Answer:
n(A)+n(B)-49/400=n(AUB)
n(B)=1-7/20+49/400
n(B)=(400+49-140)/400
n(B)=309/400
Triangles ABC and DEF are similar. The height of
triangle DEF is 4 cm. Find the area of triangle ABC.
a. 1.5 cm
b. 2 cm
c. 6 cm
d. 3 cm
Option C
Height of DEF = 4cm
Therefore ratio = 1:2
Base = 3cm
Height of ABC = 2cm
Area of ABC = 1/2×b×h
= 1/2×3×4
= 6cm²
Option C
Answered by Gauthmath must click thanks and mark brainliest
Express 0.6(27..).)))) as a fraction
I assume you mean the number x = 0.6272727….
You have
10x = 6.272727…
1000x = 627.272727…
==> 1000x - 10x = 990x = 621
==> x = 621/990 = 69/110
David can receive one of the following two payment streams:
i. 100 at time 0, 200 at time n, and 300 at time 2n
ii. 600 at time 1 0
At an annual effective interest rate of i, the present values of the two streams arc equal. Given v^n = 0.75941.
Determine i.
Answer:
3.51%
Step-by-step explanation:
From the given information:
For the first stream, the present value can be computed as:
[tex]= 100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}}[/tex]
Present value for the second stream is:
[tex]=\dfrac{600}{(1+i)^{10}}[/tex]
Relating the above two equations together;
[tex]100 +\dfrac{200}{(1+i)^n}+ \dfrac{300}{(1+i)^{2n}} =\dfrac{600}{(1+i)^{10}}[/tex]
consider [tex]v = \dfrac{1}{1+i}[/tex], Then:
[tex]\implies 100+200v^n + 300v^{2n} = 600 v^{10}[/tex]
where:
[tex]v^n = 0.75941[/tex]
Now;
[tex]\implies 100+200(0.75941) + 300(0.75941))^2 = 600 (v)^{10}[/tex]
[tex](v)^{10} = \dfrac{100+200(0.75941) + 300(0.75941))^2 }{600}[/tex]
[tex](v)^{10} = 0.7082[/tex]
[tex](v) = \sqrt[10]{0.7082}[/tex]
v = 0.9661
Recall that:
[tex]v = \dfrac{1}{1+i}[/tex]
We can say that:
[tex]\dfrac{1}{1+i} = 0.9661[/tex]
[tex]1 = 0.9661(1+i) \\ \\ 0.9661 + 0.9661 i = 1 \\ \\ 0.9661 i = 1 - 0.9661 \\ \\ 0.9661 i = 0.0339 \\ \\ i = \dfrac{0.0339}{0.9661} \\ \\ i = 0.0351 \\ \\ \mathbf{i = 3.51\%}[/tex]
The average cost for a product is C (x )equals 2 x plus 54 plus 98 over x, where C is measured in dollars and x is the number of units. How many units must be produced in order to minimize average cost
Answer:
7 units
Step-by-step explanation:
Given
[tex]C(x) = 2x + 54 + \frac{98}{x}[/tex]
Required
The units that minimize the average cost
[tex]C(x) = 2x + 54 + \frac{98}{x}[/tex]
Differentiate
[tex]C' = 2 + 0 - 98x^{-2}[/tex]
[tex]C' = 2 - 98x^{-2}[/tex]
Equate to 0 to solve for x
[tex]0 = 2 - 98x^{-2}[/tex]
Collect like terms
[tex]98x^{-2} = 2[/tex]
Divide by 98
[tex]x^{-2} = \frac{1}{49}[/tex]
Rewrite as:
[tex]\frac{1}{x^2} = \frac{1}{49}[/tex]
Take square roots of both sides
[tex]\frac{1}{x} = \±\frac{1}{7}[/tex]
Take multiplicative inverse of both sides
[tex]x = \±7[/tex]
Only positive value will produce critical value. Hence, 7 units will produce the minimum average cost
How long will it take for a home improvement loan for 22,800to earn interest of 608.00at 8 %ordinary interest
9514 1404 393
Answer:
120 days
Step-by-step explanation:
Using the formula for simple interest, we can solve for t:
I = Prt
t = I/(Pr) = 608/(22800×.08) = 608/1824 = 1/3 . . . . year
For "ordinary interest", a year is considered to be 360 days, so 1/3 year is ...
(1/3)(360 days) = 120 days
It will take 120 days for the loan to earn 608 in interest.
Which of the following numbers could not be used to describe a distance walked?
129 feet
12 feet
- 140 feet
|-125 feet
Answer:
-140 ft is not a distance
Step-by-step explanation:
Distance must be a positive number
-140 is negative
1 1/5 + 17/2 - 3/2 Helppppp
Answer:
[tex]\frac{82}{10}[/tex]
Step-by-step explanation:
[tex]1\frac{1}{5} +\frac{17}{2} -\frac{3}{2}[/tex]
→ Convert the mixed number into an improper fraction
[tex]\frac{6}{5} +\frac{17}{2} -\frac{3}{2}[/tex]
→ Complete the takeaway operation
[tex]\frac{6}{5} +\frac{14}{2}[/tex]
→ Make the denominators the same
[tex]\frac{12}{10}+\frac{70}{10}[/tex]
→ Simplify
[tex]\frac{82}{10}[/tex]
Answer:
8.2
Step-by-step explanation:
I have 3 questionssss
∠A and ∠T are supplementary. Given m∠T = (7x+11)° and m∠A = (8x+19)°, what is m∠T?
The other two are in the pics attached! PLS!
Answer:
<T = 81
x = 10, angle = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
Step-by-step explanation:
Supplementary angles add to 180
(7x+11) + (8x+19) = 180
Combine like terms
15x + 30 = 180
Subtract 30 from each side
15x +30-30 = 180-30
15x= 150
Divide by 15
15x/15 = 150/15
x = 10
We want angle T
T = 7x+11 = 7(10)+11 = 70+11 = 81
The two angles add to 90
5x+10 + 30 = 90
Combine like terms
5x+40 = 90
5x+40-40 = 90-40
5x = 50
Divide by 5
5x/5 = 50/5
x=10
5x+10 = 5(10) +10 = 50+10 = 60
Angle 5 and Angle 3 are vertical angles. They are acute angles
25 POINTS!
Factor the polynomial f(x)=x^5+2x^3−8x^2−16
and find its real zeros using the Zero Product Property.
Answer:
Factor form,
f(x) = (x²+2)(x-2)(x²+2x+4)
Zeroes:
x-2=0
x=2
one real zeros of the function is, 2
Answered by GAUTHMATH
Complete factorization of x^3+4x^2-20x-48
Answer:
(x + 6) • (x + 2) • (x - 4)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((x3) + 22x2) - 20x) - 48
STEP
2
:
Checking for a perfect cube
2.1 x3+4x2-20x-48 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+4x2-20x-48
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x3-48
Group 2: 4x2-20x
Pull out from each group separately :
Group 1: (x3-48) • (1)
Group 2: (x-5) • (4x)
In triangleABC, AC = 15 centimeters, m
Answer:
16.17 cm
Step-by-step explanation:
The solution triangle attached below :
To obtain BC ; we use the sine rule ;
a/ sin A = b / sin B
A = (180 - (68 + 24))
A = 180 - 92
A = 88°
a / Sin 88 = 15 / sin 68
Cross multiply :
(a * sin 68) = (15 * sin 88)
a = 14.990862 / sin 68
a = 16.168165
a = 16.168 cm
In the Fuel Economy Guide for 2018 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles. There are a number of outliers, mainly hybrid gas electric vehicles. If we ignore outliers, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.
Required:
a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?
b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?
Answer:
a) The probability is the p-value of [tex]Z = \frac{X - 22.6}{5.2}[/tex], in which X is the gas mileage of the 2020 Honda Civic.
b) Your dad's truck is 1.65 standard deviations below the mean.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.
This means that [tex]\mu = 22.6, \sigma = 5.2[/tex]
a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?
This is the p-value of Z, given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{X - 22.6}{5.2}[/tex]
In which X is the gas mileage of the 2020 Honda Civic.
b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?
This is Z when X = 14. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14 - 22.6}{5.2}[/tex]
[tex]Z = -1.65[/tex]
Your dad's truck is 1.65 standard deviations below the mean.
Two buses leave towns 1060 kilometers apart at the same time and travel toward each other. One bus travels 14 kilometers an hour faster than the other. If they meet in 5 hours, what is the rate of each bus?
Answer:
99, 113
Step-by-step explanation:
X-the first bus
X+14-the second bus
5x+5(x+14)=1060
10x+70=1060
10x=990
X=99-the first bus
99+14=113-the second bus
I need help please I don’t understand
Answer:
Step-by-step explanation:
180 = ∠BAC + 52 +62
66 = ∠BAC
Explain the Skill
Watch the following video on fractions and then try the exercises.
13
12
14
Practise the Skill
Mia is having a party with friends.
The pizzas and pies have already been cut into portions.
Match the shaded area of the pizzas and pies to the correct fraction.
an image
Correct
an image
Correct
an image
Correct
Practise the Skill
One fifth of the people coming to the party are under 18.
Select this fraction.
14
1
4
Incorrect 110
1
10
15
1
5
12
1
2
Mia has been very creative and made a pizza with different toppings.
an image
What fraction of the pizza is mushrooms?
Incorrect - Correct Answer: 14
1
4
Practise the Skill
At the party, two-fifths of the crisps for guests will be ready salted. Select this fraction.
12
1
2
34
3
4
15
1
5
25
2
5
Correct 23
2
3
52
5
2
Mia cuts a cake equally into ten pieces. Three pieces are left.
an image
What fraction is left?
Correct
One tenth of the guests have brought food for the party. Select this fraction.
110
1
10
18
1
8
15
1
5
14
1
4
12
1
2
Explain the Skill
Finding a Fifth
When an amount is shared into 5 equal parts, each part is called a fifth.
The amount is divided by 5. A fifth is one of five equal parts.
Example
A minibus is carrying 10 people. 15
1
5
of the people on the minibus are children.
Calculate how many people on the minibus are children.
To find a fifth of an amount, divide the amount by 5.
The calculation is 10 ÷ 5 = 2
So, the minibus is carrying 2 children.
Explain the Skill
Finding a Tenth
When an amount is shared into 10 equal parts, each part is called a tenth.
The amount is divided by 10. A tenth is one of ten equal parts.
Example
There are 50 people at a party. 110
1
10
of the people at the party are vegetarian.
Calculate how many people at the party are vegetarian.
To find a tenth of an amount, divide the amount by 10.
The calculation is 50 ÷ 10 = 5
So, 5 people at the party are vegetarian.
Practise the Skill
550 people attend a conference.
15
1
5
of the attendees have a dietary requirement.
Calculate the number of people who have dietary requirements by completing the calculation below.
ILL MARK BRAINILEST IF YOU ANSWER!!!
Jerry decides to participate in the horseshoe
tournament at the Wellesley Apple Butter and Cheese
festival. The toss of the shoes can be modelled using
the equation, h = -0.1(d + 1)(d - 12), where h represents
height in metres and d represents distance in metres.
a) Sketch the graphical model.
b) What is the maximum height of a horseshoe?
Answer:
[tex]h_{max}=5.5[/tex]
Step-by-step explanation:
Given
[tex]h = -0.1(d + 1)(d - 12)[/tex]
Solving (a): The graph
To do this, we plot h on the vertical axis and d on the horizontal
See attachment for graph
Solving (b): The maximum of h
From the attached graph, h has the maximum value when:
[tex]d = 4.225[/tex]
So, the maximum of h is:
[tex]h_{max}=5.5[/tex]
What is considered the most famous impossible problem from Greek
antiquity?
A. Riemann's negation
B. Doubling the cube
C. Playfair's axiom
D. Bisecting any angle
Answer:
B. Doubling the cube.
Step-by-step explanation:
Riemann's negation was formulated by German mathematician Hermann Riemann in the 19th Century.
Playfair's axiom was an axiom alternative to the Euclid' fifth postulate, which was formulated in the 19th Century.
The method of bisecting any angle was proposed in late Antiquity thanks to the development of Euclidean Geometry.
The question of double the cube was investigated by Egyptians, Indians and Greeks in antiquity without any success. This question cannot be solved by compass and straightedge according to conclusions of French mathematician Pierre Wantzel in 1.837.
Hence, doubling the cube was the most famous impossible problem from Greek antiquity. (Answer: B)
Which of the following describes the diagonals of a square?
Select the best answer from the choices provided.
A. They are not congruent.
B. They are not perpendicular to each other.
C. They bisect the opposite angles.
D.
All of the answers are correct.
Answer:
ALL OF THE ANSWERS ARE CORRECT .
HOPE IT HELP YOU.
A pharmaceutical company conducted an experiment to test a drug for managing morning sickness for school children. The
company enrolled students for the experiment in the age group of 10 to 15 and divided them into two groups. One group
received sugar pills and the other group received pills that have compounds to manage morning sickness. Which group
receives the placebo?
Answer:
In an experiment, one group receives a new antidepressant medication and the other group receives a sugar pill. the group receiving the new antidepressant medication is called the ________ group.
a. dependent
b. placebo
c. experimental
d. control.
Find the Distance in Coordinate Plane (23-24)
Find the distance AB Show Work.
Answer:
i am not sure but i think its 1.16
Step-by-step explanation:
convert 657 as binary form in computer language
Answer:
1010010001
Step-by-step explanation:
Keep dividing 657 by 2, and record the quotient and remainder
657
328,1
164,0
82,0
41,0
20,1
10,0
5,0
2,1
1,0
So chain the remainders from bottom up to get the binary number:
1010010001
Check:
1+16+128+512=657 checks.
What is the equation of the line that passes through the point (-4, 2) and has a
slope of -2?
Step-by-step explanation:
use the equation of the straight line
y-y1=m (x-x1)
y-2=-2(x+4)
y-2= -2x-8
y= -2x-8+2
y= -2x-6
I hope this helps
How far can you travel in 19 hours at 63 mph
Answer:
1197 miles.
Step by step explanation:Speed(s) = 63 mph
Time(t) = 19 hours
Distance(d) = ?
We know,
D = S × T
= 63 × 19
= 1197 miles
I will give brainliest
Answer:
uncertain for the first image and words to choose for the second image
Step-by-step explanation:
The text implies that she does not know and that there are many words to choose.
I have trouble with these two questions, even i did my equation but i don’t get the answers
Answer:
$318.17, out of state college is $161.12 cheaper per month
Step-by-step explanation:
72*24 = 1728 + 410*4 = 1728 + 1640 = 3368 + 450 = 18/12 = $318.17
8700+650*9 = 8700 + 5850 = 14550/9 = 1616.66
8500+400*9 = 8500 + 3600 = 12100 + 1000 = 13100/9 = 1455.56
1616.67 - 1455.56= $161.11 (use $161.12)
Find m(angle) and give a trig equation
Step-by-step explanation:
Just using the Pythagoras theorem
A paper factory makes cardboard sheets like the one shown below. If the area of each sheet is given by the expression 6x ^ 2 + 7x + 2, what are the dimensions of each sheet of cardboard?
Answer:
67^2+76+2
that's my answer towards this question
Math property
-75+(23+75)=(75+75)-23=0-23=-23
Given:
Consider the expression is:
[tex]-75+23+75[/tex]
To find:
The value of the given expression by using the math properties.
Solution:
We have,
[tex]-75+23+75[/tex]
It can be written as:
[tex]=-75+(23+75)[/tex]
[tex]=-75+(75+23)[/tex] [Commutative property of addition]
[tex]=(-75+75)+23[/tex] [Associative property of addition]
[tex]=0+23[/tex]
[tex]=23[/tex]
Therefore, the value of the given expression is 23.
Consider a political discussion group consisting of 4 Democrats, 9 republicans, and 4 independents. Suppose that two group members are randomly selected in succession to attend a political convention. Find the probability of selecting two Democrats.
On July 9, Mifflin Company receives a $10,200, 90-day, 6% note from customer Payton Summers as payment on account. What entry should be made on July 9 to record receipt of the note?
Answer:
Since on July 9, Mifflin Company receives a $ 10,200, 90-day, 6% note from customer Payton Summers as payment on account, to determine what entry should be made on July 9 to record receipt of the note the following calculation must be performed :
90 days = 3 months
6/12 x 3 = 1.5%
10,200 x 1,015 = 10,353
Therefore, a debt cancellation for $ 10,200 must be made in the company's accounting records, plus an interest generation for $ 153, which will be justified by the cash income of $ 10,353.
