Answer:
C. m<c = 140°
Step-by-step explanation:
Let's analyse each of the given options:
A. m<a = 140° is TRUE
Rationale: angle a and 140° are vertical angles. Vertical angles are congruent.
B. m<b = 140° is TRUE.
Rationale: angle a and 140° are alternate interior angles. Alternate interior angles are congruent.
C. m<c = 140° is NOT TRUE.
Rationale: angle c and 140° are same side interior angles. Same side interior angles are supplementary.
D. m<d = 140° is TRUE.
Rationale: angle d and 140° are corresponding angles. Corresponding angles are congruent.
Ted buys wood to build his guitars. Find the number of blocks of mahogany that Ted can afford to buy if he wishes to spend a total of $5000 this month, mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.
Answer choices:
7
8
11
10
Answer:
the answer is 8
Step-by-step explanation:
Total amount Ted wishes to spend this month is $5000.
Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.
So, money spent on spruce = dollars
Money left after buying spruce = dollars
Now as $450 will be spent on buying 1 block of mahogany.
So, $3600 will be spent
and then your answer will be 8
Four complex numbers lie at the vertices of a square in the complex plane.
Three of the numbers are 1 + 2i, -2 + i and -1 – 2i. What is the fourth
number?
9514 1404 393
Answer:
2 -i
Step-by-step explanation:
The two diagonals have the same center point. Here, it is ...
(1 +2) +(-1 -2i) = 0 +0i
The fourth point is found by reflecting the 2nd point across the origin:
p4 = -p2 = -(-2 +i) = 2 -i . . . . . fourth corner of the square
Simplify the ratio.
2.25 to 0.5
Answer:
9:2
Step-by-step explanation:
Ms. Ambrose paid $10 for 1.25 pounds of almonds. How much did the almonds cost per pound???
Determine whether the following propositions are true or false:
(a) 5 is an odd number and 3 is a negative number.
(b) 5 is an odd number or 3 is a negative number.
(c) 8 is an odd number or 4 is not an odd number.
(d) 6 is an even number and 7 is odd or negative.
(e) It is not true that either 7 is an odd number or 8 is an even number (or both).
Answer:
a) false
b) true
c) true
d) true
e) false
Step-by-step explanation:
In a statement of the type:
p ∧ q
where ∧ means "and"
The statement is true only if both p and q are true
the statement is false if p, q, or both, are false.
and in the case of:
p ∨ q
where ∨ means "or"
The statement is true if at least one of p or q (or both) are true.
The statement is false if both are false.
Now that we know that, let's solve the problem:
a) "5 is an odd number and 3 is a negative number."
Here we have:
p = 5 is an odd number
We know that this is true
q = 3 is a negative number
This is false.
then the complete statement is false.
b) "5 is an odd number or 3 is a negative number."
here we have:
p = 5 is an odd number.
this is true
q = 3 is a negative number
because in this case we have an "or", with only p being true, the whole statement is true.
c) "8 is an odd number or 4 is not an odd number."
p = 8 is an odd number (this is false)
q = 4 is not an odd number (this is true, 4 is a even number)
Again, we have an "or", so we need only one true proposition, then the statement is true.
d) "6 is an even number and 7 is odd or negative."
p = 6 is an even number (true)
q = 7 is odd or negative (notice that we have an or, and 7 is odd is true, so this proposition is true)
Then both propositions are true, then the statement is true.
e) "It is not true that either 7 is an odd number or 8 is an even number (or both)."
This is most complex, this will be true if at least one of the propositions is false.
but:
7 is an odd number is true
8 is an even number is true.
Then both statements are true, which means that the statement is false.
9.
Find the area of the shaded region.
6
6
The exact area is A =
square units.
Answer:
8. 36
Step-by-step explanation:
8.
The diameter of the square is x=[tex]\sqrt{6^{2} +6^{2} }\\[/tex] = [tex]\sqrt{72}[/tex] = 6 [tex]\sqrt{2}[/tex]
The diameter of the square is the diameter of the circle, therefore the radius of the circle is r = 6 [tex]\sqrt{2}[/tex]/2 = 3[tex]\sqrt{2}[/tex]
The area of the shaded region, which is a circle is A= π[tex]r^{2}[/tex] = π[tex](3\sqrt{2} )^{2}[/tex] = 36π
Help ASAP!! A triangle has side lengths of 11in, 15in, and 20in. Find the angle measures of the triangle. Round decimal answers to the nearest tenth. Someone help pls.
Answer:
<A = 47.7°
<B = 99.4°
<C = 32.9
Step-by-step explanation:
When given the measurements of all three sides, you can calculate the angles using the Cosine Law.
c² = a² + b² - 2ab cos C
(based on Pythagorean Theorem)
If we say: a = 15
b = 20
c = 11
11² = 15² + 20² - 2(15)(20) cos C
121 = 625 - 2(15)(20) cos C
121 = 625 - 600 cos C
⁻504 = ⁻600 cos C
cos⁻¹ (504 ÷ 600) = C
< C = 32.9°
a² = b² + c² - 2bc cos A
15² = 20² + 11² - 2(20)(11) cos A
225 = 521 - 2(20)(11) cos A
225 = 521 - 440 cos A
⁻296 = ⁻440 cos A
cos⁻¹ (296 ÷ 440) = A
<A = 47.7°
Then, since we know the sum of all three angles of a triangle equals 180°:
180° - 32.9° - 47.7° = 99.4°
<B = 99.4°
Using the graph below, if f(x) = 4, find x.
Find the value of x. Round to the nearest tenth.
A raffle has a grand prize of a European cruise valued at $10000 with a second prize of a Rocky Point vacation valued at $700. If each ticket costs $4 and 11000 tickets are sold, what are the expected winnings for a ticket buyer?
Answer:
- 3.027
Step-by-step explanation:
First price = 10000 ; second price = 700
Number of tickets sold = 11000
Ticket cost = $4
Probability that a ticket wins grand price = 1 / 11000
Probability that a ticket wins second price = 1 / 11000
X ____ 10000 _____ 700
P(x) ___ 1 / 11000 ___ 1/11000
Expected winning for a ticket buyer :
E(X) = Σx*p(x)
E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost
E(X) = 0.9090909 + 0.0636363 - 4
E(X) = - 3.0272728
E(X) = - 3.027
Which of the following is a polynomial?
Answer:
(D.) 3x^2 + 6x
Step-by-step explanation:
the other options aren't complete and some don't even create a parabola.
Movie Selections The Foreign Language Club is showing a three-movie marathon of subtitled movies. How many ways can they
choose 3 from the 17 available?
Answer:
Step-by-step explanation:
This is a beginning counting problem, or is it?
If order matters then the answer is
17P3 = 17! / (14!) = 17 * 16 * 15 = 4080
However if it does not matter then
17C3 = 17!/(3! * 14!)
680
Which shows the best estimate of the quotient of 4,346 ÷ 82?
between 50 and 60
between 60 and 70
between 500 and 600
between 600 and 700
Answer:
Between 50 and 60
Step-by-step explanation:
4,346/82 is 53 which is between 50 and 60.
Hope this helps!
Diana adds either 2 or 5 to every whole number from 1 to 9. She wants to achieve as few different sums as
possible. What is the minimum number of different values she obtains?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
=
The solution set is
1/2(10x+16)-13=-3/5(15x-35)
Answer: 13/7 or as a decimal 1.857142857
How did i get the answer:
Step 1: Simplify both sides of the equation.
so 1/2 of 10 is 5, 1/2 of 16 is 8
-3/5 of 15 is -9 and -3/5 of -35 is POSITIVE 21
all together should look like 5x+8+−13=−9x+21
(now we have to combine like terms)
8+ -13= -5
5x -5 = -9x+21
Step 2: Add 9x to both sides
5x + 9x= 14x
14x -5 = 21
Step 3: Add 5 to both sides.
21+5= 26
14x=26
Step 4: Divide both sides by 14.
26/14= 1.85714286 or 13/7
(4 + 4i)/(5+4i) = divide
Answer:
B.
Step-by-step explanation:
[tex] \frac{4 + 4i}{5 + 4i} [/tex]
Multiplying both numerator and denominator by (5 - 4i) , the conjugate of the denominator, i. e, (5 + 4i).[tex] \frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5-4i} [/tex]
[tex] \frac{(4 + 4i)(5 - 4i)}{(5 + 4i)(5 - 4i)} [/tex]
Multiplying (4+4i) and (5-4i) using distributive propertyUsing the identity (a+b)(a-b)= a² - b² where 5 will act as a and 4i will act as b[tex] \frac{20-16i+20i-16i^2}{(5) {}^{2} - (4i) {}^{2} } [/tex]
i² = -1(combining like terms)
[tex] \frac{20+(-16i+20i)-(-16)}{25-(-16)} [/tex]
[tex] \frac{(20+16)+4i}{25+16} [/tex]
[tex] \frac{36+4i}{41} [/tex]
distributing the denominator
[tex] \frac{36}{41} + \frac{4}{41}i [/tex]
That is, option B.
Find the surface area and volume of the solid given the figure below
Answer:
Volume - 582.8848178 cm cubed
Step-by-step explanation:
Volume - to fine the volume start with the cone...
The formula is 1/3 pi r^2h
so for this problem it would be
1/3 * 3.14 * 26.01 * 11.2
so your answer would be...
305.061213 cm cubed
Your next step is to find the volume of the dome. to do that the formula is (4/3 pi r^3)/2
so for this problem it would be
(4/3 * 3.14 * 132.651)/2
so your answer would be...
277.8236048 cm cubed
Finally you add together those 2 volumes and get 582.8848178 cm cubed as your final answer.
-32=?
it told me to write atlest 20 words so ignore this
Answer:
I don't think it's possible.
You are given the following information about x and y.
x y Independent Dependent Variable Variable 15 5 12 7 10 9 7 11
The least squares estimate of b 0 equals ______.
a. 16.41176
b. â1.3
c. 21.4
d. â7.647
Answer:
[tex]b_0 = 16.471[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccc}x & {15} & {12} & {10} & {7} \ \\ y & {5} & {7} & {9} & {11} \ \end{array}[/tex]
Required
The least square estimate [tex]b_0[/tex]
Calculate the mean of x
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{15+12+10+7}{4} =\frac{44}{4} = 11[/tex]
Calculate the mean of y
[tex]\bar y = \frac{\sum y}{n}[/tex]
[tex]\bar y = \frac{5+7+9+11}{4} =\frac{32}{4} = 8[/tex]
Calculate [tex]\sum(x - \bar x) * (y - \bar y)[/tex]
[tex]\sum(x - \bar x) = (15 - 11) * (5 - 8)+ (12 - 11) * (7 - 8) + (10 - 11) * (9 - 8)+ (7 - 11) * (11 - 8)[/tex]
[tex]\sum(x - \bar x) = -26[/tex]
Calculate [tex]\sum(x - \bar x)^2[/tex]
[tex]\sum(x - \bar x)^2 = (15 - 11)^2 + (12 - 11)^2 + (10 - 11)^2 + (7 - 11)^2[/tex]
[tex]\sum(x - \bar x)^2 = 34[/tex]
So:
[tex]b = \frac{\sum(x - \bar x) * (y - \bar y)}{\sum(x - \bar x)^2}[/tex]
[tex]b = \frac{-26}{34}[/tex]
[tex]b_0 = y - bx[/tex]
[tex]b_0 = 5 - \frac{-26}{34}*15[/tex]
[tex]b_0 = 5 + \frac{26*15}{34}[/tex]
[tex]b_0 = 5 + \frac{390}{34}[/tex]
Take LCM
[tex]b_0 = \frac{34*5+ 390}{34}[/tex]
[tex]b_0 = \frac{560}{34}[/tex]
[tex]b_0 = 16.471[/tex]
PLSHELPASAPDFFFFFFFFFFFFFFFFFFFFFFFFFF
im struggling with the same one
Select the correct answer.
Which is the simplified form of the expression ?
Answer:
a) b^5/12
Step-by-step explanation:
b^2/3 ÷ b^1/4 [if bases are the same then subtract the exponents]
2/3 - 1/4 = 5/12
which pair of fractions are equivalent? 2/3 and 12/9 20/40 and 45/ 55 20/40 and 4/8 5/5 and 25/50
Answer:
[tex]\frac{20}{40} \ and \ \frac{4}{8} \ is \ equivalent[/tex]
Step-by-step explanation:
1.
[tex]\frac{2}{3} \ and \ \frac{12}{9} \\\\\frac{2}{3} \ and \ \frac{4}{3}\\\\Not \ equivalent[/tex]
2.
[tex]\frac{20}{40} \ and \ \frac{45}{55}\\\\\frac{1}{2} \ and \ \frac{9}{11}\\\\Not\ equivalent[/tex]
3.
[tex]\frac{20}{40} \ and \ \frac{4}{8}\\\\\frac{1}{2} \ and \ \frac{1}{2} \\\\Equivalent[/tex]
4.
[tex]\frac{5}{5} \ and \ \frac{25}{50} \\\\\frac{1}{1} \ and \ \frac{1}{2} \\\\not \ equivalent[/tex]
What is the slope of the line?
An urn has 21 balls that are identical except that 8 are white, 7 are red, and 6 are blue. What is the probability that all are white if 3 are selected randomly without replacement?
Answer:
.0421
about 4.21%
Step-by-step explanation:
[tex]\frac{{8\choose3}}{{21\choose3}}=\frac{56}{1330}=.042105263[/tex]
Given the following formula, solve for r.
What is the solution to the linear equation?
-12 + 3b - 1 = -5 - b
Answer:
b=2
Step-by-step explanation:
(a) Starting with the geometric series [infinity] xn n = 0 , find the sum of the series [infinity] nxn − 1 n = 1 , |x| < 1.
Let f(x) be the sum of the geometric series,
[tex]f(x)=\displaystyle\frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]
for |x| < 1. Then taking the derivative gives the desired sum,
[tex]f'(x)=\displaystyle\boxed{\dfrac1{(1-x)^2}} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=1}^\infty nx^{n-1}[/tex]
Choose the system of inequalities that best matches the graph below.
Answer:
"D" is the correct answer
Step-by-step explanation:
Can someone just check my answers please? Please let me know which questions are wrong. Thank you for your time.
You deposit $2000 in an account earning 4% interest compounded monthly. How much will you have in the account in 10 years? $ Enter an integer or decimal number (more..]
Answer:
$2,981.67
Step-by-step explanation: