YZ
and ∠P = ∠X,
∠Q = ∠Y and ∠R = ∠Z.
Then we can say that Δ PQR ≅ ΔXYZ.
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The price of a phone is decreased by 19% and now is $319.14. Find the original price
The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.
what is percentage ?In arithmetic, a percentile is a number or statistic that is given as a fraction of 100. Occasionally, the acronyms "pct.," "pct," nor "pc" are also used. But it is broadly classified into the following by the cent sign, "%." The % amount has no characteristics. Percentages are essentially integers when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it close to it. For instance, you score a 75% if you properly answer 75 so out 25 pages on a test (75/100). Divide the money by the whole and multiply the results by 100 you compute percentages. The formula for calculating the percentage is (value/total) x 100%.
given
Put this together using the conditions given: 319.14 / (1- 19%)
Determine the total or difference: 319.14 / 0.81
Diminish the fraction: 394
Response: 394
The cost of a phone has lowered by 19% to $319.14 from its original $394 pricing.
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a video has 42 thumbs down what integer represents its score in points
Answer: -42
Step-by-step explanation:
Please help!!! Have to show work
Step-by-step explanation:
It is explained in the figure above.
چار
is constructed so MP = and PN = y.
M
1
K
D
T
4
O
Complete part A of the proof.
5
Part A: Prove a² = c.x
P
Below is the proof of the Pythagorean theorem, that a² + ² = c². The proof is divided into
three parts, where the title of each part indicates its main purpose.
Statement
ZNOM
ZOMN
C
AMNO AMOP
Pick ratio v
a² = c.x
Show the steps.l
ZOPM
PMO
y
[Show the steps.
Part B: Prove 6² = C. Y
b
#
N
Reason
All right angles are congruent.
Part C: Prove a² + b² = c²
Pick reason
Pick criterion ✓
Lengths of corresponding pairs of sides of similar triangles
have equal ratios. (3)
similarity
Multiply both sides by a 2. (4)
21
Stuck? Review related articles/videos or use a hint.
Report a problem
By the given explanation,
It is proven that in given right angle triangles a² = cx.
Congruent angles:The angles that are identical to each other are known as Congruent angles. The measure of these concurrent angles is always equal to each other.
They can be acute, obtuse, exterior, or interior angles because the congruence of angles is unaffected by the type of angle. As we know a right angle is 90° all right angles are congruent angles.
Here we have
Two right-angle triangles MOP and MNO
Measurements of Δ MNO side are a, b, and c is the hypotenuse
Measurements of Δ MOP sides are a, x, and OP is the hypotenuse
Here we need to prove that a² = c x
We can prove its as follows
As we know all right angles are concurrent
Statement Reason
=> ∠NOM ≅ ∠OPM [ ∵ right-angles are concurrent ]
=> ∠OMN≅ ∠PMO [ ∵ Common angle ]
=> ΔMOP ~ ΔMNO [ By Angle - Angle - Angle criteria ]
Since ΔMOP ~ ΔMNO
=> a/x = c/a [ ratio of the corresponding side ]
=> a² = cx [ Corss multiplication ]
Therefore,
It is proven that in give right angle triangles a² = cx.
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The copay to see a specialist who is a network provideThe copay to see a specialist who is a network provider was $ . Her father needed outpatient surgery, and he found a network provider who could help him. After he paid a deductible of $1,000, he paid 20% coinsurance on a surgery that cost $21,000. Therefore, he paid only $ for the surgery. The total amount Gina’s dad paid for his care was $ .r was $
The amount paid for the surgery is given as follows:
$4,000.
The total amount Gina’s dad paid for her care was of:
$5,000.
How to obtain the amounts?The amounts are obtained applying the proportions in the context of this problem.
The coinsurance of 20% means that Gina's dad pays only 20% of the surgery's price after the deductible.
The deductible is given as follows:
$1,000.
Hence the price of the surgery after the deductible is of $1,000, and the amount paid for the surgery is given as follows:
0.2 x $2000 = $4,000.
Considering the deductible, the total amount paid is given as follows:
1000 + 4000 = $5,000.
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Answer: $20, $4,000, $5,020
Step-by-step explanation:
i got it right
Consider statmet
None of the members of the club can vote.
For each statement below, determine whether it is a negation of the given statement.
Every member of the club can vote. Yes or No
At least one member of the club cannot vote. Yes or No
Some members of the club can vote. Yes or No
At least one member of the club can vote. Yes or No
The negation of the given statement
Some members of the club can vote.At least one member of the club can vote.What is Negation of statement?In Mathematics, the negation of a statement is the opposite of the given mathematical statement.
Given:
Statement: None of the members of the club can vote.
We have to focus on the word "None" and the negation of word None is Some or at least.
So, Every member of the club can vote is not negation of the statement.
and, At least one member of the club cannot vote is not negation of the statement.
and, Some members of the club can vote is negation of the statement.
and, At least one member of the club can vote is negation of the statement.
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Ada left home for school at 6:50am and got to school at 7:15am.
How many minutes does it take him to get to school?
Answer:
25 min
Step-by-step explanation:
60-50=10
10+15=25
Step-by-step explanation:
from 6:50am to reach 07:00 it takes 10min and he reach at 07:15am means another 15 min added10min + 15 min=25minWrite down the complex number that has a real part 0 and an imaginary part ✓11
Answer:
0 + 11i
Step-by-step explanation:
A complex number is a number in the form a + bi, where a is the real part and b is the imaginary part. In this case, the real part is given as 0 and the imaginary part is given as 11. Therefore, the complex number is:
0 + 11i
where 0 is the real part and 11i is the imaginary part.
CAN SOMEONE HELP I WILL GIVE BRAINLIST IT'S DUE TODAY :(
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
0.25
0.35
0.50
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is orange.
A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
The probability of landing on yellow is less than the probability of landing on blue.
The probability of landing on orange is equal to the probability of landing on yellow.
The probability of landing on purple is equal to the probability of landing on blue.
List the sample space for rolling a fair eight-sided die.
S = {1}
S = {8}
S = {1, 2, 3, 4, 5, 6}
S = {1, 2, 3, 4, 5, 6, 7, 8}
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
ulia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = 1, 2, 3
Sample space = 1, 2, 3, 4, 5, 6
Sample space = lemon-lime, watermelon, grape
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Answer:
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.23
If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Likely
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
90%
A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.
Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4
Determine the experimental probability of drawing a spade.
0.15
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is red.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple.
Sections 2 and 3 are yellow.
Sections 4, 5, and 6 are blue.
Section 7 is orange.
Which statement about probability is true?
The probability of landing on orange is greater than the probability of landing on purple.
List the sample space for rolling a fair eight-sided die.
S = {1, 2, 3, 4, 5, 6, 7, 8}
There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.
Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11
Likely
Equally likely and unlikely
Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Julia had a bag filled with gumballs. There were 1 lemon-lime, 2 watermelon, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = lemon-lime, watermelon, watermelon, grape, grape, grape
In ΔHIJ,
m
∠
�
=
(
�
−
1
)
∘
m∠H=(x−1)
∘
,
m
∠
�
=
(
2
�
+
5
)
∘
m∠I=(2x+5)
∘
, and
m
∠
�
=
(
7
�
+
6
)
∘
m∠J=(7x+6)
∘
. What is the value of
�
?
x?
Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
If in ΔHIJ, m∠H = x - 1, m∠I = 2x + 5, and m∠J = 7x + 6.
The value of x is 17.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
Example:
Triangle ABC:
m∠A + m∠B + m∠C = 180
here, we have,
We have,
ΔHIJ
m∠H = x - 1
m∠I = 2x + 5
m∠J = 7x + 6
We know that,
The sum of the angles of the triangle is 180 degrees.
m∠H + m∠I + m∠J = 180
(x - 1) + (2x + 5) + (7x + 6) = 180
x - 1 + 2x + 5 + 7x + 6 = 180
10x + 10 = 180
Take 10 common.
10 (x + 1) = 180
Divide both sides by 10.
x + 1 = 180/10
x + 1 = 18
Subtract 1 on both sides.
x = 18 - 1
x = 17
Thus,
If in ΔHIJ,
m∠H = x - 1, m∠I = 2x + 5, m∠J = 7x + 6.
The value of x is 17.
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The length-to-width ratio of a television screen is 4 to 3. Mya bought a television with a length of 32 inches. What is the width of the television?
a. 16 inches
b. 24 inches
c. 30 inches
d. 42 inches
⇒SOMONE I NEED HELP ASAP
Which value is incorrect? 1, 2, 4, 6, 42, 21, 14, or 7?
Answer:
42?
Step-by-step explanation:
Homework 1 triangle mid segments
The triangle mid-segments will be the two opposite or adjacent sides of a triangle.
What is the triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angle of triangle = 180
A line connecting the midpoints of two of a triangle's sides is known as the midsegment. There are always three midsegments in a triangle. The midsegment between any two sides of a triangle is parallel to and half the length of the third side, according to the Triangle Midsegment Theorem, often known as the midsegment theorem.
A midsegment of a triangle is a line segment that joins the midpoints or center of two opposite or adjacent sides of a triangle.
Hence The triangle mid-segments will be the two opposite or adjacent sides of a triangle.
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Complete question:
Define the triangle mid segments.
12. The circle graph represents the jobs at a digital
animation company with 1540 employees
How many more story artists are there
than interns?
Answer:
231
Step-by-step explanation:
From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number
In actual values
Number of story artists = 1540 x 20% = 1540 x 20/100 = 308
Number of interns = 1540 x 5% = 1540 x 5/100 = 77
Difference = 308 - 77 = 231
X is the midpoint of VW. Complete the proof that you UVX = UWX
The options for VX = WX additive property of length, all right angles are congruent, definition of angle, bisector, definition of equilateral triangle, definition of midpoint, reflexive property of congruence, reflexive property of equality, substitution, transitive property of congruence, transitive property of equality, vertical angle, theorem
The answer choice for UX = UX additive property of length, all right angles are congruent, definition of angle, bisector, definition of equilateral triangle, definition of midpoint, reflexive property of congruence, reflexive property of equality, substitution, transitive property of congruence, transitive property of equality, vertical angle theorem
The answer choices for UVX = UWX are CPCTC definition of congruent SAS SSS
I do not need you to show your work , I just need the answers.
Note that the statement that completes the above proof is "Definition of Angle Bisector"
What does the Angle Bisector Theorem Say?
An angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.
The angle bisector theorem asserts that if a point is on an angle's bisector, the point is equidistant from the angle's sides. The opposite of the angle bisector theorem asserts that if a point is in the interior of an angle and equidistant from the sides, it sits on the angle's bisector.
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DIRECTIONS: Use this information to answer Parts A and B. −5=−y−3x Question 1 Part A Write the equation in slope-intercept form. Enter the correct equation in the box.
Answer:
y=3x+5
Step-by-step explanation:
tjrjrkrlrorlp3ñ34mrmrr
Answer:
y=mx+c
Step-by-step explanation:
-5/y=3x meaning that y=mx+c, hope this helps :)
find the domain and range of the relation
{(22,21), (5,-16), (20, -24), (-17,4), (-9,2)}
What is the estimated product? 93 x .26
Answer:
2418
Step-by-step explanation:
Step 1: Setup
Set up your multiplication problem like this:
9 3
x 2 6
Step 2: Multiply
3 x 6 = 18. Put 8 below the line and 1 as a reminder on top:
1
9 3
x 2 6
8
Step 3: Multiply
6 x 9 = 54. Take 54 and add 1 from the previous step to get 55. Enter 55 at the bottom:
9 3
x 2 6
5 5 8
Step 4: Add 0
Enter a 0 at the bottom right as a place holder, because you now move over one digit:
9 3
x 2 6
5 5 8
+ 0
Step 5: Multiply
2 x 3 = 6. Put 6 below the line and 0 as a reminder on top:
0
9 3
x 2 6
5 5 8
+ 6 0
Step 6: Multiply
2 x 9 = 18. Take 18 and add 0 from the previous step to get 18. Enter 18 at the bottom:
9 3
x 2 6
5 5 8
+ 1 8 6 0
Step 7: Add to get an answer
Add up the bottom two numbers (558 + 1860 = 2418) to get the answer:
9 3
x 2 6
5 5 8
+ 1 8 6 0
= 2 4 1 8
The bottom line is the answer. Therefore, 93 times 26 equals:
2418
A block of wood has a volume of 270 cubic centimeters and weight 0.280 kilograms. what's its density? will it float in water?
The destiny of the block of wood is _______ 9/cm³
The density of the block of wood is 1.04g/cm³
What is density ?Density is the ratio of the mass of an object to its volume. It is a scalar quantity and it is measured in g/cm³ or kg/m³.
Density = mass/volume
Mass = 0.280kg = 0.280 × 1000 = 280g
volume = 270cm³
Density = mass/volume
Density = 280/270
= 1.04g/cm³
Because the density of the object is just slightly higher than the density of water which is 1g/cm³
, therefore the object will float in water.
For an object to float in water, it must be equal to the weight or density of the water
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-The diagram shows a triangular prism.
-The base, ABCD, of the prism is a square side 14cm.
-Angles ABE and CBE are right angles.
-Angle EAB =32 degrees
-M is the point on DA such that DM : MA = 3:4
-Calculate the size of the angle between EM and the base of the prism.
-Give your answer to 1 decimal place.
The size of the angle between EM and the base of the prism is equal to 28.5°.
How to calculate the size of the angle between EM and the base of the prism?First of all, we would determine side length MA based on the ratio between side lengths DM and MA as follows;
DM : MA = 3 : 4
Total side parts = 14 cm
(3 + 4) parts = 14 cm
7 parts = 14 cm
1 part = 2 cm
Therefore, side length MA = 2 × 4 = 8 cm.
By applying Pythagorean's theorem to right triangle MAB, we have the following:
c² = a² + b²
Where:
a, b, and c represents the side lengths of a right triangle.
c² = 8² + 14²
c² = 260
c = √260
c = 16.1245 cm.
By applying tan trigonometry to right triangle AEB, we have:
tanθ = opposite/adjacent
opposite = tan32° × 14
opposite = 8.7482 cm.
By applying tan trigonometry to right triangle EMB, we have:
tanθ = opposite/adjacent
θ = tan⁻¹(opposite/adjacent)
θ = tan⁻¹(8.7482/16.1245)
θ = tan⁻¹(0.5425)
θ = 28.5°.
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Please help me answer this question
Answer:
Improper: 7/4
Mixed: 1 3/4
Step-by-step explanation:
Each little pie slice shape is a fourth (there are 4 in one circle)
Count them. In total there are 7. There are seven pie slices. There are seven fourths.
7/4
This is called an improper fraction because the bigger number is on top and the smaller number is below.
If you consider one circle to be a "whole" then you have one whole and 3/4.
1 3/4
This is a mixed number because it has a whole part and a fraction part.
Please solve
-5|x+3|-3=-15
I got the x + 3 =12/5 part but I don’t know what to do after that
please help me including the steps to get the next part.
Thank you!
To solve the equation, you can use the following steps:
Start by isolating the absolute value expression on one side of the equation:
-5|x+3| = 18
Now, since the absolute value is positive, it has two solutions:
x + 3 = -18 or x + 3 = 18
Solving for x in each case:
x = -21 (if x + 3 = -18) or x = 15 (if x + 3 = 18)
So the two solutions to the equation are x = -21 and x = 15.
using numerators that are even numbers, write two different substraction that each have a different of 1
The two different subtraction that each have a different of 1 are 1/2 and 1/2
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25.
To solve the problem we must know about fractions.
The number should be odd, therefore, the number should be 1, 3, 5, 7, etc.
1 9/8 - 5/8 = 4/8 = 1/2
2 7/8 -5/4 = 2/4 = 1/2
These for the two different subtraction that each have a different of 1
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find the number of degrees moved by the minute hand of a clock in the give amount of time 2/3 hour ??
The number of degrees moved by the minute hand of a clock in 2/3hours is 240°
What is angle at a point?Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.
The hand of minute will move 360° to complete an hour.
If a full round will make angle at a point. Which is 360°
Therefore 2/3 of an hour will give an angle of 2/3 of 360°
= 2/3 × 360
= 240°
therefore the number of degrees moved by the minute hand in 2/3 hour is 240°
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Given the function of f(x)
To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).
[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]
How to solve the given equation?A relationship between a number of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs that are individually connected to exactly one output. There are two domains or scopes for each function. f is typically used to represent functions (x). The input is x. Y = f is a common way to represent the function (x).
To evaluate [tex]f(g(3))[/tex], we need to first evaluate g(3), then evaluate f(g(3)).
[tex]$$g(3)=7 \cdot 3^2+6 \cdot 3+2=65$$[/tex]
So
[tex]f(g(3))=f(65)=\frac{1}{2} \cdot 65-4=\frac{1}{2} \cdot 65-4=28[/tex]
To evaluate [tex]g(f(8))[/tex], we need to first evaluate [tex]f(8)[/tex], then evaluate [tex]f(8)[/tex].
[tex]f(8)=\frac{1}{2} \cdot 8-4=2\\\\g(f(8))=g(2)=7 \cdot 2^2+6 \cdot 2+2=46\\g(f(8))=46[/tex]
[tex]g\left(\frac{1}{8}\right)=7\left(\frac{1}{8}\right)^2+6 \cdot \frac{1}{8}+2=\frac{121}{8}+\frac{3}{2}+2=\frac{135}{8}[/tex]
[tex]f\left(g\left(\frac{1}{8}\right)\right)=f\left(\frac{135}{8}\right)=\frac{1}{2} \cdot \frac{135}{8}-4=\frac{135}{16}-4=\frac{135-64}{16}=\frac{71}{16}\\f\left(\frac{1}{2}\right)=\frac{1}{2} \cdot \frac{1}{2}-4=-4[/tex]
So,
[tex]$$f\left(f\left(\frac{1}{2}\right)\right)=f(-4)=\frac{1}{2} \cdot-4-4=-8-4=-12$$[/tex]
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Use the definition of continuity and the properties of limits to show that the function is continuous at x = 3.
The given function is continuous at x = 3, RHL = LHL = F(3)
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = x² + 5(x - 2)⁷
To check whether it is continuous at x = 3
First taking LHL,
[tex]\lim_{h \to \00 } F(x)[/tex]
[tex]\lim_{h \to \00 }[/tex] (3-h)² + 5(3 - h - 2)⁷
⇒ 9 + 5
⇒ 14
Now, taking RHL
[tex]\lim_{h \to \00 }[/tex] (3+ h)² + 5(3 + h - 2)⁷
⇒ 9 + 5
⇒ 14
The value at x = 3
F(3) = 3² + 5(3 - 2)⁷
= 14
Hence Proved, RHL = LHL = F(3)
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Help 50 points (show your work)
The solution to the above problems are given as follows:
7) m∠A = 102°. m∠B = 102.°
8) ∠QSR = 59.6°
9) ∠ADC = 55°
What is the rationale for the above solutions?7) Since both angles are vertical, it, therefore, means they are congruent. Ths,
4x + 6 = 7x-66; collect like terms
6+66 = 7x -4x
72 = 3x
x = 72/2
Thus,
x = 24
Plugging in the value of x back into the expressions, we have:
m∠A = 4x + 6
= 4(24) + 6
= 96+6
= 102°
Thus, m∠A = 102.
Since both angles are congruent, that means m∠B is also 102°
8) To find ∠QSR, we need to find x. Note that Angle on a Straight line sums up to 180°. Thus,
4x-8+34+72-x = 180
4x - 8 + 34 + 72 - x = 180
5x + 98 = 180
5x = 82
x = 16.4
So the solution is x = 16.4.
Since ∠QSR = 76-x
∠QSR = 76-16.4
Thus,
∠QSR = 59.6°
9) Applying the same rule (Angles on a straight line to the above problem, we can state that:
2x+1 + (x-7) = 180°;
To solve for x, we can simplify both sides of the equation and then isolate x:
2x + 1 + x - 7 = 180
3x - 6 = 180
3x = 186
x = 62
So the solution is x = 62.
Thus, ∠EDF = 62 - 7
= 55°
since ∠EDF and ∠ADC are opposite angles, and opposite angles are congruent,
∠ADC = 55°
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