Answer:
0.68
Step-by-step explanation:
Given
Mean = μ = 6 cm
SD = σ = 1.5 cm
We have to find the z-scores for 4.5 and 7.5
z-score for 4.5 = z_1 = (x-μ)/σ = (4.5-6)/1.5 = -1.5/1.5 = -1
z-score for 4.5 = z_2 = (x-μ)/σ = (7.5-6)/1.5 = 1.5/1.5 = 1
We have to find area to the left of z-scores
Using the rule of thumb for SD from mean, 68% of data lies between one standard deviation from mean. So the probability of choosing a band with length between 4.5 and 7.5 cm is 0.68 ..
Select the correct location on the coordinate plane. Ruhana owns a workshop where her team of technicians refurbishes TV sets and DVD players, and then she sells them for a profit. She has set a weekly sales target of at least 35 TV sets or DVD players. Additionally, she must ensure that her team collectively works at least 100 hours each week. It takes 4 hours to refurbish a TV set and 2 hours to refurbish a DVD player. It costs $75 to refurbish a TV set and $40 to refurbish a DVD player. If Ruhana wants to minimize costs, which point represents the optimal number of TV sets and DVD players that her team should refurbish each week?
Answer:
Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.
Step-by-step explanation:
For the given situation let the number of tv sets be x and number of dvd players be y.
Now we have to minimize the cost as it costs $75 to refurbish a tv set and $40 to refurbish a dvd player.
i.e. Minimize z=75x+40y
it gives subject to the constraints
4x+2y≥100......(1)(100 hours each week. It takes 4 hours to refurbish a tv set and 2 hours to refurbish a dvd player.)
x+y≥35.......(2)(weekly sales target is to refurbish at least 35 tv sets or dvd players.)
To plot equation (1) we need to find coordinates of points lying on line (1)
put x=0 gives 2y=100⇒y=50
put y=0 gives 4x=100⇒x=25
So we got points (0,50) and(25,0) for (1)..............(3)
Similarly for equation (2)
put x=0 gives y=35
put y=0 gives x=35
so we got points (0,35) and(35,0) for (2).................(4)
with the help of (3) and (4) we plot the following graph (assume x≥0 and y≥0)
The unbounded feasible region determined by constraints gives the corner points as A(0,50),B(15,20)and C(35,0).
from we get the value of z is minimum at point B (15,20) .
hence we got our optimal solution at B (15,20), where x is the number of tv sets and y is the number of dvd players .therefore Ruhana and her team should refurbish 15 tv sets and 20 dvd players each week to minimize the cost.
(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]
A river is flowing at the rate of 2.4 miles an hour when a boy rows across it. If the boy rows at a still-water speed of 3.1 miles per hour and heads the boat perpendicular to the direction of the current. The ground speed of the boat is _____ miles per hour.
Answer:
3.9 mi/h
Step-by-step explanation:
If the boy is rowing perpendicular to the current, the two vectors form a right triangle.
AB represents the downstream current, BC is the speed across the river, and AC is the ground speed of the boat
AC^2 = 2.4^2 + 3.1^2 =5.76 + 9.61 = 15.37
AC = sqrt(15.37) = 3.9 mi/h
The boat's speed over the ground is 3.9 mi/h.
The ground speed is found to be approximately 3.92 miles per hour.
we use the Pythagorean theorem to solve this problem.
Step-by-step solution:
Identify the speeds: still-water speed of the boat (3.1 miles per hour) and the river's current speed (2.4 miles per hour).Represent the total ground speed as the hypotenuse of a right-angled triangle, where the other two sides are the still-water speed and the current speed.Calculate the ground speed using the Pythagorean theorem: \(ground speed = \sqrt{(still-water speed)^2 + (current speed)^2}\).Substitute the values: \(ground speed = \sqrt{(3.1)^2 + (2.4)^2} = \sqrt{9.61 + 5.76} = \sqrt{15.37}\).Therefore, the ground speed of the boat is approximately 3.92 miles per hour.This demonstrates how mathematical principles can be applied to real-world scenarios, such as navigating a boat across a river with a current.
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.
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.
You find a mutual fund that offers approximately 5% APR compounded monthly. You will invest enough each month so that you will have $1000 at the end of the year. How much money will you have invested in total after one year?
Answer:
The amount you need to invest in a year is $951.3
Step-by-step explanation:
Consider the provided information.
The future value can be calculated as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where, A represents future value, P represents Principal value, r represents interest rate in decimal, n represents number of time interest is compounded and t represents time in years.
Now use the above formula to find the money needed to invest i.e P.
Substitute, n = 12 , t = 1, A = 1000 and r = 5% or 0.05 in the above formula.
[tex]1000=P(1+\frac{0.05}{12})^{12 \times 1}[/tex]
[tex]1000=P(1.00417)^{12}[/tex]
[tex]1000=P(1.0512)[/tex]
[tex]P=951.3[/tex]
Thus, the amount you need to invest in a year is $951.3
977.38 -_- ..........
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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A point on the circumference of the circle with the equation of (x+10)²+(y+1)²=25 is?
A) (-14, -4)
B) (4, 14)
C) (-14, 4)
D) (-4, 14)
Answer:
Option A) (-14, -4)
Step-by-step explanation:
we know that
If a ordered pair lie on the circumference of a circle , then the ordered pair must satisfy the equation of the circle
we have
[tex](x+10)^{2}+(y+1)^{2}=25[/tex]
Verify each ordered pair
case A) we have (-14, -4)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-14+10)^{2}+(-4+1)^{2}=25[/tex]
[tex](-4)^{2}+(-3)^{2}=25[/tex]
[tex]25=25[/tex] ----> is true
therefore
The ordered pair is on the circumference of the circle
case B) we have (4,14)
substitute the value of x and the value of y in the equation and then compare the results
[tex](4+10)^{2}+(14+1)^{2}=25[/tex]
[tex](14)^{2}+(15)^{2}=25[/tex]
[tex]421=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
case C) we have (-14,4)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-14+10)^{2}+(4+1)^{2}=25[/tex]
[tex](-4)^{2}+(5)^{2}=25[/tex]
[tex]41=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
case D) we have (-4,14)
substitute the value of x and the value of y in the equation and then compare the results
[tex](-4+10)^{2}+(14+1)^{2}=25[/tex]
[tex](6)^{2}+(15)^{2}=25[/tex]
[tex]261=25[/tex] ----> is not true
therefore
The ordered pair is not on the circumference of the circle
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
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
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)
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.
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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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.
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
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.
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 %.
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.
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.
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
The rectangle has an area of 24 square centimeters. Find the length a of the rectangle.
The Length of the rectangle is A and the Width of the rectangle is A - 5
To find the length of the rectangle with an area of 24 square centimeters and width of (a-5), solve the quadratic equation a^2 - 5a - 24 = 0, which gives a length a = 8 centimeters.
Explanation:The question asks us to find the length a of a rectangle that has an area of 24 square centimeters, given that the width is a-5. Since area of a rectangle is found by multiplying the length by the width, we can set up the equation a*(a-5) = 24. To find the value of a, we need to solve this quadratic equation.
First, we expand the equation:
a² - 5a = 24
Then, we set the equation to zero:
a² - 5a - 24 = 0
Next, we factor the quadratic equation:
(a - 8)(a + 3) = 0
There are two possible solutions for a:
a = 8a = -3Since a length cannot be negative, we discard a = -3 and conclude that the length a of the rectangle is 8 centimeters.
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]
HELP ME!!!
Find the resulting vector matrix of this matrix multiplication.
The resulting matrix is , where a = and b = .
Answer:
a = 2 and b = 2
Step-by-step explanation:
It is given a matrix multiplication,
To find the value of a and b
It is given that,
| 3 2 | * | -2 | = | a |
|-1 0 | | 4 | | b |
We can write,
a = (3 * -2) + (2 * 4)
= -6 + 8
= 2
b = (-1 * -2) + (0 * 4)
= 2 + 0
= 2
Therefore the value of a = 2 and b = 2
Answer:
a=2 and b=2.
Step-by-step explanation:
The given matrix multiplication is
[tex]\begin{bmatrix}3&2\\ -1&0\end{bmatrix}\begin{bmatrix}-2\\ 4\end{bmatrix}[/tex]
We need to resulting vector matrix of this matrix multiplication.
[tex]\begin{bmatrix}3\left(-2\right)+2\cdot \:4\\ \left(-1\right)\left(-2\right)+0\cdot \:4\end{bmatrix}[/tex]
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}[/tex]
It is given that [tex]\begin{bmatrix}a\\ b\end{bmatrix}[/tex] is resulting matrix.
[tex]\begin{bmatrix}2\\ 2\end{bmatrix}=\begin{bmatrix}a\\ b\end{bmatrix}[/tex]
On comparing both sides, we get
[tex]a=2,b=2[/tex]
Hence, a=2 and b=2.
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 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....
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.
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.
Learn more about Profit calculation here:https://brainly.com/question/32944523
About 1% of the population has a particular genetic mutation. 700 people are randomly selected. Find the standard deviation for the number of people with the genetic mutation in such groups of 700.
Answer: 2.632
Step-by-step explanation:
Given : The probability that the population has a particular genetic mutation = 1 % = 0.01
Let X be a random variable representing the number of people with genetic mutation in a group of 700 people.
Now, X follows the binomial distribution with parameters:
[tex]n=700;\ p=0.01[/tex]
The standard deviation for binomial distribution is given by :-
[tex]\sigma=\sqrt{np(1-p)}\\\\=\sqrt{700\times0.01(1-0.01)}\\\\=2.6324893162\approx2.632[/tex]
Hence, the standard deviation = 2.632
Circle O has a circumference of 367 cm.
What is the length of the radius, r?
6 cm
18 cm
36 cm
72 cm
Answer:
none of the above
Step-by-step explanation:
The applicable relationship is ...
C = 2πr
Solving for r, we get
r = C/(2π) ≈58. (367 cm)/(2·3.14159) ≈ 58.41 cm . . . . no matching choice
_____
When the problem does not include a correct answer choice, I usually suggest you ask your teacher to show you the working of it.
18cm I hope this helps
Nancy and Harry are sliding a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal. What is the magnitude of the horizontal force exerted on the statue?
Answer:
197,8879 N.
Step-by-step explanation:
The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.
The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.
With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.
The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.
F= (120 N cos 60°) + (180 N x cos 40°)
F= 197,8879 N
To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components. Nancy's horizontal force is 60N and Harry's horizontal force is 137.48N. The magnitude of the horizontal force exerted on the statue is 197.48N.
Explanation:To find the magnitude of the horizontal force exerted on the statue, we need to resolve the forces applied by Nancy and Harry into their horizontal components.
Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal, so the horizontal component of her force is 120N * cos(60°) = 60N.
Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal, so the horizontal component of his force is 180N * cos(40°) = 137.48N.
To find the magnitude of the horizontal force exerted on the statue, we sum up the horizontal components of both forces: 60N + 137.48N = 197.48N.