Using the Pythagorean Theorem, the altitude to side c has a length of 11.3 inches.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
To find the altitude relative to side c, we bisect this side, which cuts it's length into half(now of 4 inches), forming a right triangle in which:
The altitude is the other leg.The side of 12 inches is the hypotenuse.Hence:
[tex]x^2 + 4^2 = 12^2[/tex]
[tex]x = \sqrt{12^2 - 4^2}[/tex]
x = 11.3 inches.
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If the price of a bicycle is increased by 9.09%,
then by 8.33% and then by 7.7%, the price
becomes Rs. 1,274. What is the original price
of the bicycle?
Answer:
Rs 1000.97
Step-by-step explanation:
x = original price
new price = x (1.0909)(1.0833)(1.077) = 1274
x = Rs 1000.97
Factorize x^2+√4x+2x+2
Answer:
x^2+4x+2
Step-by-step explanation:
among 175 students 100 study math 70 study phisycs 46 study chemistry 30 study math and phisycs 28 study math and chemistry 23 study phisycs and chemistry and 18 study all three how many study only one subject
The number of people that studied only one subject is 108.
What is a set?A set is a collection of well-defined objects.
Objects in a set are called elements or members of a set.
Set notation or the use of Venn diagrams are the methods used to solve set problems.
Analysis:
let P = physics
C = chemistry
M = mathematics
n(P) = 70
n(C) = 46
n(M) = 100
n(M n P n C) = 18
n(M n P) = 30
n(M n P n C') = 30 - 18 = 12
n(M n C) = 28
n(M n C n P') = 28 - 18 = 10
n(P n C ) = 23
n(P n C n M') = 23 - 18 = 5
n(P n C' n M') = 70-(12+18+5) = 70 - 35 = 35
n(P' n C n M') = 46-(18+5+10) = 46-23 = 13
n(P' n C' n M) = 100 - (10+18+12) = 100 - 40 = 60
people that studied only one subject are = 35 + 13 + 60 = 108
In conclusion 108 students studied only one type of subject.
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Can I please get a full answer? Thanks a bunch!
Consider a triangle ABC like the one below. Suppose that A=57°, C=73°, and b = 13. (The figure is not drawn to scale.) Solve the triangle. Round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".
By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.
How to determine the missing variables of a triangle
In this triangle we know the length of a side (b = 13) and the measure of two adjacent angles (A = 57°, C = 73°). First, we determine the measure of the missing angle by using triangles properties:
B = 180° - 57° - 73°
B = 50°
Lastly, we determine the missing lengths by the law of the sines:
[tex]a = 13 \times \frac{\sin 57^{\circ}}{\sin 50^{\circ}}[/tex]
a ≈ 14.232
[tex]c = 13 \times \frac{\sin 73^{\circ}}{\sin 50^{\circ}}[/tex]
c ≈ 16.229
By using triangle properties and the law of the sines twice, we find that the missing angle is 50° and the missing lengths are 14.232 and 16.229, respectively.
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please solve this question please
Answer:
a) 57
b) 19.476
c) 1.106 (rounded)
Step-by-step explanation:
a) note: the very first step here is to find the number of people of age 21 which is found through subtraction. We have a total of 250 people, and we currently have data on 193 (64 + 60 + 69) people. This means there are (250 - 193 = 57) 57 remaining people of age 21.
The first thing we're trying to find here is the mean, which we sometimes refer to as the average, of this data set.
To find the mean, we add all values together and then divide by the number of values we've combined.
We could write out 18 + 18 + 18... sixty-four times, and then to the same thing for 19's, but that would take a while. So, we can find this value through multiplication (remember, multiplication is the same thing as repeated addition).
18 × 64 = 1152
19 × 60 = 1140
20 × 69 = 1380
21 × 57 = 1197 *see above
Now, we find the sum of our values added together:
Now, we know we have 250 values, so we will divide 4869 by 250:
4869 / 250 = 19.476
So, the mean of this sample is 19.476
Now, we are finding the standard deviation, which is found through the formula:
∑ (x - x^(line over x) ) ²
√ _______
n - 1
(this is hard to write on this website sorry)
find difference between each value and mean (that's what "x - x^(line over x)" is)
18 - 19.476 = -1.476
19 - 19.476 = -0.476
20 - 19.476 = 0.524
21 - 19.476 = 1.524
square each difference: (that's what " (x - x^(line over x))² " is)
now, we need to add up our squared values. But first, we must account for how many of each value there are
now, let's add up our squared values: (that's what "∑" is )
we now need to divide this number by n - 1 (we have 250 samples, so we need to divide by 250 - 1 (249) to find our variance)
now, we find our standard deviation by taking the square root of the variance that's what the "√" is )
we can round this number to:
1.106 (or any other rounded decimal place, I did it this way to match our previous answer)
So, the standard deviation of this set is 1.106 (rounded)
hope this helps! have a lovely day :)
You and your classmates create 18 watercolor paintings to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the watercolor paintings, you need to sell each of the watercolor paintings for $2.25. When transporting the watercolor paintings to the auction, one of your parents accidentally drops four of the watercolor paintings in the street and they are run over by a garbage truck. What is the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials?
Using proportions, it is found that the new minimum price you need to set for the remaining watercolor paintings in order to pay for the materials is of $2.89.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To pay for the materials, you need to sell 18 paintings at $2.25 each, hence the total is:
T = 18 x 2.25 = $40.5.
If you lose four paintings, you will sell 14, and still need to make $40.5, hence the price will be of:
P = $40.5/14 = $2.89.
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Kenji earned the test scores below in English class
79, 91, 93, 85, 86, and 88
After his next test, his Mean and Median scores both change to 88.
How much does he earn on this test?
Please help me!!
The mean is 87 and median is 86.
What is mean and median?The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.
The median is the middle value in a list ordered from smallest to largest.
Given:
79, 91, 93, 85, 86, and 88
So,
79+85+86+88+91+93/6 = 87
and, the median
79, 85, 86, 88, 91, 93
median = 86
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can somebody please explain question (i) and (ii) to me
hey buddy, if u attach your question to this we can help you to find an answer for your question.
☆...hope this helps...☆
_♡_mashi_♡_
Choose the equation for the graph.
V
1
a) y = 2x - 3| +1
b) y = −2|x - 3| +1
c) y = 2x - 3|-1
d) y = −2|x + 3| − 1
e) y = 2x + 3| +1
Answer: e
Step-by-step explanation:
The vertex is at (-3, 1).
The x coordinate being -3 eliminates a, b, and c.The y coordinate being 1 eliminates d.This leaves e.
Two lines, A and B, are represented by the equations given below:
Line A: y = x − 6
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(−5, −11), because the point satisfies both equations
(−5, −11), because the point does not lie on any axis
(−3, −5), because the point satisfies one of the equations
(−3, −5), because the point lies between the two axes
The solution to the system of equations (−3, −5)
We have given that,
Two lines, A and B, are represented by the equations given below:
Line A: y = x − 6
Line B: y = 3x + 4
Line A
y = x - 2
Line B
y = 3x + 4
If we equate those 2 equations
x - 2 = 3x + 4
2x = -6
x = -3
y = -5
So the answer is
(−3, −5), because the point satisfies both equations.
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What is the 25th term given a₁ = 8 and r = 2?
Answer:
134217728
Step-by-step explanation:
The geometric sequence formula is:
[tex]\displaystyle{a_n = a_1r^{n-1}}[/tex]
We know that [tex]\displaystyle{a_1=8}[/tex] and [tex]\displaystyle{r=2}[/tex], we also want to find the 25th term, substitute n = 25:
[tex]\displaystyle{a_{25}=8\cdot 2^{25-1}}\\\\\displaystyle{a_{25}=8\cdot 2^{24}}\\\\\displaystyle{a_{25}=134217728}[/tex]
Therefore, the 25th term of sequence is 134217728
I'm comfused on this
Answer:
Step-by-step explanation:
can you show part a nd b for a better understanding of the question
Choose what the expressions below best represent within the context of the word problem.
The tens digit of a number is twice the ones digit. The sum of the digits in the number is 12. What is the number?
x represents
the tens
digit
2x represents
the tens
digit
By solving a system of equations we will see that the two-digit number is 84.
Which expression best represents the word problem?
"The tens digit of a number is twice the ones digit"
"The sum of the digits is 12".
A two-digit number can be written as:
a*10 + b
Where a is the tens digit and b is the ones digit.
The word problem can then be written as:
a = 2*b
a + b = 12
So we have a system of equations.
To find the number we need to solve these, if we replace the first equation into the second one:
a + b = 12
(2b) + b = 12
3b = 12
b = 12/3 = 4
Then:
a = 2b = 2*4 = 8
So the two-digit number is 84.
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A regular six-sided die is rolled 1000 times. Use the binomial distribution to determine the standard deviation for the number of times an odd number is rolled
The standard deviation for the number of times an odd number is rolled is 15.8
How to determine the standard deviation?The given parameters are:
Die = regular six-sided die
n = 1000
The probability of rolling an odd number is:
p = 1/2 = 0.5
The standard deviation is then calculated as;
[tex]\sigma = \sqrt{np(1 - p)[/tex]
This gives
[tex]\sigma = \sqrt{1000 * 0.5 * (1 - 0.5)[/tex]
Evaluate the products
[tex]\sigma = \sqrt{250[/tex]
Evaluate the root
[tex]\sigma = 15.8[/tex]
Hence, the standard deviation is 15.8
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Please help!!!! Consider the region shaded in yellow. Which inequality does the shaded region correspond to?
Answer:
y-x-1 < 0
Step-by-step explanation:
according to the graph (0,1) and (-1,0) lies on the doted line,
equation of the dotted line is y-x-1=0
shaded region = y-x-1 < 0
A researcher needs to ask a question “what impact does a new curriculum have on a student achievement?” Which of the following is the most appropriate method for answering the question?
A) observation
B)textual analysis
C)experiment
D) survey
Answer:
C) Experiment
Step-by-step explanation:
With a controlled experiment, a researcher can use a student batch that studied the old curriculum as a control group, and the new batch of students as the 'test' group. To measure student achievement, the researcher would need to either:
1. compare test results for the 2 groups
2. do a longitudinal study - follow the 2 groups of students across several years, and track their 'achievements' (university admissions, jobs, income, etc)
With the other 3 options, the results wouldn't necessarily be accurate or relevant.
2/5 of the pupils in Year 9 say
their favourite colour is red.
There are 75 pupils in Year 9
How many students said red is
their favourite colour?
Answer:
30 pupils
Step-by-step explanation:
first you divide 75 and 2.5 to get 30.
Answer:
30 prefer red
Step-by-step explanation:
Multiply the fraction by the number of students:
[tex]75(\frac{2}{5})=\frac{(75)(2)}{5} =\frac{150}{5} =30[/tex]
Hope this helps
Simplify the following expression.
A.
B.
C.
D.
Answer:
D
Step-by-step explanation:
Let's start by crossing everything out!
12/3 can be crossed out to 4.
a^3/a^2 can be crossed out to a.
b^6/b^4 can be crossed out into b^2.
c^5/c^5 is just 1.
So which the results we got, we can multiply them, so that it is 4ab^2.
4ab^2 is our final answer!
Please give answer to this problem
The two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
Conjugate of a radicalThe conjugate of a radical is the value which when multiplied with the radical expression clears the radical. Conjugates have the same numbers but the opposite sign in the middle.
The given roots are
[tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex]
They have the same numbers but opposite signs in the middle.
Hence, the two roots [tex]a +\sqrt{b}[/tex] and [tex]a -\sqrt{b}[/tex] are called conjugate radicals
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Which number line represents the solutions to -21x1 = -6?
+
+
-8-7-6-5-4-3 -2 -1 0 1
-8-7-6-5-4-3-2-1
0
++ +
-8-7 -6 -5 -4 -3 -2 -1 0
-8-7-6 -5 -4 -3 -2 -1 0
1
2 3
2
2
3
4
FR
+3
64
2 3 4
5
6 7
5 6
5 6
+4
8
5 6
+ +
7 8
7 8
7
8
Answer + Step-by-step explanation:
-2|x| = -6
⇔ 2|x| = 6
⇔ |x| = 3
⇔ x = 3 or x = -3
THe square root of 10 x 15 x 24 is
[tex]\large\blue\implies \tt \large \: \sqrt{10 \: \times \: 15 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{150 \: \times \: 24} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} [/tex]
[tex]\large\blue\implies \tt \large \: \sqrt{3600} \: = \: 60[/tex]
[tex]\large\blue\implies \tt \large \:60[/tex]
Volume round to nearest tenth
The total volume of the given figure is:
[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]
How to find the volume of the given figure?
Here we have two simple shapes.
Half a sphere, and a cone.
The volume of half a sphere of radius R is:
[tex]V = \frac{2}{3}*3.14*R^3[/tex]
And here we know that R = 5.3cm, replacing that we get:
[tex]V = \frac{2}{3}*3.14*(5.3cm)^3 = 311.65cm^3[/tex]
For a cone of radius R and height H, the volume is:
[tex]V = \frac{3.14*R^2*H}{3}[/tex]
In this case, R = 5.3cm and H = 8.4cm
The volume of the cone is:
[tex]V = \frac{3.14*(5.4cm)^2*8.4cm}{3} = 246.97cm^3[/tex]
Then the total volume is:
[tex]V = 311.65cm^3 + 246.97cm^3 = 558.62cm^3[/tex]
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when a relation is drawn on an xy-plane what is another name for the set of all x values from its graph?
Another name for the set of all x-values for a relation is: domain.
What is the Domain of a Relation?
The domain of a relation can be defined as all the x-values that corresponds to the y-values that are plotted on a graph.
They are referred to as the input or the domain of the relation. Therefore, another name for the set of all x-values plotted for a relation on a graph is: domain.
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A committee of 4
is being formed randomly from the employees at a school: 4
administrators, 30
teachers, and 4
staff. What is the probability that all 4
members are teachers? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability that all 4 are teachers is 0.0000135.
How to solve for the probabilityThe total number is =
4 + 30 + 4
= 38
The committee of 4 from 38 =
38C4 = 73815
The committee of 4 from 4 teachers =
4C4 = 1 way
The total favorable cases = 1 way
Probability = favorability/ total cases
= 1/73815
= 0.0000135
Hence the probability that all 4 are teachers is 0.0000135.
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Which is a term in both the sequence f(n)=f(n-1)+4 and the sequence f(n)=3(5)^n-1 if f(1)=3?
a. 7
b. 15
c. 27
d. 135
Answer:
[tex] \small{\boxed{ \sf{Term \: in \: both \: the \: sequence \: is \: 15}}}[/tex]
Step-by-step explanation:
To determine the common term in both the sequence let's solve for each sequence individually.
Let's solve for first sequence
[tex]f(n) = f(n-1)+4[/tex]
we are already told that f(1) = 3
let's solve for f(2),f(3),f(4)........ and so on till we get the highest digit or more than the highest digit from given option.
f(2) = f(2-1)+4 = f(1)+4
f(2) = 3+4
[tex]\small{ \fbox{f(2) = 7}}[/tex]
f(3) = f(3-1)+4 = f(2)+4
f(3) = 7+4
[tex] \small{\fbox{f(3)= 11}}[/tex]
on solving further..
The series obtained is 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99, 103, 107, 111, 115, 119, 123, 127, 131, 135.....
Let's solve for second series
[tex]f(n) = 3×5^{n -1}[/tex]
given that f(1) = 3,
f(2) = 3×5¹ = 15
f(3) = 3×5² = 75
f(4) = 3×5³ = 375
The series obtained is 3, 15, 75, 375.....
The term obtained in both the sequence is 15 hence option B is correct Answer.
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(a) Write the next whole number after DDD fourteen in the base-fourteen system.
Answer:
1000 in base 14
Step-by-step explanation:
DDD + 1 = 1000 in base 14
Solve for x: 1
04>x>7
04
O-2>x> 1
0-2
Answer: -2 < x < 1
Step-by-step explanation:
move all terms not containing x from the center section of the inequality
1 < x + 3 < 4
subtract 3 from both terms outside the center
1 - 3 = -2
4 - 3 = 1
therefore our answer is:
-2 < x < 1
Which inequality is equivalent to 2/3 X-5 < 11
Answer:
2/3 x - 5 < 11
2/3 x < 16 (add 5 to both sides)
x < 16 * 3/2 (multiply both sides by 3/2)
x < 24
Step-by-step explanation:
32) The cost of mailing a first-class letter is $.22 for the first ounce and $.17 for each additional ounce or fraction
thereof. What is the cost of mailing a 7.4-ounce letter?
Oa.) $1.56
Ob.) $1.36
Oc.) $1.41