Answer:
He spent ⅓ of the time on the remaining three questions.
Step-by-step explanation:
Let's first figure out what the question gives us, and what we need to find.
Given:
Test - 2 hours, 5 questions
Candidate - 80 minutes, 2 questions
Find:
Fraction of time he spent on remaining three questions
Start by finding the fraction of time that he spent on the first two questions.
Set up an unit converter to convert two hours to minutes.
[tex]2$ hours($\frac{60\text{ minutes}}{1 \text{ hour}})=2\cdot 60\text{ minutes}=120$ minutes[/tex]
Let "x" represent the fraction of time the candidate spent on the first two questions...
[tex]x=\frac{\text{Amount of Time spent on First Two Questions}}{\text{Total Time}}\\x=\frac{80\text{ minutes}}{120\text{ minutes}}[/tex]
[tex]x=\frac{80}{120}[/tex]
[tex]x=\frac{8}{12}[/tex]
[tex]x=\frac{2}{3}[/tex]
Let "y" represent the fraction of time the candidate spent on the remaining three questions...
[tex]y=1-\text{Fraction of Time spent on First Two Questions}\\y=1-\frac{2}{3}\\[/tex]
[tex]y=\frac{3}{3}-\frac{2}{3}\\[/tex]
[tex]y=\frac{1}{3}[/tex]
He spent ⅓ of the time on the remaining three questions.
Which is the equation of the line with slope 3 that contains point (-1,5)?
y-1 = 3(x + 5)
y - 1 = 3(x - 5)
y - 5= 3(x - 1)
y - 5= 3(x + 1)
Answer:
D
[tex]y-5=3(x+1)[/tex]
Step-by-step explanation:
We can see that the question is asking for the Point-Slope Form;
[tex]y-y_{1} =m(x-x_{1})[/tex]
The points go into the equation for [tex]y_{1}[/tex] and [tex]x_{1}[/tex]
[tex]y-5=m[x-(-1)][/tex]
M would be the slope;
[tex]y-5=3[x-(-1)][/tex]
Which basically is:
[tex]y-5=3(x+1)[/tex]
Need some math help thanks in advance!
Answer:
x = 10
y = 6
Step-by-step explanation:
Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal to each other.
⇒ m∠1 = m∠3 and m∠2 = m∠4
⇒ m∠1 = m∠3
⇒ 10x = 100
⇒ x = 10
Linear pair: Two adjacent angles which sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ m∠3 + m∠4 = 180°
⇒ 100 + 10y + 20 = 180
⇒ 120 + 10y = 180
⇒ 10y = 60
⇒ y = 6
you roll two fair dice, a green one and a red one.
(a) are the outcomes on the dice independent?
(b) find p(1 on green die and 2 on red die)
(c) find p(2 on green die and 1 on red die)
(d) find p[(1 on green die and 2 on red die) or (2 on green die and 1 on red die)]
Answer:
(a) yes
(b) 1/36
(c) 1/36
(d) 1/18
Step-by-step explanation:
(a) yes they are independent as the outcome of one does not affect the outcome of the other.
(b) As the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(1 on green die) = 1/6
P(2 on red die) = 1/6
Therefore, P(1 on green die) AND P(2 on red die) = 1/6 × 1/6 = 1/36
(c) Again, as the dice are fair, each possible number (1 through 6) has the same probability of being rolled.
P(2 on green die) = 1/6
P(1 on red die) = 1/6
Therefore, P(2 on green die) AND P(1 on red die) = 1/6 × 1/6 = 1/36
(d) p[(1 on green die and 2 on red die) OR (2 on green die and 1 on red die)
= 1/36 + 1/36
= 2/36
= 1/18
These numbers are multiples of __________.
4, 8, 16, 24
A) 3
B) 4
C) 5
D) 6
Answer:
4
Step-by-step explanation:
All these numbers multiply by 4
Answer:
The answer is B.
Step-by-step explanation:
4÷4=1
8÷4=2
16÷4=4
24÷4=6
The circumference of the inner circle is 22 ft. The distance between the inner circle and the outer circle is 2 ft. By how many feet is the circumference of outer circle greater than the circumference of the inner circle? Use 22/7 for pi .
Answer: 25.1
Step-by-step explanation:
1. Find the radius of the inner circle
(the formula for the circumference of a circle is ) C =2pi r
To find the radius of the inner circle, you would plug in the given information so that your equation looks like this:
22 = 2(22/7)r
then solve for r
r = 3.5
2. add 4 to the radius of the inner circle
3.5 + 4 = 7.5
3. find the circumference of the outer circle using 7.5 as the radius
22 = 2 (22/7) 7.5
C = 47.1
4. Subtract the circumference of the inner circle from the circumference of the outer circle
47.1 - 22 = 25.1
Mia drew a scale drawing of a game room. The air hockey table is 6 inches wide in the
drawing. The actual air hockey table is 4 feet wide. What scale factor does the drawing use?
Simplify your answer and write it as a fraction.
Answer:
8x
Step-by-step explanation:
The drawing of the air hockey table is 1/8th the size of the actual air hockey table so the scale factor the drawing uses is 8x
What number is in the tenth's place? 41.53
Answer: The number in the tenth's place is 5
Step-by-step explanation:
There is no ones place in decimals
41.53
the tenth's place come first then the hundredth's and so on.
Answer:
5
Step-by-step explanation:
4 = tens
1 = ones
.
5 = tenths
3 = hundredths
Hey ! Can anyone help me solve these problems please. Thank you !
Use the slope formula to find the slope of the line through the points (2, 10) and (-3,-6).
Answer:
3.2
Step-by-step explanation:
Your input: find the slope given two points P=(2,10) and Q=(−3,−6).
The slope of a line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by
m=y2−y1/x2−x1
We have that x1=2, y1=10, x2=−3, y2=−6.
Plug the given values into the formula for slope: m=(−6)−(10)/(−3)−(2)=−16/−5=16/5.
Answer: the slope of the line is m=16/5≈3.2.
Tony works 25 hours per week. His take home pay is $19.20 per hour. If Tony is able to save all of his earnings, how
long will it take him to save at least $5760? Show your work.
Answer:
He'll have to work for 12 weeks.
Step-by-step explanation:
19.20×25=480.00(how much he earns in a week)
5760/480=12
Susan has a collection of 44 nickels and dimes. If the number of nickels is three times the number of dimes, how many nickels and how many dimes does she have?
Answer:
33 nickels and 11 dimes
Step-by-step explanation:
11*3= 33
11 + 33 = 44
please help
cos40∘=sin(x+30∘)
Answer:
x = 20 degrees.
Step-by-step explanation:
cos40∘=sin(x+30∘)
sin (x + 30) = 0.766
x + 30 = arcsin 0.766 = 50
x = 50 - 30 = 20.
Answer:
x = 20
Step-by-step explanation:
cos(angle) = sin(complement of angle) , then
cos40 = sin(90 - 40) = sin50 , then
sin(x + 30) = sin50 , that is
x + 30 = 50 ( subtract 30 from both sides )
x = 20
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
A 34
B 47.5
C 68
D 95
Answer:
A
Step-by-step explanation:
If the mean of a standardized test with a normal distribution is 54.3 and the standard deviation is 4.6. what is the best approximation of the percent of the scores
that fall between 54.3 and 63.5?
a
Laura and Martin obtain a 25-year, $90,000 conventional mortgage at 9.5% on a house selling for $120,000. Their monthly mortgage payment, including principal and
interest, is $786.60.
a) Determine the total amount they will pay for their house.
b) How much of the cost will be interest?
c) How much of the first payment on the mortgage is applied to the principal?
Part a)
The home value is $120,000 and they get a loan for $90,000.
This must mean the down payment was 120,000 - 90,000 = 30,000 dollars. This is the payment made up front.
The mortgage has a monthly payment of $786.60 which is done for 25 years = 25*12 = 300 months. They pay back 786*300 = 235,800 dollars.
Therefore, the total amount they pay for the house is:
downPayment + loanRepayment = 30,000 + 235,800 = 265,800
Answer: $265,800=======================================================
Part b)
Refer to the previous part. Laura and Martin pay back $235,800 after being loaned $90,000
The total amount of interest is 235,800 - 90,000 = 145,800 dollars.
Answer: $145,800=======================================================
Part c)
The annual interest rate is 9.5% which converts to the decimal form 0.095
Divide this over 12 to get the monthly interest rate in decimal form.
0.095/12 = 0.00791667 approximately
Then multiply this with the initial balance of $90,000
90,000*0.00791667 = 712.5003
This rounds to 712.50 and this represents the interest for the first month.
This leads to:
principal = monthlyPayment - interest
principal = 786.60 - 712.50
principal = 74.10
It is unfortunately common practice that the starting monthly payments will be mostly interest. As time goes on, the increase payments decrease because they are tied directly to the remaining balance.
Answer: $74.10
8. (10 pts) A square plate is being heated so that the length of a side increases at a rate of 0.08 cm/min. How fast is the area increasing when the length of a side is 12cm?
Answer:
none of the fruit are not ripe
A group of students is writing a phone message app to provide better word suggestions based on the context of the word and the words the person used in the past. They will earn an A on the project if their teacher is convinced that their program suggests the correct word at least 54% of the time. The current success rate for this app is 54%. The teacher randomly selects 100 words and finds that the students’ program correctly suggests 64 of the words. To determine if this data provide convincing evidence that the proportion of correct words is more than 54%, 150 trials of a simulation are conducted. The results are shown in the dotplot. The teacher is testing the hypotheses: H0: p = 54% and Ha: p > 54%, where p = the true proportion of words the app will correctly predict. Based on the results of the simulation, what is the estimate of the P-value of the test?
Find the equation of the tangent to the circle x2 + y2 = 109 at point (-10,3)
Answer:
10x - 3y = -109 .
Step-by-step explanation:
x^2 + y^2 = 109
Implicit Differentiation:
2x + 2y.y' = 0
y' = -2x/2y = -x/y
So at the point (-10,3) the gradient of the tangent is -(-10)/3 = 10/3.
Equation of the tangent:
y - y1 = m(x - x1)
y - 3 = 10/3(x + 10)
y - 3 = 10/3 x + 100/3
3y - 9 = 10x + 100
-109 + 3y = 10x
10x - 3y = -109
12) Write the equation of a rational function
Vertical asymptote at x = 0 and x = -1
Horizontal asymptote at y = -4
Hole at x = 12
X-intercepts at x = 5, x=-7 L
Answer:
[tex] \frac{4(x - 5)(x + 7)(x - 12)}{(x + 1)(x)(x - 12)} [/tex]
Step-by-step explanation:
A rational function is
[tex] \frac{p(x)}{q(x)} [/tex]
where q(x) doesn't equal zero.
If p is a asymptote, or hole at that value, then we will use
[tex](x - p)[/tex]
Step 1: We have asymptote as 0 and -1 so our denomiator will include
[tex](x - 0)(x - ( - 1)[/tex]
Which is
[tex](x)(x + 1)[/tex]
So our denomator so far is
[tex] \frac{p(x)}{x(x + 1)} [/tex]
Step 2: Find Holes.
Since 12 is the value of the hole,
[tex](x - 12)[/tex]
is a the binomial.
This will be both on the numerator and denomator so qe have
[tex] \frac{(x - 12)}{x(x + 1)(x - 12)} [/tex]
Step 3: Put the x intercepts in the numerator.
Since 5 and -7 is the intercepts,
[tex] \frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)} [/tex]
Step 4: Horinzontal Asymptotes,
Multiply the numerator and denomiator out fully,
[tex] \frac{ {x}^{3} - 10 {x}^{2} - 59x + 420 }{ {x}^{3} - 12 {x}^{2} + x - 12} [/tex]
Take a L
look at the coefficients,
Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.
Multiply the numerator by 4.
[tex] \frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)} [/tex]
Above is the function,
a manufacturer wishes to recieve $4800 for a batch of items. when 1200 items were found to be defective, the selling cost per item increased by $0.20. how many items were manufactured.
Answer:
Abput 12000 items were produced yes and i think it is nice that yk like yes
Step-by-step explanation:
Jason drew a square with a side length of 8 cm. and Bella drew a rhombus with a side length of 8 cm. Jason says the perimeter of the square is smaller than the perimeter of the rhombus. Bella says they have the same perimeter. Which of them is correct and why? A. Jason is correct because a square is always smaller than a rhombus. B. Bella is correct because the rhombus and square have equal side lengths. C. Jason is correct because a square has fewer sides than a rhombus. D. Bella is correct because a square is half the perimeter of the rhombus. 5 / 18 4 of 18 Answered
Answer:
B
Step-by-step explanation:
to find the perimeter of a square its side*number of sides
which would be 8*4
to find the perimeter of a rhombus its 4*side length
which would be 4*8
therefore, its b they both have the same perimeter
Simplify (X-2)(x+3)(2x+1)
Answer:
Step-by-step explanation:
Use FOIL method.
(x -2)(x+3) = x*x + x*3 + (-2)*x + (-2)*3
= x² + 3x - 2x -6 {Combinelike terms}
= x² + x - 6
(x² + x -6)*(2x + 1) = x²*2x + x²*1 + x*2x +x*1 + (-6)*2x + (-6)*1
= 2x³ + x² + 2x² + x -12x - 6
= 2x³ + 3x² - 11x - 6
what is the measure of the space occupied by a solid. (Measured in cubic units)
6 · 6 · 6 · 6 = 1,296. Using exponents, write two more expressions that also have a value of 1,296.
GEOMETRY Find the diameter d of the circle in the figure at the right. Round to the nearest tenth if necessary.
18 ft
d ft
22 ft
12.6 ft
O 160 ft
O 4'ft
28,4 ft
Answer:
d = 12.6 ft
Step-by-step explanation:
From inspection of the given diagram, the diameter of the circle is equal to the shortest leg of the right triangle.
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, use Pythagoras Theorem to find the measure of d.
Given values:
a = db = 18 ftc = 22 ftSubstitute the given values into the formula and solve for d:
[tex]\implies d^2+18^2=22^2[/tex]
[tex]\implies d^2+324=484[/tex]
[tex]\implies d^2=484-324[/tex]
[tex]\implies d^2=160[/tex]
[tex]\implies d=\sqrt{160}[/tex]
[tex]\implies d=12.6491106...[/tex]
Therefore, d = 12.6 ft (nearest tenth).
Learn more about Pythagoras Theorem here:
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer:13.1
Step-by-step explanation:
Area equation:S=[tex]S=\frac{1}{2} ab sinθ[/tex]
The 92 children who were asked when they took their first lesson
Answer:
I need more to solve!!
Have an amazing day!!
If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose
Answer: 1250 square feet!
Step-by-step explanation:
A (25)=25•(100-2•25)=25•50=1250 Sq Ft
If you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral. The area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall.
Any rectangle's length and width differences must be as small as possible for the area to be maximized.
The largest area you can enclose
A =25×(100-2•25)
A=25•50
A=1250 Sq Ft
Thus, if you have 100 feet of fencing and want to enclose a rectangular area up against a long, straight wall, The largest area you can enclose will be 1250 sq Ft.
Learn more about the rectangle here:
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Kyle lives in a state that has a 6% (or 0.06) sales tax. If c represents the cost of an item and t represents the sales tax on the item, which equation expresses the relationship between these two variables?
Group of answer choices
t = 6c
t = 0.6c
t = 0.06c
t = c + 0.06
Answer:
The answer is the 3rd option
t = 0.06c
Answer:
t = 0.06c
Step-by-step explanation:
7 – (5t - 13) = -25
i need help with this question
Answer:
t=9
Step-by-step explanation:
Solve -
Distribute :7-(5t - 13) = - 25
7 - 5t + 13 = - 25
Add the numbers :7 – 57 + 13 = -25
20-51 = -25
Rearrange terms :20-51 = -25
-51+ 20 = -25
Subtract 20 from both sides :-51 + 20 = -25
-51+20-20-25-20
Simplify :Subtract the numbers
-51+ 20-20-25-20
-5:=-25-20
Subtract the numbers
-51 = -25-20
-51 = -45
-51 = -45
Divide both sides by the same factor : -51 = -45 -5t -5 -45- -5 =
Simplify : Cancel terms that are in both the numerator and denominator :: -5t - = -45 - -5
t = - 45 - -5
Divide the numbers :
t = - 45 - -5 ” t=9 ” here’s the answer
Which phrase best describes the relationship indicated by the scatter plot? A. Constant correlation B. negative correlation C. Positive correlation D. no correlation