Answer:
35
Step-by-step explanation:
3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9
a+b=?
------
all numbers get cancelled apart from the first denominator and the last numerator:
1/2*a= 9
a= 18then
b= a-1= 18-1= 17a+b= 18+17= 35
find the slope of the line through points 8,2 and -1,-4
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m= (y2-y1)/(x2-x1)
= (-4-2)/(-1-8)
= -6/ -9
= 2/3
The histogram to the right represents the weights (in pounds) of members of a certain high-school debate team. What is the class width? What are the approximate lower and upper class limits of the first class? The class width is_______.
Answer:
Class width = 20
Approximate lower class limit of the first class = 110
Approximate Upper class limit of the first class = 119
Step-by-step Explanation:
The class width of the histogram attached below can be gotten by finding the difference between successive lower class limits.
Thus, class width = 130 - 110 = 20
The approximate lower class limit of the first class is the lowest score we have in the first class = 110
The approximate upper class limit of the first class is the closest highest score that fall within the first class and is below the lower limit of the second class. Thus approximate upper class limit of the first class = 129
Please answer this correctly
Answer:
d = 2
Step-by-step explanation:
Using the formula
A=pq/2
Dont forget to click THANKS
Convert decimal +61 and +27 to binary using the signed 2’s complement representation and enough digits to accommodate the numbers. Then perform the binary equivalent of (27) + (-61), (-27) + (+61), and (-27) + (-61). Convert then answers back to decimal and verify that they are correct.
Answer:
the sum is 01011000₂ = 88
Step-by-step explanation:
For numbers of magnitude less than 128, it is convenient to use an 8-bit representation. I find it works will to convert back and forth through the octal (base-8) representation, as each base-8 digit converts nicely to three (3) base-2 bits.
61 = 8·7 +5 = 075₈ = 00 111 101₂
27 = 8·3 +3 = 033₈ = 00 011 011₂
Then ...
[tex]\begin{array}{cc|ccc}&61&&00111101\\+&27&+&00011011\\ &\overline{88}&&\overline{01011000}\end{array}[/tex]
__
Starting from the right, we can convert the binary back to octal, then to decimal by considering 3 bits at a time:
01 011 000₂ = 130₈ = 1·8² +3·8 +0 = 64 +24 = 88
The binary sum is the same as the decimal sum.
PLEASE HELP !!
Problem:
Find P(3).
Answers:
1/6
1/8
3/6
1
Answer:
The probability of spinning a 3 out of the 6 options is 1/6.
Answer: 1/6
Step-by-step explanation:
Im assuming the p stands for probability. There is a total of 6 slices, the 3rd slice takes up 1/6th of the circle
Barbara can pay either $80 per month or one lump sum of $800 per year for car insurance. How much does she save yearly if she chooses the lump sum payment option?
Answer:
$160
Step-by-step explanation:
In the monthly payment option she would pay $80 per month, therefore in a year (12 months) she would pay:
$80*12 = $960
We can see that this amount is greater than the $800 she would pay in the lump sum payment option.
The money she would save is:
$960 - $800 = $160
She would save $160 yearly with the lump sum payment option.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
Answer:
Step-by-step explanation:
The formula is y = mx + b
m being the slope, rise over run. And b being the y-intercept. Right off the bat we can visually see the y-intercept is -4.
To find slope, we need to take two sets of coords and apply the slope fomula. The slope fomula is change in y divided by the change in x. The function itself is straight, so that means the slope will be the exact same no matter which points you choose.
(4, -1) and (8, 2) are coords on the line. Do 2 - (-1) to get 3. then do 8 - 4 to get 4. Finally, we just gotta do 3/4 which is simply [tex]\frac{3}{4}[/tex].
We have the slope of 3/4 and we have the y-intercept of -4. Just plug it in the standard formula of y = mx + b to get:
[tex]y=\frac{3}{4} x-4[/tex]
Give your answers in pi
Answer:
36π
Step-by-step explanation:
area=πr²
=πx6x6
6x6=36
area = 36π
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 3.0 + 0.25 sin 2πt 4.2 . (a) Find the rate of change of the brightness after t days. dB dt =
Answer:
a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]
Step-by-step explanation:
a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:
[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]
b) The rate of increase after one day is:
[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]
[tex]\frac{dB}{dt}\approx 5.595[/tex]
Age (years) Population Under 15 2600 15 - 64 16000 Over 64 4000 Calculate the child dependency ratio from the chart above. Round to 3 decimals places.
Answer:
16.25%
=0.163 (correct to 3 decimal places)
Step-by-step explanation:
The child dependency ratio of a population is defined as the number of children (Under 15 years) divided by the working-age population (15–64 years old).
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{{\mathrm{ Population}\,\left( \text{Under 15} \right)}}{{\mathrm{ Population}\,\left( {15-64} \right)}}\times 100[/tex]
From the given table:
Population Under 15 years = 2600
Population of the working class (between 15-64) = 16000
Therefore:
[tex]\mathrm{ Child}\;\mathrm{ dependency}\;\mathrm{ ratio}=\dfrac{2600}{16000}\times 100\\\\=16.25\%[/tex]
=0.163 (correct to 3 decimal places)
Alex is paid $30/hr at full rate, and $20/hr at a reduced rate. The hours of work are paid at a ratio of 2:1, full rate : reduced rate. For example, if he worked 3 hours, he would be paid 2 hours at full rate and 1 hour at reduced rate. Calculate his pay for 4 hours of work
Answer:
His pay for 4 hours of work is $106.67.
Step-by-step explanation:
2:1, full rate : reduced rate.
This means that for each 2+1 = 3 hours that he works, 2 he has full pay and 1 he has reduced pay.
4 hours
How much are full pay?
For each 3, 2 are full pay. For four?
3 hours - 2 full pay
4 hours - x full pay
[tex]3x = 8[/tex]
[tex]x = \frac{8}{3}[/tex]
So for [tex]\frac{8}{3}[/tex] hours he makes the full pay($30) and for [tex]4 - \frac{8}{3} = \frac{12}{3} - \frac{8}{3} = \frac{4}{3}[/tex] he makes reduced pay($20).
Calculate his pay for 4 hours of work
[tex]30*\frac{8}{3} + 20*\frac{4}{3} = 106.67[/tex]
His pay for 4 hours of work is $106.67.
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
what is the solution set for the equation (x+3)(x-8)=0
Answer:
x= -3 x=8
Step-by-step explanation:
(x+3)(x-8)=0
We can use the zero product property to solve
x+3 =0 x-8 =0
x= -3 x=8
Answer:
x=8
Step-by-step explanation:
Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematical notation, and clearly identify the claim and type of testing.
Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
3. Bob the Builder wants to earn an annual rate of 10% on his investments,
how much (to the
nearest cent) should he pay for a note that will be worth $3,000 in 9 months?
Answer:
He should pay $2,790.7.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
In this question:
Rate of 10%, so I = 0.1.
9 months, so [tex]t = \frac{9}{12} = 0.75[/tex]
How much should he pay for a note that will be worth $3,000 in 9 months?
We have to find P for which T = 3000. So
[tex]T = E + P[/tex]
[tex]3000 = E + P[/tex]
[tex]E = 3000 - P[/tex]
Then
[tex]E = P*I*t[/tex]
[tex]3000 - P = P*0.1*0.75[/tex]
[tex]1.075P = 3000[/tex]
[tex]P = \frac{3000}{1.075}[/tex]
[tex]P = 2790.7[/tex]
He should pay $2,790.7.
On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer: D 180 degrees rotation about the origin.then a dilation by a scale factor of one-third.
Step-by-step explanation:
A( -9,3) B(-9,6) C (0,3)
After a rotation of 180 degrees you will have the new points as
A (9,-3) B( 9,-6) C (0, -3)
The you after dilating it by a scale factor of 1/3
you will get the coordinates
A ( 3,-1) B( 3,-2) C(0,-1)
which match is what was given in the question.
Answer:
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Step-by-step explanation:
took the test
Please help! Correct answer only, please! Jason has the following averages in his math class: homework avg: 80 quiz avg: 84 test avg: 74 final exam: 60 if the teacher weights homework at 20%, quizzes at 30%, tests at 40%, and the final exam at 10%, what is jason's class average? A. 74 B. 77 C. 79 D. 82
Answer:
77
Step-by-step explanation:
80*0.2 + 84*0.3 + 74*0.4 + 60*0.1 = 76.8 = 77
(02.04 MC) Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3. y = −3x − 13 y = −3x + 11 y = −3x + 13 y = −3x + 1
Answer:
it is b
Step-by-step explanation:
the answer is b because
algebra parabola question see picture above
Answer:
see below
Step-by-step explanation:
(-1, -9) is a vertex or minimum.
(-4, 0) is an x-intercept / zero of the function / solution
(2, 0) is also an x-intercept / zero of the function / solution
The parabola has a minimum.
An intravenous fluid is infused at the rate shown in the table. What is the missing value?
Minutes
Milliliters
3
ܢܚܪ
2.
?
3
9
4
12
3
6
9
24
Answer:
the answer is 6!!!!!!
Step-by-step explanation:
The missing value in the table is 5
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
An intravenous fluid is infused at the rate shown in the table
Minutes Milliliters
3 4
? 12
2. 3
? 6
3 9
9 24
Slope=24-9/9-3
=15/3
=5
Now 5=12-4/x-3
5=8/x-3
5x-15=8
5x=23
x=23/5
x=4.6
x=5
The missing number is 5.
Hence, the missing value in the table is 5
To learn more on slope of line click:
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There are two fields whose total area is 56 square yards. One field produces grain at the rateof34bushel per square yard; the other field produces grain at the rate of23bushel per squareyard. If the total yield is 40 bushels, what is the size of each field
Answer:
the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
Step-by-step explanation:
With the statement we can make a system of 2x2 equations, where:
"x" is the area of the first field
"y" is the area of the second field
However,
x + y = 56 => x = 56 - y
3/4 * x + 2/3 * y = 40
replacing we have:
3/4 * (56 - y) + 2/3 * y = 40
42 - 3/4 * y + 2/3 * y = 40
-0.0833 * y = 40 - 42
y = -2 / -0.0833
y = 24
now for x:
x = 56 - 24
x = 32
This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
— 3х + 7 < 19 ?
Help plz
Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
How do you find arc length???
Answer:
π
Step-by-step explanation:
For a circle, arc length is equal to the radius times the angle.
s = rθ
s = (1) (π − 0)
s = π
What is the surface area of a hemisphere with a radius 10
Answer:
Maths keeps one mentally active. The total surface of a hemisphere = 3(pi)r^2. So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Step-by-step explanation:
hope this helps you :)
Answer:
The total surface of a hemisphere = 3(pi)r^2.
So if the radius = 10 cm, then the TSA = 3(pi)r^2 = 300(pi) = 942.8571429 sq cm.
Classify the following triangle .check all that apply
Answer:
acute and scalene
Step-by-step explanation:
Answer:no entiendo esta en ingles
Step-by-step explanation:
What’s the correct answer for this?
Answer:
1) Antonio's statement
2) <A = 123
Step-by-step explanation:
1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.
2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)
Now
7x+5 = 180
7x = 175
x = 25
<A = 5x-2
= 5(25)-2
= 125-2
= 123
Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4
Answer:
x=-2,y=-4
Step-by-step explanation:
By dividing to lowest terms
5x – 5y = 10= x-y=2.......(1)
6x – 4y = 4=3x-2y=2........(2)
By elimination method
Multiply equation (1) by 3 so as to correspond with equation (2)
3(x-y)=3(2)
3x-3y=6..........(3)
Multiply equation (2) by 1 so as to correspond with equation (1)
1(3x-2y)=1(2)
3x-2y=2..........(4)
Then equation (3)-equation (4)
(3x-3y=6)
-
(3x-2y=2)
__________
-y=4
y=-4
Substitute y=-4 into equation(1)
x-(-4)=2
x+4=2
x=-2
Therefore x=-2,y=-4
A start-up news company is looking to expand their audience and is interested in studying the how many adults regularly use social media as a source of news. According to the Pew Research Center, 62% of adults get their news from social media, but researchers want to determine of this proportion is actually greater than 62% in region they plan on advertising on.
They take a random sample of 200 adults in the region they are interested in advertising in and what they use to typically get their news. A total of 137 adults reported regularly getting their news from social media.
The point estimate for this problem is: (report your answer to 3 decimal places)
Checking Conditions: We are told that the sample was randomly selected. Are the other conditions met to perform a hypothesis test for p?
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
C) Yes, the population standard deviation is known.
D) No, the population mean is unknown.
Answer:
Step-by-step explanation:
The point estimate is the sample proportion.
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 137
n = number of samples = 200
p = 137/200 = 0.685
From the information given,
Population proportion = 62% = 62/100 = 0.62
The correct options are
A) Yes, the sample size is greater than 30.
B) Yes, there are at least 10 adults saying they get their news from social media and at least 10 that do not.
Solve using
elimination 5y+3x=9 and 4y-3x=32
Answer:
(x,y)= (-124/27, 41/9)
Step-by-step explanation:
1) Add the equation to eliminate x.
5y+3x=9
4y-3x=32
2) Add 5y and 4y.
5y=9
4y=32 --> 9y=41
3) Get y by itself by dividing 9 on both sides:
y=41/9
4) Substitute Value in the equation 5y+3x=9
5(41/9)+3x=9
5) solve for x
x=-124/27
Step-by-step explanation:
5y + 3x = 9
4y - 3x = 32
using elimination method
subtracting equation 1 from 2 gives
y = -23
substitute to get value of X
5(-23) + 3X = 9
-115 +3x = 9
3x= 124
x = 41.33
Amar wants to make lemonade for a birthday party. He wants to mix 12 tablespoons of sugar in water. He only has a teaspoon which needs to be used 4 times to be equivalent to one tablespoon. At this rate, how many teaspoons of sugar will Amar need to make the lemonade?
Answer:48
Step-by-step explanation:
Given
Amar wants 12 tablespoons of sugar in water.
Amar has teaspoon whose four times is equivalent to 1 tablespoon
i.e. [tex]4\ \text{teaspoon}\equiv 1\ \text{tablespoon}[/tex]
therefore
[tex]12 tablespoon is 4\times 12[/tex]
[tex]\Rightarrow 4\times 12[/tex]
[tex]\Rightarrow 48\ \text{teaspoons}[/tex]
So, amar need to add [tex]48\ \text{teaspoons}[/tex] for lemonade
Answer:6328565394729
Step-by-step explanation:213
sorry