Answer:
Step-by-step explanation:
height = 14tan(24°)
area = 0.5(base)(height)
Find the angle that triples the height.
tanθ = 3×14tan(24°)
θ = arctan(3×14tan(24°)) ≅ 53.2°
The base angle will be 53.3 degrees when the area gets treble.
What is isosceles triangle?A triangle with two sides of equal length is an isosceles triangle.
What are base angles?The angles that have the base as one of their sides are called base angles.
Formula for area of triangle[tex]Area = \frac{1}{2} bh[/tex]
Where,
b is the base of the triangle
h is the height of the triangle
According to the given question
We have,
Base angle of the isosceles triangle is 24 degrees.
Base of the isosceles triangle is 28 cm.
In triangle ABC
We have
BC = 28cm, BD = 14cm, AD = h and ∠ABD = 24 degrees
Now, in right angle triangle ABD
[tex]tan24 = \frac{h}{14}[/tex]
⇒ tan24 × 14 = h
Therefore,
Area of triangle ABC = [tex]\frac{1}{2}[/tex] × 28 × 14 × tan 24
Area of triangle ABC = 196tan24
Therefore, the base angles of an new isosceles triangle when the area get treble is given but with the same base by
Area of new isosceles = 3× area of triangle ABC
⇒ [tex]\frac{1}{2}[/tex]× 28 × tanθ × 14 = 3×196tan24
⇒tanθ = 3 × 0.4452
⇒ tanθ = 1.3356
⇒ θ = [tex]tan^{-1}(1.34)[/tex]
⇒ θ = 53.3 degrees
Hence, the base angle will be 53.3 degrees when the area gets treble.
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Camden invested $7,200 in an account paying an interest rate of 4.4% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $13,140?
The value of the account to reach $13,140 will take 14 years assuming no deposits or withdrawals are made .
What is compound interest?Compound interest is an interest accumulated on the principal and interest together over a given time period. The interest accumulated on a principal over a period of time is also accounted under the principal.
Formula of compound interest :[tex]A = P (1+ \frac{r}{100} )^{n}[/tex]
Where,
A = final Amount
P = initial principal
r = rate per annum
n = time in years
According to the question
Camden invested (P) = $7,200
Interest rate per month (r) = 4.4%
Amount to reach = $13,140
now , using Formula of compound interest
[tex]A = P (1+ \frac{r}{100} )^{n}[/tex] ere , n = n/12 (as concluding monthly wise )
Substituting the values
[tex]13140 = 7200 (1+ \frac{4.4}{100} )^{\frac{n}{12} }[/tex]
1.825 = [tex](1+ \frac{4.4}{100} )^{\frac{n}{12} }[/tex]
1.825 = [tex](1..044 )^{\frac{n}{12} }[/tex]
n ≈ 168 months (approx.)
n = 14 years (nearest year)
Hence, the value of the account to reach $13,140 will take 14 years assuming no deposits or withdrawals are made .
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Any one 100% kno these two answers
ratios into their simplest form a)35:56
Answer:
Reduced fraction: 58. Therefore, 35/56 simplified to lowest terms is 5/8
Answer:
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator. GCD of 35 and 56 is 7.
35 ÷ 756 ÷ 7.
Reduced fraction: 58. Therefore, 35/56 simplified to lowest terms is 5/8.
round 7.49 to the nearest tenth
Answer:
7.5
7.49 rounded to the nearest tenth is 7.5 because there is a 9 in the hundredths place.
After the Sutton family finished their meal at a local restaurant, the waiter brought them a check for $48.86. If Mrs. Sutton leaves a 20% tip, what amount of tip wages will the waiter receive?
What will the total meal cost?
How much should you tip a hairstylist, pizza delivery person, and taxi driver?
Answer:
58.23
Step-by-step explanation:
The amount of tip wages will the waiter receive will be $9.77. Then the total meal cost will be $58.63.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
After the Sutton family finished their meal at a local restaurant, the waiter brought them a check for $48.86. If Mrs. Sutton leaves a 20% tip. Then the amount of the tip will be
Tip = 20% of $48.86
Tip = 0.20 x $48.86
Tip = $9.772
Then the total meal cost will be
Total cost = $48.86 + $9.772
Total cost = $58.63
The amount of tip wages will the waiter receive will be $9.77. Then the total meal cost will be $58.63.
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HELP PLS DONT NEED TO DO THE PROVLEMS JUST HELP
Answer:
i have NO idea dud
Step-by-step explanation:
The school flagpole is 28 feet tall. How many yards is that?
Answer: the answer is 9.33---
Which is equivalent to the ratio 4:5?
A. 95: 100
B. 80: 100
C. 60: 100
D. 40: 100
E. 20 : 100
Answer:
B) 80:100
Step-by-step explanation:
80:100
/20 /20
4:5
B is the correct one
Find the value of x with the equation
Answer:
x=4
Step-by-step explanation:
SU=TR
x+1=2x-3
-x. -x
1=x-3
+3. +3
x=4
Find the distance between the points.
(7,9) and (-1,9)
Answer:
The distance is 8 between (7,9) and (-1,9)
Step-by-step explanation:
For:
(X1, Y1) = (7, 9)
(X2, Y2) = (-1, 9)
d=(−1−7)2+(9−9)2√
d=(−8)2+(0)2√
d=64+0√
d=6–√4
d=8
giving out 20 points for correct answer only answer if yk. thx hagd
The following table shows the number of hours some middle school students in two cities spend texting each week:
City A 9 27 17 24 21 12 25 25 18
City B 6 20 26 15 23 25 14 14 11
Part A: Create a five-number summary and calculate the interquartile range for the two sets of data.
Part B: Are the box plots symmetric? Justify your answer.
Answer:
the five number summary for city a is the following:
min- 9
q1- 17
median- 21
q3- 25
max- 27
Eighteen technicians in a cell phone repair shop are randomly selected to participate in a study comparing two screen repair techniques. They are randomly assigned one of the two techniques. The manager trains 9 technicians on one technique and trains the other 9 technicians on the second technique. He then records the number of screen repairs each technician does in one week. Which inferential statistical test would be most appropriate for this scenario?
A one-sample z-test
A paired t-test
A chi-square goodness-of-fit test
A one-sample t-test
A two-sample t-test
Answer:
a two sample t test
Step-by-step explanation:
The inferential statistical test that would be most appropriate for this scenario is a two-sample t-test option fifth is correct.
What is a t-test?A t-test is a hypothesis-testing technique for analyzing the means of one or two populations. A t-test can be used to see if a single group differs from a known value, if two groups differ from each other (an independent two-sample t-test), or if paired measurements show a significant difference.
Based on the information provided, there are two techniques, each with nine technicians. The sample sizes are tiny, in other words. Furthermore, the two samples are unrelated to one another. As a result, a two-sample t-test is appropriate.
Thus, the inferential statistical test that would be most appropriate for this scenario is a two-sample t-test option fifth is correct.
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-4Runner -2r+5 what is the answer
A school gymnasium is being remodeled. The basketball court will be similar to an NCAA basketball court, which has a length of 94 feet and a width of 50 feet. The school plans to make the width of the new court 45 feet. Find the perimeters of an NCAA court and of the new court in the school.
Answer:
Perimeter of NCAA court=288 feet
Perimeter of new court=259.2 feet
Step-by-step explanation:
We are given that
Length of NCAA court, l=94 feet
Width of NCAA court, b=50 feet
Width of new court, b'=45 feet
We have to find the perimeter of an NCAA court and new court in the school.
Perimeter of NCAA court=[tex]2(l+b)[/tex]
Perimeter of NCAA court=[tex]2(94+50)[/tex]feet
Perimeter of NCAA court=288 feet
When two rectangles are similar then the ration of their corresponding sides are equal.
Using the property
[tex]\frac{Perimeter\;of\;NCAA\;court}{Perimeter\;of\;new\;court}=\frac{Width\;of\;NCAA\;court}{Width\;of\;new\;court}[/tex]
[tex]\frac{288}{Perimeter\;of\;new\;court}=\frac{50}{45}[/tex]
Perimeter of new court=[tex]\frac{288\times 45}{50}[/tex] feet
Perimeter of new court=259.2 feet
The perimeter of the NCAA basketball ground is 288 feet, while the school basketball ground is 259.2 feet.
Given to us,
For NCAA basketball court,
Length, [tex]\bold {L_{NB}}[/tex] = 94 feet,
Width, [tex]\bold {W_{NB}}[/tex] = 50 feet,
For School basketball court,
Width, [tex]\bold {w_{school}}[/tex] = 45 feet,
As discussed in the question, school basketball court will be similar to an NCAA basketball court. Thus, they will be in ratio,
[tex]\bold {\dfrac{L_{NB}}{W_{NB}} = \dfrac{l_{school}}{w_{school}}}[/tex]
Substituting the value,
[tex]\bold {\dfrac{94}{50} = \dfrac{l_{school}}{45}}[/tex]
[tex]\bold{ l_{school} = \dfrac{94\times 45}{50}}[/tex]
[tex]\bold{ l_{school} = 84.6 }[/tex]
We know that, perimeter of rectangular = 2(length+width),
[tex]\begin{aligned}Perimeter_{NB}&= 2(length+width)\\&= 2(94+50)\\&= 288 \end{aligned}[/tex]
[tex]\bold{\begin{aligned}Perimeter_{school}&= 2(length+width)\\&= 2(84.6+45)\\&= 259.2\end{aligned}}[/tex]
Hence, the perimeter of the NCAA basketball ground is 288 feet, while the school basketball ground is 259.2 feet.
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Use the functionſ to answer the question. f () = 3x2 - 7x - 32 What is the value of f (-4)? A. -52 B. -12 O c. 44 D. 140 +
[tex]f{x} = 3x2 - 7 x - 32 = [/tex]
Step-by-step explanation:
step 1. please write it f(x) = 3x^2 - 7x -32
step 2. f(-4) = 3(-4)^2 -7(-4) - 32
step 3. f(-4) = 48 + 28 - 32
step 4. f(-4) = 44.
Checkpoint
Which ratios are equivalent to the given ratio?
9:36
Select each correct answer.
1:4
2 to 8
4/1
12 to 3
18/72
in the diagram, what is the measure of
Answer:
your question is incomplete
Step-by-step explanation:
ehem
Answer: I need a question to answer
Step-by-step explanation:
Pls help ASAP if you can
Does coordinate a or coordinate b represent a greater number?
(0,4)
(6, b)
(0,0)
(a,0)
Answer:
A is correct.
Step-by-step explanation:
Answer:
BTS YA"LL
Step-by-step explanation:
BTS BTS BST BST SBTS BTS IS THE CURE
Match each equation to the line of best fit that it models.
Where are the the equations?
A road is
4/5
of a mile long. A crew needs to repave 2/5
of the road. How long is the section that needs to be repaved?
Write your answer in simplest form.
Answer: 20/10
Step-by-step explanation:
Take (calculate) 4/5 of 2/5 mile:
4x5= 20
---- * ---- = 20/10
2x5= 10
The section that needs to be repaved is 1/2 of a mile.
What is a fraction?Fractions represent the parts of a whole or collection of objects.
A fraction has two parts. The number on the top of the line is called the numerator and the number on the top of the line is called the denominator.
Now it is given that,
Length of road = 4/5 of a mile
Road needs to repave = 2/5 of the road
Thus, road needs to repave = 2/5 of 4/5
⇒ road needs to repave = (2*4)/(5*5)
⇒ road needs to repave = 10/20
or, road needs to repave = 1/2
Thus, the section that needs to be repaved is 1/2 of a mile.
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2 kilometers to 72 meters write each ratio in simplest form
Hi there!
1:36
1.Find common denominator:
[tex]2*2/72*2[/tex]
Commonest denominator: 2
2.Divide the two terms:
[tex]2*2=1/72*2=36[/tex]
3.Convert into rate form:
[tex]1,36=1:36[/tex]
This means, 2 kilometers to 72 meters simplest form is 1:36.
If a man were to sell his T.V set for 7200, he would have lost 25%. For what price must he sell it to
Answer:
Step-by-step explanation
S.P of a t.v = rs 7200
Loss % = 25%
Therefore, C.P = S.P (100/100-loss)
=7200(100/100-25)
=7200 x 100/75
=9600
So,now C.P = 9600
Profit% = 25%
Therefore, S.P = C.P (100+profit/100)
=9600(100+25/100)
=9600 x 125/100
=12000
So,the price he should sell to gain 25%
=12000
Hope it helps...!!!
Find the value of x. Round to the nearest tenth.
Answer:
rounded to nearest 10th is 30
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!
Answer:
9
Step-by-step explanation:
9x9=81
Date:
.
'. Due to coxid-19 pandimec, the Jacinto
Family donated 180 pos Face Shield
and the aguinaldo family also don
213 pcs of pace shield to the front
liner, If a face shield cost 8m pesos
How much
the total cost of
donation.
tone soola
Answer:
It's 3,114: )
Step-by-step explanation:
Because if you multiply the 8m to 180 it will remain to 1,440 plus additional 1,704 so it will be 3,114, the main answer
Solve the inequality.
|5 - 2x|> 14
Answer:
x < −9/2
or
x > 19/2
I hope this helps <333
I need help I don't understand this
Answer:
Proportional
Step-by-step explanation:
The Bags of Screws (input) is multiplied by 5 to get the Price (output) each time, so the situation is proportional. If one or two numbers were not multiplied by 5 to get the Price (output), the situation would not be proportional.
Hope it helps!
The anticoagulant warfarin is often used as a pesticide against house mice, Mus musculus. Some populations of the house mouse have acquired a mutation in the vkorc1 gene from hybridizing with the Algerian mouse, M. spretus (Song et al. 2011). In the Algerian mice, this gene confers resistance to warfarin. In a hypothetical follow-up study, researchers collected a sample of house mice to determine whether presence of the vkorc1 mutation is associated with warfarin resistance in house mice as well. They fed warfarin to all the mice in a sample and compared survival between the individuals possessing the mutation.
a. Identifiy the two variables measured in the study and indicate which is the explanatory and which is the response variable.
i. Explanatory:
ii. Response:
b.Identify the scales on which each of the two variables is quantified (nominal, ordinal, inteval, ratio).
c. What do you think was the intended target population for the study? Why?
d. Do you consider the follow up study to be a manipulative experiment or an observational experiment? Explain.
e. Do you think the researchers used a random sample? Explain.
Solution :
Response variable is the variable whose value is to be predicted or the value is influenced. It is also known as the dependent variable. While the variable which affects the values and is used for the prediction is known as the explanatory variable or the independent variable.
i. The explanatory variable in the study is the Vkorc I mutation.
ii. The response variable in the study is the Warfarin resistance.
b). The explanatory variable which comes under the nominal scale in this study is the Vkorc I mutation.
While the response variable or the independent variable that comes under the interval scale in the study is the Warfarin resistance.
c). The group of the individuals in this study is called as population. The target population in the study is the house mouse which is required as the mutation in Vkorc 1 gene from the hybridizing with Algerian mouse.
d). The study is a manipulative experiment as the changes that have already introduced in house mice and the treatments are under control.
e). No in this study the researcher did not use any random sample.
Given the function h(x) = x^2+2x -2 determine the average rate of change of the
function over the interval —7≤x≤2
Answer: Good luck my friend I have no idea
Step-by-step explanation:
how many different three digit numbers can be formed using the digits 9 3 4 7 and 6 assume the number can be used more than once?
Answer:
60
Step-by-step explanation: