Answer:
916.67 (corrected to 2 decimal places)
Hope I'm right, fingers crossed
Step-by-step explanation:
[tex]55 \times 50 = 2750 \div \frac{3}{4 } = 916.6666667[/tex]
If 5x = 3x+12 then x = …..
↦ [tex]\huge\underline{ \underline{Answer:-}}[/tex]
[tex]5x = 3x + 12 \\ 5x - 3x = 12 \\ 2x = 12 \\ x = \frac{12}{2} \\ x = 6[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Step-by-step explanation:
Explanation is in the attachmenthope it is h helpful to you
In any triangle ABC,Prove by vector method c^2=a^2+b^2-2abcosC
Answer:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
Step-by-step explanation:
Let be [tex]\vec A[/tex], [tex]\vec B[/tex] and [tex]\vec C[/tex] the vector of a triangle so that [tex]\vec C = \vec A + \vec B[/tex]. By definition of Dot Product:
[tex]\vec C \,\bullet\,\vec C = (\vec A + \vec B) \,\bullet \vec C[/tex]
[tex]\vec C \,\bullet \,\vec C = (\vec A\,\bullet \,\vec C) + (\vec B \,\bullet \,\vec C)[/tex]
[tex]\|\vec C\|^{2} = [\vec A \,\bullet \,(\vec A + \vec B)] + [\vec B\,\bullet \,(\vec A + \vec B)][/tex]
[tex]\|\vec C\|^{2} = \vec A \,\bullet \, \vec A + \vec B\,\bullet \vec B + 2\cdot (\vec A \,\bullet \, \vec B)[/tex]
[tex]\|\vec C\|^{2} = \|\vec A\|^{2} + \|\vec B\|^{2} + 2\cdot \|\vec A\|\cdot \|\vec B\|\cdot \cos\theta_{C}[/tex]
Solve (x + 3)2 + (x + 3) – 2 = 0.
9514 1404 393
Answer:
x = -5 or x = -2
Step-by-step explanation:
Factoring, we have ...
((x +3 +2)((x +3) -1)) = 0
(x +5)(x +2) = 0
x = -5 or x = -2 . . . . . . . . values that make the factors zero
Assume one individual from the group is randomly selected. Find the probability of getting someone who tests negative, given that he or she had the disease. the probability is approximately?
Answer:
[tex]P(Negative | Yes) = 0.0486[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccc}{} & {Yes} & {No} & {Positive} & {137} & {24} & {Negative} & {7} & {132} \ \end{array}[/tex]
Required
[tex]P(Negative | Yes)[/tex]
This is calculated as:
[tex]P(Negative | Yes) = \frac{n(Negative\ n\ Yes)}{n(Yes)}[/tex]
So, we have:
[tex]P(Negative | Yes) = \frac{7}{137+7}[/tex]
[tex]P(Negative | Yes) = \frac{7}{144}[/tex]
[tex]P(Negative | Yes) = 0.0486[/tex]
Simultaneous equations 5x-4y=19
X+2y=8
Answer:
x=5
y=3/2
Step-by-step explanation:
Take it or leave it, that's what the computer said.
Kobe is a basketball player. He is able to make a free throw 70% of the time. What is the probability that Kobe makes his 10th free throw on his 14th shot
Answer:
0.1636 = 16.36% probability that Kobe makes his 10th free throw on his 14th shot
Step-by-step explanation:
For each free throw, there are only two possible outcomes. Either he makes it, or he misses. The probability of making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
He is able to make a free throw 70% of the time.
This means that [tex]p = 0.7[/tex]
What is the probability that Kobe makes his 10th free throw on his 14th shot?
9 of his first 13(P(X = 9) when n = 13), and then the 10th with 0.7 probability.
Thus
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{13,9}.(0.7)^{9}.(0.3)^{3} = 0.2337[/tex]
0.7*0.2337 = 0.1636
0.1636 = 16.36% probability that Kobe makes his 10th free throw on his 14th shot
Ellen, Nick, and Ryan went shopping together. One of them bought a hat, another bought sunglasses, and another bought a belt. One paid $6, another paid $8, and another paid $10.
1) Nick bought the hat.
2) Ellen spent $8.
3) The belt did not cost $10.
4) Ryan spent the most. Which of the following is true?
(a) Nick bought the hat for $10.
(b) Ellen bought the belt for $8.
(c) Ryan bought the sunglasses for $8.
(d) Ryan bought the belt for $10
(e) Ryan bought the hat for 56.
Answer:
see down
Step-by-step explanation:
d is correct answer
ES
What is the mZACB?
А.
10°
B
O 50°
(4x)
O 90°
O 180°
(7x-20)
С
Done
Intro
Answer:
B
O 50° is the mZACB out of the options
Simplify this math problem plz show your work
9514 1404 393
Answer:
(8a -a²)/(a +2)
Step-by-step explanation:
Cancel common factors from numerator and denominator.
[tex]\dfrac{-56+15a-a^2}{a^2+2a}\div\dfrac{a-7}{a^2}=-\dfrac{(a-7)(a-8)(a^2)}{a(a+2)(a-7)}\\\\=-\dfrac{a(a-8)}{a+2}=\boxed{\dfrac{8a-a^2}{a+2}}[/tex]
if angle ACB = angle DCD, angle BAC = 3x-10, angle ECD= 45degrees, and angle EDC = 2x+10 wgat is x
Answer:
x = 20
Step-by-step explanation:
3x -10 = 2x +10
x = 20
A university found that 25% of its students withdraw without completing the introductory statistics course. Assume that 30 students registered for the course.Use Microsoft Excel whenever necessary and answer the following questions:Compute the probability that 2 or fewer will withdraw
Answer:
0.0106 = 1.06% probability that 2 or fewer will withdraw
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they withdraw, or they do not. The probability of an student withdrawing is independent of any other student, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
25% of its students withdraw without completing the introductory statistics course.
This means that [tex]p = 0.25[/tex]
Assume that 30 students registered for the course.
This means that [tex]n = 30[/tex]
Compute the probability that 2 or fewer will withdraw:
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{30,0}.(0.25)^{0}.(0.75)^{30} = 0.0002[/tex]
[tex]P(X = 1) = C_{30,1}.(0.25)^{1}.(0.75)^{29} = 0.0018[/tex]
[tex]P(X = 2) = C_{30,2}.(0.25)^{2}.(0.75)^{28} = 0.0086[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0002 + 0.0018 + 0.0086 = 0.0106[/tex]
0.0106 = 1.06% probability that 2 or fewer will withdraw
-09
2 1 point
The amount of a radioactive substance y that remains after t years is given by the equation y = a (e)^kt, where a is the initial
amount present and k is the decay constant for the radioactive substance. If a = 100, y = 50, and k = -0.035, find t.
Answer:
19.80
Step-by-step explanation:
Given the equation :
y = a (e)^kt
If a = 100, y = 50, and k = -0.035, find t.
50 = 100(e)^(-0.035t)
50/100 = e^(-0.035t)
0.5 = e^-0.035t
Take the In
In(0.5) = - 0.035t
-0.693147 = - 0.035t
-0.693147 / - 0.035 = t
19.8042 = t
Hence, t = 19.80
Find the size of angle XZY give your answer
Answer:
yeah u forgot to add the picture ig
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
I need help pleaseeee
Answer:
1) has bigger answer
Step-by-step explanation:
1)
solving parenthesis first we get
5 × 10
so, the answer = 50
2)
solving 3 × 5 first as we have to see multiplication first then addition
2 + 15 + 5
22
comparing both
50 > 22
so problem 1 has a bigger answer
Find the circumference of a circle with a diameter of 50 centimeters. Round your answer to the nearest
centimeter.
Given :-
Diameter of circle = 50 cm .To Find :-
The circumference of the Circle.Solution :-
We know that the circumference of the Circle with radius r is given by ,
=> C = 2πr .
Here r is 50cm .=> C = 2 × 3.14 × 50 cm
=> C = 314 cm .
Hence the required answer is 314 cm .
Answer:
Step-by-step explanation:
b 75
Which of the following is an acute triangle?
70
30*
24°
45
126
132
36°
90°
45
559 55°
Triangle A
Triangle B
Triangle C
Triangle D
A. Triangle B
B. Triangle A
O
C. Triangle C
O.
D. Triangle D
The correct answer will be option (B) Triangle A
Acute triangleAn acute-angled triangle is a type of in which all the three internal angles of the triangle are acute, that is, they measure less than 90°
How to solve this problem?
The steps are as follow:
In acute triangle the the internal angle should not or greater than 90 degreeIn triangle B one of internal angle is 126 degree which is greater than 90 degree so it is not acute triangleOne internal angle of triangle C is 90 degree so it is also not acute triangleFor triangle D one angle is 132 degree which is greater than 90 degree so it also not acute triangleIn triangle A all the internal angle is less than 90 degree so it is acute triangleSo the triangle A is acute triangle
Learn more about Acute triangle here:
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In 2006, there were 160 teachers in College A, and three fourth of them had their own vehicles. In 2007, 20 new teachers came to the school and 6 of them had own vehicles. Calculate the percentage increase in the numbers of teacher who had own vehicles.
Answer: 5%
Step-by-step explanation:
In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:
= 3/4 × 160
= 120
In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:
= 120 + 6
= 126
The percentage increase will be:
= Increase / Old vehicle owners × 100
= 6/120 × 100
= 1/20 × 100
= 5%
The Percentage increase is 5%.
In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation.
Point A′ is at
, and point D′ is at
.
Answer:
b
Step-by-step explanation:
What is the inverse of function f? f(x)=3-x/7
Answer:
[tex] {f}^{ - 1} (x) = \frac{x}{3} + \frac{7}{3} [/tex]
hence option d is the correct option.
Answer:
Option C is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = (3-x) /7
Let f(x) be "y".
y = (3-x) /7
Interchanging "x" and "y".
x = (3-y)/7
7x = 3-y
y = 3-7x
Therefore, f'(x) = 3-7x.
Hope it helps!
What is the y-coordinate of the point that divides the
directed line segment from J to k into a ratio of 2:3?
13
12+
11+
10
9
8
7+
v = ( my mom n Ilv2 – va) + ve
O 6
0-5
6+
05
5
07
5
4+
3+
1 27
Mi
Answer:
5
Step-by-step explanation:
took the test
The coordinates of the point that divides the line segment from J to K into a ratio of 2:3 are P(-5,7), and the y-coordinate is 7, the correct option is D.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
Ratio= 2:3
Now,
Let the point we are looking for be denoted as P(x,y), and let the ratio be 2:3, which means that the distance from J to P is 2/5 times the distance from J to K.
Using the distance formula, we can find the distance between J and K as:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
= sqrt((-8 - (-3))^2 + (11 - 1)^2)
= sqrt(25 + 100)
= sqrt(125)
The distance from J to P is 2/5 of the total distance, which is:
(2/5)d = (2/5)sqrt(125) = 2sqrt(5)
Using the ratio formula, we get:
x = (3* (-3) + 2 * (-8)) / (3+2) = -5
y = (31 + 211) / (3+2) = 7
Therefore, by the given ratio answer will be 7.
Learn more about the ratio here:
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A lift in a building starts with 7 passengers and stops at 10 floors.if each passenger is equally likely to get off at any floor and all passengers leave independently.what is the probability that atleast two passengers will get off at the same floor?
Answer:
Correct option is
C
10
5
10P
5
Total ways in which one passenger can stop =10
Total ways in which 5 passengers can stop =10∗10∗10∗10∗10
=10
5
We will select 5 floors from 10 floors and assign each individual to each floor to keep everyone isolated from each other
No. of ways in which no two persons stop at the same floor =10C
5
∗5!
=10P
5
⇒P(E)=10P
5
/10
5
find the length of a rhombus if the lengths of its diagonals are: 5 cm and 12 cm
9514 1404 393
Answer:
6.5 cm
Step-by-step explanation:
The length of the rhombus is the length of the long diagonal: 12 cm.
Perhaps you want the length of one side. We recognize the given lengths as the legs of a 5-12-13 right triangle. Since each side is the hypotenuse of a right triangle whose legs are half the diagonals, the side length of the rhombus will be half of 13 cm.
The side lengths of the rhombus are 6.5 cm.
Write the geometric sequence in function notation.
4,2,1,1/2,1/4,...
A) AX) = (2) - (1/4)x - 1
OB) Ax) = (2) - (1/2)x - 1
C) Ax) = (4) · (/4)x - 1
D AX) = (4) · (1/2)x - 1
Answer:
D
Step-by-step explanation:
Carly is the principal at a middle school and wants to know the average IQ of all the female, seventh-grade students. She does not know anything about what the population distribution looks like. She took a simple random sample of 31 seventh-grade girls in her school and found the average IQ score in her sample was 105.8 and the standard deviation was 15. Assume that all conditions are met, construct the 96% Confidence interval for the average IQ score of all seventh-grade girls in the school.
Answer:
The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 31 - 1 = 30
96% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 30 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.96}{2} = 0.98[/tex]. So we have T = 2.15
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.15\frac{15}{\sqrt{31}} = 5.8[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 105.8 - 5.8 = 105.
The upper end of the interval is the sample mean added to M. So it is 105.8 + 5.8 = 111.6
The 96% confidence interval for the average IQ score of all seventh-grade girls in the school is (105, 111.6).
How many degrees are in a quarter circle? 25° 40° 90° 100°
Answer:
90
Step-by-step explanation:
360 ÷ 4 = 90
help with this please !!
Answer:
B
Step-by-step explanation:
The coeffecients (I totally didn't spell that right) and variables match up.
4. Bonus: A computer programmer was told
that he would be given a bonus of 5% of any
money his programs could save the company.
How much would he have to save the company
to earn a bonus of $500?
Answer:
$10,000
Step-by-step explanation:
.05 x = 500
x = 500/.05
x = $10,000
If the actual price in this market were below
the equilibrium price, what would drive the
market toward the equilibrium?
Step-by-step explanation:
If the price is below the equilibrium level, then the quantity demanded will exceed the quantity supplied. Excess demand or a shortage will exist. If the price is above the equilibrium level, then the quantity supplied will exceed the quantity demanded. Excess supply or a surplus will exist.Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium. A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.
Two systems of equations are given below. For each system, choose the best description of its solution.
x - 5y = 5
-x + 5y = -5
a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________
Answer:
Infinitely many solutions.
They must satisfy [tex]y = \frac{1}{5}(x - 5)[/tex]
Step-by-step explanation:
Given
[tex]x - 5y = 5[/tex]
[tex]-x + 5y = -5[/tex]
Required
The best description
Add both equations
[tex]x - x - 5y + 5y = 5 - 5[/tex]
[tex]0+0 =0[/tex]
[tex]0 = 0[/tex] ---- this means that the system has infinitely many solutions.
Make y the subject in: [tex]-x + 5y = -5[/tex]
Add x to both sides
[tex]5y = x - 5[/tex]
Divide through by 5
[tex]y = \frac{1}{5}(x - 5)[/tex]
Hence, they must satisfy: [tex]y = \frac{1}{5}(x - 5)[/tex]
The sum of two numbers is 85. If four times the smaller number is subtracted from the larger number, the result is 5. Find the two numbers.
The larger number is
The smaller number is
Answer:
the larger number is 69
the smaller number is 16
Step-by-step explanation:
x is the smaller number
y is the larger number
x + y = 85
y - 4x = 5
y = 5 + 4x
x + 5 + 4x = 85
5x = 80
x = 16
y = 69