Answer: [tex]\dfrac{3}{10}[/tex]
Step-by-step explanation:
Let A be the event of getting a factor of 15 when a fair spinner numbered 1 - 5 spins and B be the event that a fair coin is tossed.
The factors of 15 = [tex]1,\ 3,\ 5[/tex]
Then ,the probability of obtaining a factor of 15 is given by :-
[tex]P(A)=\dfrac{3}{5}[/tex]
The probability of getting a tail :-
[tex]P(B)=\dfrac{1}{2}[/tex]
Since both the events are independent , thus
The probability of obtaining a factor of 15 and a tail is given by :-
[tex]P(A)\times P(B)\\\\=\dfrac{3}{5}\times\dfrac{1}{2}=\dfrac{3}{10}[/tex]
Hence, the required probability : [tex]\dfrac{3}{10}[/tex]
6. For a particular pickup truck, the percent markup is known to be 115% based on cost to the seller. If the seller paid $15,800 for the truck, what would be the percent markup be based on the sale price? (Round to the nearest tenth percent)
Answer:
53.5 %Explanation:
You can convert the percent markup into a multiplicative factor in this way:
Base price: 15,800 . . . (cost to the seller)
Percent mark up: 115% . . . (based on the cost to the seller)
Sale price: 15,800 + 115% of x = 15,800 + 115 × 15,800 /100 =
= 15,800 + 1.15 × 15,800 = 15,800 (2.15) = 33,970
The markup is:
Markup = price paid by the seller - cost to the seller = 33,970 - 15,800 = 18,170 (notice that this is 115% of 15,800)And the percent markup based on the sale price is:
% = (markup / sale price) × 100 = (18,700 / 33,970) × 100 == 53.49 %
Rounding to the nearest tenth percent that is 53.5 %.
The average price of a gallon of orange juice from October 2013 to September 2014 can be modeled by the function f shown, where x represents the number if months since October 2013,
f(x)=6.12+0.03x
Complete the sentence to describe the change in average price of a gallon of orange juice from October 2013 to September 2014
The average price of a gallon of orange ( 1st-Blank) by (2nd-Blank) each month
1st -Decreased OR Increased
2nd- 3% OR 612% Or $0.03 OR $6.12
Answer:
The average price of a gallon of orange increased by $0.03 each month.
Step-by-step explanation:
It is 11 months between October 2013 and September 2014 so the price after 11 months =
f(11) = 6.12 + 0.03(11)
= 6.12 + 0.33
= $6.45.
This is an increase of 0.33 / 11 = 0.03 / month.
Assume that there is a 55% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on threethree independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to four decimal places as needed.) b. With threethree hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to six decimal places as needed.)
Answer:
a. 0.6975
b. 0.833625
Step-by-step explanation:
a. The probability of both drives failing is 0.55² = 0.3025, so the probability that both drives won't fail is 1 -0.3025 = 0.6975.
__
b. The probability of all three drives failing is 0.55³ = 0.166375, so the probability that all three drives won't fail is 1 -0.166375 = 0.833625.
Calculate the value of x in the illustration below.
Answer:
x = 8.75
Step-by-step explanation:
The measure of angle C is half the measure of arc RS, so ...
6x = (1/2)(105)
x = 105/12 = 8.75 . . . . divide by 6
Answer:
[tex]x=8.75[/tex]
Step-by-step explanation:
We have been given a circle. We are asked to find the value of x for our given circle.
Upon looking at our given circle, we can see that angle RCS is an inscribed angle of arc RS.
We know that measure of an inscribed angle is half the measure of its intercepted arc, so we can set an equation as:
[tex]m\angle RCS=\frac{\widehat{RS}}{2}[/tex]
[tex]6x^{\circ}=\frac{105^{\circ}}{2}[/tex]
[tex]6x^{\circ}=52.5^{\circ}[/tex]
[tex]\frac{6x^{\circ}}{6}=\frac{52.5^{\circ}}{6}[/tex]
[tex]x^{\circ}=8.75^{\circ}[/tex]
[tex]x=8.75[/tex]
Therefore, the value of x is 8.75 for the given circle and option A is the correct choice.
What are the discontinuity and zero of the function f(x) = quantity x squared plus 5 x plus 6 end quantity over quantity x plus 2?
A. Discontinuity at (−2, 1), zero at (3, 0)
B. Discontinuity at (−2, 1), zero at (−3, 0)
C. Discontinuity at (2, 5), zero at (3, 0)
D. Discontinuity at (2, 5), zero at (−3, 0)
Answer:
B. Discontinuity at (−2, 1), zero at (−3, 0)
Step-by-step explanation:
The given function is:
[tex]\frac{x^{2}+5x+6}{x+2}[/tex]
The expression in numerator can be expressed as factors as shown below:
[tex]\frac{x^{2}+5x+6}{x+2}\\\\ =\frac{x^{2}+2x+3x+6}{x+2}\\\\ =\frac{x(x+2)+3(x+2)}{x+2}\\\\ =\frac{(x+2)(x+3)}{x+2}[/tex]
Note that for x = -2, both numerator and denominator will be zero. When both the numerator and denominator of a rational function are zero for a given value of x we get a discontinuity at that point. This discontinuity is known as a hole. This means there is a hole at x = -2
Cancelling the common factor from numerator and denominator we get the expression f(x) = x + 3
Using the value of x = -2 in previous expression we get:
f(x) = -2 + 3 = 1
Thus, there is a discontinuity(hole) at (-2, 1)
For x = -3, the value of the expression is equal to zero. This means x = -3 is a zero or root of the function.
Thus, (-3, 0) is a zero of the function.
Therefore, option B would be the correct answer.
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 95% confidence if she uses a previous estimate of 0.32?
Answer: 8359
Step-by-step explanation:
The formula for sample size needed for interval estimate of population proportion :-
[tex]n=p(1-p)(\frac{z_{\alpha/2}}{E})^2[/tex]
Given : The significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}}=z_{0.025}=\pm1.96[/tex]
Previous estimate of proportion : [tex]p=0.32[/tex]
Margin of error : [tex]E=0.01[/tex]
Now, the required sample size will be :-
[tex]n=0.32(1-0.32)(\frac{1.96}{0.01})^2=8359.3216\approx8359[/tex]
Hence, the required sample size = 8359
To estimate the proportion of adults with high-speed Internet access with a 95% confidence level and a margin of error of 0.01, a sample size of 752 should be obtained.
Explanation:To estimate the proportion of adults who have high-speed Internet access with a 95% confidence level and a margin of error of 0.01, we can use the formula:
Sample Size = (Z^2 * p * (1-p)) / (E^2)
Where Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion from a previous study, and E is the desired margin of error.
With a previous estimate of 0.32, a confidence level of 95% (corresponding Z-score of 1.96), and a margin of error of 0.01, the sample size required would be:
(1.96^2 * 0.32 * (1-0.32)) / (0.01^2) = 752
A sample size of 752 should be obtained to achieve the desired confidence level.
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Nicole has a job transporting soft drinks by truck. Her truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. There is a combined total of 980 cans and bottles in her truck. Let x be the number of 14 -ounce cans in her truck. Write an expression for the combined total weight (in ounces) of the cans and bottles in her truck.
Answer:
[tex]W_{total} = -56X + 68600[/tex]
Step-by-step explanation:
We wil define:
1) "x" as number of cans inside the truck.
2) "y" as number of bottles inside the truck.
We now that the amount of both cans and bottles inside the truck is "980". This quantity is equal to the sum of cans and bottles, so now we can write:
[tex]X+Y=980[/tex]
We will call this expression equation n° 1.
On the other hand, we know that the total weight is a sum of the weight of the cans and the weight of the bottles. The total weight of the cans, for example, is the result of multiplying the numbers of cans in the truck with the weight of each can, like here: ([tex]W_{cans} = X * 14 oz[/tex]
So now we can write:
[tex]W_{total} = (X*14oz) + (Y*70oz)[/tex]
We well call this expression equation n° 2.
From equation n°1 we obtain "y", like this:
[tex]X + Y = 980\\Y = 980 - X[/tex]
And we replace it in equation n°2:
[tex]W_{total} = (X*14) + (Y * 70)\\\\W_{total} = 14X + 70Y\\W_{total} = 14X + 70(980-X)\\W_{total} = 14X + 68600 - 70X\\W_{total} = -56X + 68600[/tex]
Now we have the expression of the total weight considering the amount of cans in the truck.
*** IMPORTANT: there is a character similar to an "A" that i can't erase, maybe is a mistake from brainly. Do not consider it as part of the solution.
Jamie has 105 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 7 kids on her block. Write an equation to show how many pieces of candy each kid will receive.
x = seven divided by one hundred five
x = one hundred five divided by seven
7 + x = 105
x = 105 − 7
Answer:
x=105÷7
Step-by-step explanation:
You have to split the candy with 7 people and you can't split people
For this case we have that the variable "x" represents the amount of candies that each child touches.
If there are a total of 105 candies and they want to be distributed equally among 7 children, then we have the following expression:
[tex]x = \frac {105} {7}[/tex]
Thus, the correct option is:
"x = one hundred five divided by seven"
Answer:
OPTION B
Find the the measure of angle T
Answer:
38.7°
Step-by-step explanation:
Use the Law of Cosines:
[tex]7^2=11^2+10^2-2(11)(10)cosT[/tex] and
49 = 121 + 100 - 220cosT so
-172 = -220cosT and
.781818181 = cosT
Using the inverse cosine function on your calculator, you find that angle T = 38.7 degrees
How would these two problems be solved? I'm very rusty.
Answer:
D, J
Step-by-step explanation:
21)
recall for a linear equation in the form
y=mx + b, where m is the slope
the slope a a line that is perpendicular to the equation is given by m' = -1/m
in this case the line is given with the slope of 3/4
hence the slope of a perpendicular line must be,
-1 / (3/4) = -4/3 (Hence D is the answer)
22)
M is the midpoint between Q (a,d) and R (c,b). Using the midpoint formula (see attached), we find the coordinates of M to be:
M [ (a+c)/2 , (d+b)/2 ]
The distance between P(a,b) and M [ (a+c)/2 , (d+b)/2 ] is given by (see other attached formula):
√ [(a+c)/2 - a]² + [(d+b)/2 - b]²
= √ [(a+c)/2 - (2a/2)]² + [(d+b)/2 - (2b/2)]²
= √ [(a+c - 2a)/2]² + [(d+b-2b)/2]²
= √ [(c - a)/2]² + [(d-b)/2]² (J is the answer)
2 more geometry questions tyty!
Answer:
[tex]\large\boxed{\bold{Q1.}\ \angle W,\ \angle Y,\ \angle X}\\\boxed{\bold{Q2.}\ \angle D>\angle E}[/tex]
Step-by-step explanation:
Q1.
2x + 9 > 2x + 1 subtract 2x from both sides
9 > 2 TRUE → ∠Y > ∠W
∠Y = (2x + 9) and ∠W = (2x + 1) are acute angles
∠X is right angle
right angle > acute angle
Therefore:
∠W < ∠Y < ∠X
Q2.
Angles B, C, and E are acute angles.
Angles A, D and F are obtuse angles.
obtuse angle > acute triangle
Therefore
∠D > ∠E
A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours. The correct value of the test statistic for the appropriate hypothesis test is
Answer: 3.5308
Step-by-step explanation:
Claim : The firm's professionals volunteer an average of more than 15 hours per month.
i.e. [tex]\mu>15[/tex]
Null hypothesis : [tex]H_0:\mu\leq15[/tex]
Alternative hypothesis : [tex]H_1:\mu>15[/tex]
Sample size : [tex]n=24[/tex]
The sample mean : [tex]\overline{x}=16.6\text{ hours}[/tex]
Sample standard deviation : [tex]\sigma=2.22\text{ hours}[/tex]
The test-statistics for the population mean is given by :-
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
i.e. [tex]z=\dfrac{16.6-15}{\dfrac{2.22}{\sqrt{24}}}=3.5307960256\approx3.5308[/tex]
Hence, the correct value of the test statistic for the appropriate hypothesis test is 3.5308.
A t-statistic can be computed using the formula: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Applied to the given scenario, it would test the hypothesis of average volunteer hours vs the claimed 15 hours/month.
Explanation:In this scenario, you are being asked to conduct a one-sample t-test.
Set up your null hypothesis (H0), which assumes no effect, so that the true volunteer hours would be equal to 15 hours/month, and the alternative hypothesis (Ha) would be that average volunteer hours are more than 15 hours/month.
The formula to calculate the t-statistic is: (sample mean - population mean) / (standard deviation / sqrt(sample size)). Using given values, it would look like this: (16.6 - 15) / (2.22 / sqrt(24))
Compute this, and the resulting value will be your t-statistic.
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Please help i have no idea what im doing, will mark brainliest! Its the fourth option right?
Answer:
D. 1, 3, 5, and 7 are congruent / 2, 4, 6, and 8 are congruent
Step-by-step explanation:
Vertical angles (such as 5 and 7) are congruent.
This means that angles 5 and 7 are congruent,
angles 1 and 3 are congruent,
angles 6 and 8 are congruent,
and angles 2 and 4 are congruent.
YOU WILL GET BRAINIEST PLEASE ANSWER 20 POINTS!!!!!
Solve the equation for 0 ≤ x < 360.
tan2x - tan(x) = 2
135 degrees
315 degrees
no solution
Both A and B
Answer:
Both A and B . . . . . and 2 more answers
Step-by-step explanation:
Completing the square, you get
tan²(x) -tan(x) +0.25 = 2.25 . . . . . add 0.25
(tan(x) -0.5)² = 1.5²
tan(x) = 0.5 ± 1.5 = {-1, 2}
For tan(x) = -1, the solutions are ...
x = arctan(-1) = 135°, 315°
For x = 2, the solutions are ...
x = arctan(2) ≈ 63.435°, 243.435°
The standard formula for the volume of a rectangular pyramid is . If the pyramid is scaled proportionally by a factor of k, its volume becomes V' = V × k3. Use your algebra skills to derive the steps that lead from to V' = V × k3 for a scaled rectangular pyramid. Show your work.
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The volume of a rectangular pyramid is equal to
[tex]V=\frac{1}{3}LWH[/tex]
where
L is the length of the rectangular base
W is the width of the rectangular base
H is the height of the pyramid
If the pyramid is scaled proportionally by a factor of k
then
the new dimensions are
L=kL
W=kW
H=kH
substitute and find the new Volume V'
[tex]V'=\frac{1}{3}(kL)(kW)(kH)[/tex]
[tex]V'=\frac{1}{3}(k^{3})LWH[/tex]
[tex]V'=(k^{3})\frac{1}{3}LWH[/tex]
[tex]V'=(k^{3})V[/tex]
The new volume is equal to the scale factor k elevated to the cube multiplied by the original volume
Answer:
V = πr2h
V' = π × (k × r)2 × (k × h)
= π × k2 r2 × kh
= k3 × πr2h
= k3 × V
Step-by-step explanation:
Question - A grapefruit is approximately spherical. Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters. What is the surface area of one-half of the cut grapefruit?
A) 72π cm2
B) 108π cm2
C) 180π cm2
D) 432π cm2
Answer:
B) 108π cm^2
Step-by-step explanation:
We assume the circumference measurement is the same as it would have been before the fruit was cut. In that case, the radius is found from ...
C = 2πr . . . . . . . . . formula relating circumference and radius
12π cm = 2πr . . . . substitute given information
6 cm = r . . . . . . divide by 2π
The surface area of a hemisphere is 3 times the area of the circular face:
S = 3πr^2
S = 3π(6 cm)^2 = 108π cm^2
The surface area of the grapefruit half is 108π cm^2.
Answer:
B) 108π cm2
Step-by-step explanation:
If a grapefruit is approximately spherical and Jane cuts the grapefruit in half and determines that the circumference of the resulting hemisphere is 12π centimeters, the surface area of one-half of the cut grapefruit is 108π cm2.
Formula: 2πr
S = 3π(6 cm)^2
Factor completely 5x2 − 50x + 120.
Select one:
a. 5(x − 3)(x − 8)
b. (5x − 15)(x − 8)
c. (x − 4)(5x − 30)
d. 5(x − 4)(x − 6)
Question 2
Factor completely 64x2 − 1
Select one:
a. (8x − 1)(8x − 1)
b. (8x − 1)(8x + 1)
c. (1 − 8x)(1 − 8x)
d. (1 − 8x)(1 + 8x)
Answer:
Q1. d. 5(x - 4)(x - 6)Q2. b. (8x - 1)(8x + 1)Step-by-step explanation:
[tex]\bold{Q1}\\\\5x^2-50x+120=5(x^2-10x+24)=5(x^2-6x-4x+24)\\\\=5\bigg(x(x-6)-4(x-6)\bigg)=5(x-6)(x-4)\\\\\bold{Q2}\\\\64x^2-1=(8x)^2-1^2=(8x-1)(8x+1)\\\\\text{Used}\ a^2-b^2=(a-b)(a+b)[/tex]
Answer:
see explanation
Step-by-step explanation:
1
Given
5x² - 50x + 120 ← factor out 5 from each term
= 5(x² - 10x + 24)
To factor the quadratic
Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term ( - 10)
The factors are - 4 and - 6, since
- 4 × - 6 = 24 and - 4 - 6 = - 10, hence
x² - 10x + 24 = (x - 4)(x - 6) and
5x² - 50x + 120 = 5(x - 4)(x - 6) → d
2
64x² - 1 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
64x² = (8x)² ⇒ a = 8x and b = 1
64x² - 1
= (8x)² - 1² = (8x - 1)(8x + 1) → b
(Please help if you can)
If f(x) = -2x - 5 and g(x) = x4, what is (g° 0(-4)?
Enter the correct answer
I assume the question is to find [tex](g\circ f)(-4)[/tex]
[tex](g\circ f)(x)=(-2x-5)^4\\\\(g\circ f)(-4)=(-2\cdot(-4)-5)^4=3^4=81[/tex]
Delaware Trust has 450 shares of common stock outstanding at a market price per share of $27. Currently, the firm has excess cash of $400, total assets of $28,900, and net income of $1,320. The firm has decided to pay out all of its excess cash as a cash dividend. What will the earnings per share be after this dividend is paid? A. $2.69 B. $2.86 C. $2.93 D. $3.07 E. $3.24
Answer:
Earnings per share is $2.93
Step-by-step explanation:
Given data
shares = 450
assets = $28,900
net income = $1,320
to find out
earnings per share
solution
Earnings per share is directly calculate by net income / total share
here we know net income and that share i.e.450
so
Earnings per share = net income / total share
Earnings per share = 1,320 / 450
Earnings per share = $2.93
so option C is right i.e. $2.93
pleasee help fast
Determine which trigonometric function to use to solve for the hypotenuse. Then,
solve for the length of the hypotneuse.
b=9
A=55.8
A.cosin, .062
B.sin,10.8
C.sin,16.0
its not D
Answer:
Cos function should be used for the determination of the length of the hypotenuse.
What are the two cases in which the Laws of Sines can be applied to solve a non-right triangle?
Case I. You know the measures of two angles and any side of the triangle.
Case II. You know the measures of two sides and an angle opposite one of the two known sides.
Case III. You know the measures of two sides and the included angle.
Case IV. You know the measures of all three sides.
Answer:
Case I, Case II
Step-by-step explanation:
For cases III and IV, you need the Law of Cosines.
The Law of Sines can be used when you have at least one side and the angle opposite. If you know two angles of a triangle, you know all three, so the given angles don't necessarily have to be opposite the given side if two angles are known.
The Laws of Sines can be applied to solve Case I and Case II.
Complete the synthetic division problem below. What is the quotient in polynomial form?
Answer:
C
Step-by-step explanation:
Answer: OPTION C
Step-by-step explanation:
You need to follow these steps:
- Carry the number 1 down and multiply it by the number 2.
- Place the product obtained above the horizontal line, below the number 5 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number 2.
- Place the product obtained above the horizontal line, below the number -14 and add them.
Then:
[tex]2\ |\ 1\ \ 5\ -14\\\\.\ \ |\ \ \ \ 2\ \ \ 14\\------\\.\ \ \ 1\ \ \ 7\ \ 0[/tex]
Therefore, the quotient in polynomial form is:
[tex]x+7[/tex]
This is a tough one :/
If f(x) = -x + 7 and g(x) = radical of x– 3,
what is (f º g)(4)
Answer:
6
Step-by-step explanation:
To solve, first plug in 4 as your x value for your g(x) equation.
[tex]g(4)=\sqrt{4-3} \\g(4)=\sqrt{1} \\g(4)=1[/tex]
Next, plug in the value of g(4) into your f(x) equation for x.
[tex]f(1)=-1+7\\f(1)=6[/tex]
At Harry's discount hardware everything is sold for 20 percent less than the price marked. If Harry buys tool kits for $80,what price should he mark them if he wants to make a 20percent profit on his cost?
Answer:
$120.
Step-by-step explanation:
The amount he sells the tool kit for = 80 + 20% of 80
= 80 + 16
= $96.
Let m be the marked price, then
m - 0.20m = 96
0.8m = 96
m = $120.
To make a 20 percent profit on tool kits costing $80, with a 20 percent discount applied, Harry should mark the tool kits for $120.
Explanation:
The subject of this question is profit calculation. This is a common topic in Mathematics, particularly in the field of business or financial mathematics. In order to understand this question, we need to consider the cost price with the profit margin and the discount offered.
In this case, if Harry buys tool kits for $80 and wants to make a 20 percent profit on his cost, he must initially price the tool kits in a way that both his profit is covered and the customer sees a discount of 20 percent.
Firstly, we calculate the 20 percent profit which is given by 0.2 x $80 = $16. This implies that the price before applying discount should be $80 (cost price) + $16 (profit) = $96.
Now, if Harry gives a 20% discount, the price $96 represents the 80% (100%-discount) of the final price (let's call it X). Therefore, we can write this as 0.8*X = $96. Solving for X gives X = $96 / 0.8 = $120. So, Harry should mark the tool kits for $120.
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I don't know how to find x. Can someone please explain.
Answer:
x° = 109°
Step-by-step explanation:
x° is a "corresponding angle" to either of the upper left or lower right interior angles of the parallelogram. (The lines marked with a single arrow are parallel, as are the lines marked with a double arrow.)
Either of those angles is supplementary to the one marked 71°, so x° and all corresponding angles are 180° -71° = 109°.
There are 100 students each enrolled in at least one of three science classes. Of those students, 60 are enrolled in chemistry, 45 in physics, and 30 in biology. Some students are enrolled in two science classes, and 10 students are enrolled in all three. (a) How many students are enrolled in exactly two science classes? (b) There are 9 students taking both chemistry and physics (but not biology), and 4 students taking both physics and biology (but not chemistry). How many are taking both chemistry and biology (but not physics)? Lewis, Harry. Essential Discrete Mathematics for Computer Science (p. 57). Princeton University Press. Kindle Edition.
Answer:
a) 15
b) 2
Step-by-step explanation:
a) The sum of the enrollments in chemistry (60), physics (45), and biology (30) counts those triply enrolled 3 times and those doubly-enrolled twice. This sum will exceed the total number of students by 1 times those double-enrolled and twice those triply-enrolled.
We know that there are 10 students triply-enrolled, so the difference ...
(60 +45 +30) -2(10) = 15
is the number of doubly-enrolled students.
There are 15 students enrolled in exactly 2 science classes.
__
b) There are 9+4 = 13 students doubly-enrolled in physics and something else. Using the result from part A, there will be 15 -13 = 2 students doubly-enrolled in chemistry and biology, but not physics.
Answer:
a) 15
b) 2
Step-by-step explanation:
There are 15 students in 2 science classes.
2 students enrolled in both chemistry and biology, but not physics.
15 -13 = 2
The formula for the sum of an infinite geometric series, S=a1/1-r, may be used to convert
0.23 (repeated) to a fraction. What are the values of a1 and r?
A. a1=23/10, r=1/10
B. a1=23, r=1/100
C. a1=23/100, r=100
D. a1=23/100, r=1/100
Answer:
D. a1=23/100, r=1/100
Step-by-step explanation:
The repeating fraction can be written as the sum ...
[tex]0.\overline{23}=0.23+0.0023+0.000023+\dots[/tex]
The first term is a1 = 0.23 = 23/100, and each successive term is shifted 2 decimal places to the right, so is multiplied by the common ratio r=1/100.
Answer:
Step-by-step explanation:
Here, a1 = 0.23 and r = 0.01. Thus, the sum of this infinite series will be
a1 0.23 0.23
------- = ------------- = ----------- = 23/99.
1 - r 1 - 1/100 99/100
Check this by dividing 23 by 99 on a calculator. Result: 0.23232323....
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Check the picture below.
Which shows the correct solution of the equation
1/2 a + 2/3b = 50 when b=30
For the given equation, if b=30, then the value of a will be equal to 60.
Like the given equation is a linear equation with two variables (a and b). You can solve this equation replacing b for the informed value (30).
Here it is important to remember the rules to the addition and the mutiplication of integers numbers:
Addition Sign RulesThe rules to addition of numbers are:
+ +
Add Final result (+)
- -
Add Final result (-)
+ -
Subtract Final result (the sign of the integer having greater value )
- +
Subtract Final result (the sign of the integer having greater value )
Multiplication Sign RulesThe rules to multiplication of numbers are:
+ + or - -
The result presents a positive sign (+) because the signs are same.
+ - or - +
The result presents a negative sign (-) because the signs are different.
If b=30, then you can find the value for a from steps below.
[tex]\frac{1}{2}*a +\frac{2}{3} *b=50\\ \\ \frac{1}{2}*a +\frac{2}{3} *30=50\\ \\ \frac{1}{2}*a +2*10=50\\ \\ \frac{1}{2}*a +20=50\\ \\ \frac{1}{2}*a =50-20\\ \\ \frac{1}{2}*a=30\\ \\ a=30*2\\ \\ a=60[/tex]
Read more about rules for adding integers here:
brainly.com/question/18375556
The function h(t)= -1100t+20,000 models the height, h in feet of an airplane t minutes after its starts descending in order for it to land. What is the height of the airplane when its begins to descend? Explain
Answer:
20,000 ft
Step-by-step explanation:
This is a linear equation. The negative sign in front of the 1100 indicates that the line is going from upper left to lower right, the path a plane would definitely travel when it is landing. The 1100 is the speed at which the plane is traveling down.
The standard form of a linear equation is y = mx + b where m is the rate of change (which is the same as the slope), and b is the y-intercept, which is found by replacing x with 0 and solving for y. This is also known as the "starting point" for a linear situation. Since the t in our equation represents the time that has gone by since the plane started its descent in hours, if we replace x with 0, we are effectively saying that NO time has gone by (and the plane has not yet begun to descend). That means that the plane begins its descent at 20,000 feet in the air.