A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50 Steps On A Bearing Of 3150 Sketch Musah's Movement Mark 41 Ii. How Far West Is Musah's Final Point From The Centre? [Mark 41 Iv. How Far North Is Musah's Final Point From The Centre? Mark 41 Describe How You Would Guide A JHS Student
Answer:
60.36 steps West from centre
85.36 steps North from centre
Step-by-step explanation:
Refer to attached
Musah start point and movement is captured in the picture.
1. He moves 50 steps to North, 2. Then 25 steps to West, 3. Then 50 steps on a bearing of 315°. We now North is measured 0°or 360°, so bearing of 315° is same as North-West 45°.
Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.
How far West Is Musah's final point from the centre?
25 + 50/√2 ≈ 60.36 stepsHow far North Is Musah's final point from the centre?
50 + 50/√2 ≈ 85.36 stepsPlease help with this
Answer:
A. 120
Step-by-step explanation:
The rest of the answers are acute.
120 is the only one that matches the type of angle <V is.
Always pay attention to the type of angle it is.
Your’re in charge of evening entertainment for an important client group You use the company credit card to take their four representatives out to dinner. Two people order the steak entree for 32.50 Two people order the grilled tuna for 28.90 and you order the lasagna for 24.95 When the bill comes you tip 20% what is the amount of tip you leave
Answer:
total amount paid = 32.5 + 28.9 + 24.95 = 86.35
20% of the total amount paid = 0.2 * 86.35 = 17.27
you tip 17.25$
What is the value of x?
Answer:
7
Step-by-step explanation:
The two angles created by the angle bisector are the same measure, so we have ...
2x +y = 14 +y
2x = 14 . . . . . . . subtract y
x = 7 . . . . . . . . . divide by 2
how many feet are in 53 yards, 2 feet? enter only the number. Do not include units
There are 161 feet are in 53 yards, 2 feet.
What is unit conversion?
Unit conversion is the process of changing a quantity's measurement between various units, frequently using multiplicative conversion factors.
As we know that;
1 yard = 3 feet
53 yards = 3 ×53 feet
53 yards = 159 feet
53 yards, 2 feet = 159 feet + 2 feet
53 yards, 2 feet = 161 feet
Hence, there are 161 feet in 53 yards, 2 feet.
To learn more about the unit conversion, refer;
https://brainly.com/question/4736731
#SPJ2
The cost in dollars y of producing x computer
desks is given by y = 20x + 3000
х
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $4300. (HintFind x when y = 4300)
a. Complete the table.
х
100
200
300
y
b. For $4300, computer desks can be produced.
Answer:
Step-by-step explanation:
a. table
x = 100,y = 20*100+3000 = 2000+3000 = 5000
x = 200,y = 20*200+3000 = 4000+3000 = 7000
x = 300,y = 20*300+3000 = 6000+3000 = 9000
b：
y = 4300
4300 = 20x+3000
20x = 4300-3000
20x = 1300
x = 1300/20
x = 65
so 65 computer desks can be produced.
What is the circumference of the following circle?
Answer:
The answer is 157 inStep-by-step explanation:
Circumference of a circle = 2πr
where
r is the radius
From the above question
radius = 25 in.
Substitute this value into the above formula
That's
Circumference = 2(25)π
= 50π
= 157.079
We have the final answer as
Circumference = 157 inHope this helps you
What does the tape measure say Measurement # 4 is?
Answer:
It looks like 6 and one eighth of an inch.
Which are perfect squares? Check all that apply. 9 , 24 , 16 , 200 , 169 , 625
Answer:
A. 9
C. 16
E. 169
F. 625
Step-by-step explanation:
#1: Simplify the expression below. Type your answer as an integer.
7 + 1 - 18 : 6
Answer:
5
Step-by-step explanation:
Steps of calculation:
7 + 1 - 18 : 6 = 7 + 1 - 3 = 8 - 3 =5Answer is 5
Give an example of when and why one would use a continuity correction factor?
Answer:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
and continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution
Step-by-step explanation:
An example of when a continuity correction factor can be used is in finding the number of tails in 50 tosses of a coin within a given range .
continuity correction factor is used when a continuous probability distribution is used on a discrete probability distribution, continuity correction factor creates an adjustment on a discrete distribution while using a continuous distribution
1 If a = p^1/3-p^-1/3
prove that: a^3 + 3a = p - 1/p
Hello, please consider the following.
We know that
[tex]a = p^{\frac{1}{3}}-p^{-\frac{1}{3}}\\\\=p^{\frac{1}{3}}-\dfrac{1}{p^{\frac{1}{3}}}[/tex]
And we can write that.
[tex](p-\dfrac{1}{p})^3=(p-\dfrac{1}{p})(p^2-2+\dfrac{1}{p^2})\\\\=p^3-2p+\dfrac{1}{p}-p+\dfrac{2}{p}-\dfrac{1}{p^3}\\\\=p^3-\dfrac{1}{p^3}-3(p-\dfrac{1}{p})[/tex]
It means that, by replacing p by [tex]p^{1/3}[/tex]
[tex](p^{1/3}-\dfrac{1}{p^{1/3}})^3=p-\dfrac{1}{p}-3(p^{1/3}-\dfrac{1}{p^{1/3}})\\\\\\\text{ So }\\\\a^3=p-\dfrac{1}{p}-3a\\\\<=>\boxed{ a^3+3a=p-\dfrac{1}{p} }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the probability of winning a lottery with the following rule. Select the winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is [tex]P(winning ) = 7.435 *10^{-7}[/tex]
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
[tex]t_{outcome}) = \left n } \atop {}} \right. C_r[/tex]
[tex]t_{outcome}) = \frac{n! }{(n-r )! r!}[/tex]
substituting values
[tex]t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}[/tex]
[tex]t_{outcome}) = \frac{ 34 ! }{28 ! 6!}[/tex]
[tex]t_{outcome}) =1344904[/tex]
The number of desired outcome is
[tex]t_{desired} = 1[/tex]
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
[tex]P(winning ) = \frac{t_{desired}}{t_{outcome}}[/tex]
substituting values
[tex]P(winning ) = \frac{1}{1344904 }[/tex]
[tex]P(winning ) = 7.435 *10^{-7}[/tex]
Monique makes $11 per hour delivering pizzas. Monique works Monday
through Friday, and on average she earns $20 a day in tips. If Monique
made no less than $450 for one week, find an inequality for the number
of hours she worked
Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 8 sin(xy), (0, 9)
Answer:
The maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Step-by-step explanation:
Given that:
F(x,y) = 8 sin (xy) at (0,9)
The maximum rate of change f(x,y) occurs in the direction of gradient of f which can be estimated as follows;
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (x,y) \hat i \ + \ \dfrac{\partial }{\partial y } (x,y) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} \dfrac{\partial }{\partial x } (8 \ sin (xy) \hat i \ + \ \dfrac{\partial }{\partial y } (8 \ sin (xy) \hat j \end {bmatrix}[/tex]
[tex]\overline V f (x,y) = \begin {bmatrix} (8y \ cos (xy) \hat i \ + \ (8x \ cos (xy) \hat j \end {bmatrix}[/tex]
[tex]| \overline V f (0,9) |= \begin {vmatrix} 72 \hat i + 0 \end {vmatrix}[/tex]
[tex]\mathbf{| \overline V f (0,9) |= 72}[/tex]
We can conclude that the maximum rate of change of f at (0, 9) is 72 and the direction of the vector is [tex]\mathbf{\hat i}[/tex]
Guess the rule and write down the missing number:
Answer:
17
Step-by-step explanation:
We are adding the previous two terms
1+5 = 6
5+6 = 11
6+11 = 17
11+17 = 28
The missing term is 17
5. During a national debate on changes to health care, a cable news service performs an opinion poll of 500 small business owners. It shows that 65% of small-business owners do not approve of health care changes. Develop a 95% confidence interval for the proportion opposing health care changes. Use 4 decimal places.
Answer:
The 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).
Step-by-step explanation:
The (1 - α)% confidence interval for the population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided is:
[tex]\hat p=0.65\\n=500\\\text{Confidence level}=95\%[/tex]
The critical value of z for 95% confidence level is:
[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]
*Use a z-table.
Compute the 95% confidence interval for the proportion opposing health care changes as follows:
[tex]CI=\hat p\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]=0.65\pm 1.96\sqrt{\frac{0.65(1-0.65)}{500}}\\\\=0.65\pm 0.04181\\\\=(0.60819, 0.69181)\\\\\approx (0.6082, 0.6918)[/tex]
Thus, the 95% confidence interval for the proportion opposing health care changes is (0.6082, 0.6918).
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below. A. The mean and standard deviation have the values of and B. The mean and standard deviation have the values of and C. The mean and standard deviation have the values of and D. The mean and standard deviation have the values of and
Answer:
In order for a Normal Probability Distribution to be a Standard Normal Probability Distribution, the mean and standard deviation must have the values of µ = 0 and σ = 1.
Where µ refers to the Mean of the distribution and σ refers to the standard deviation.
µ is pronounced 'mu' and σ is pronounced sigma.
Cheers!
Simplify 5(R + 2) - 6.
5R + 4
5R - 4
5R - 6
Step-by-step explanation:
Hey, there!!
5(R+2)-6.
Fistly multiply (R+2) by 5.
=5R + 10 - 6
Subtract 6 from 10.
= 5R +4.
Therefore, 5R + 4 is correct answer.
{ While simplifying the expression if there is multiplication or divide do it first and then add or or subtract like terms to get the simplified form of the expressions. }
Hope it helps..
The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals for six different teams in each division.
Eastern Western
9 9
3 8
4 7
3 6
4 5
4 3
Does the data show there is a difference in the annual goals for the eastern and western divisions? Test the claim at the 0.05 significance level.
A) The null and alternative hypothesis would be:
1. H0: PE = Pw
H1: PE > PW
2. H0: PE - Pw
H1: PE Pw
3. H0: Ps Pw
H1: PE Pw
4. H0: ME MW
H1: MMW
5. H0: HEW
H1: TME > HW
6.H0: ME Hw
H1: EMW
B) Determine the test statistic.
Answer:
A)
2. H0: Pe = Pw
H1: Pe [tex]\neq[/tex] Pw
B) Test statistics 1.96
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. In the given scenario the test is to identify whether there is any difference in annual goals between western division and eastern division. The null hypothesis will be the Goals of western are equal to eastern division and alternative hypothesis will be Goals of western are not equal to eastern division.
Find the sum (x^3+5x^2+3x-7)+(8x-6^2+6)
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
Answer:
x^3 - x^2 + 11x - 1
-x^3 - 8x^2 + 5x + 7
Step-by-step explanation:
Find the sum
(x^3+5x^2+3x-7)+(8x-6x^2+6)
=x^3+5x^2+3x-7+8x-6x^+6
Collect like terms
=x^3 +5x^2-6x^2+3x+8x-7+6
Add the like terms
= x^3 - x^2 + 11x - 1
Find the difference (7x-3x^2+2)-(x^3+5x^2+2x-5)
(7x-3x^2+2)-(x^3+5x^2+2x-5)
= 7x-3x^2+2-x^3-5x^2-2x+5
Collect like terms
= -x^3-3x^2-5x^2+7x-2x+2+5
Add the like terms
= -x^3 - 8x^2 + 5x + 7
5 STARS IF CORRECT! Can you translate a phrase or sentence into symbols? Explain the answer.
Answer:
See below.
Step-by-step explanation:
It depends on the sentence or phrase. If the sentence includes an operation of numbers or something related to comparing numbers, then maybe it can be translated into symbols. If the sentence or phrase has nothing to do with quantities, or operations or comparison of quantities, then probably it can't.
Examples:
1) The boy went for a walk.
There's nothing to translate into symbols in this case.
2) I had $10 in my bank account, then I deposited n dollars. Now I have $30 in my account.
In this case, I can translate the sentence into an equation.
10 + n = 30
Amir throws a stone off of a bridge into a river. The stone's height (in meters above the water) ttt seconds after Amir throws it is modeled by h(t)=-5t^2+20t+160h(t)=−5t 2 +20t+160h, left parenthesis, t, right parenthesis, equals, minus, 5, t, squared, plus, 20, t, plus, 160 Amir wants to know when the stone will reach its highest point. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many seconds after being thrown did the stone reach its highest point?
Answer:
-5*(t-2)^2+180
Step-by-step explanation:
That's the answer on khan academy.
Also the second question is 2.
Answer:
-5(t-2)^2+180 and 2
Step-by-step explanation:
hi there enjoy ur answer have a great day bye !!! :D oh wait seems sone wants to say something ʕ•ᴥ• (please give brainiest) whisperered the mysterious koala.
How many fluid ounces are there in 4pints?
Answer: 64 fluid ounces
Step-by-step explanation:
1 pint=16 fl oz
16*4=64
Look at the chore chart--write a notice and a wonder about the chart. Click on the image to see the chart. Enter ur answer
Answer:
I noticed that to babysit my cousin was the chore that doled out the most, and I wonder why pet my dog is even a chore. Do they not love their pets?
A city is holding a referendum on increasing property taxes to pay for a new high school. In a survey of 434 likely voters, 202 said that they would vote "yes" on the referendum. Create a 95% confidence interval for the proportion of likely voters who would vote "yes" on the referendum. Use a TI-83, TI-83 plus, or TI-84 calculator, rounding your answers to three decimal places.
Answer: 0.418 < p < 0.512
Step-by-step explanation: A 95% conifdence interval for a population proportion is given by:
[tex]p + z\sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the proportion
z is score in z-table
n is sample size
The proportion for people who said "yes" is
[tex]p=\frac{202}{434}[/tex] = 0.465
For a 95% confidence interval, z = 1.96.
Calculating
[tex]0.465 + 1.96*\sqrt{\frac{0.465(0.535)}{434} }[/tex]
[tex]0.465 + 1.96*\sqrt{0.00057}[/tex]
0.465 ± 1.96*0.024
0.465 ± 0.047
Interval is between:
0.465 - 0.047 = 0.418
0.465 + 0.047 = 0.512
The interval with 95% of confidence is between 0.418 and 0.512.
Complete the square: x2+7x+?=(x+?)2
Answer:
[tex] {x}^{2} + 7x + \frac{49}{4} = {(x + \frac{7}{2}) }^{2} [/tex]
Explanation:
[tex] {x}^{2} + 7x + a = {(x + b)}^{2} [/tex]
[tex] {x}^{2} + 7x + a = {x}^{2} + 2bx + {b}^{2} [/tex]
compare the x co-efficient
[tex] 7 = 2b[/tex]
[tex] b = \frac{7}{2} [/tex]
compare the constants
[tex]a = {b}^{2} [/tex]
[tex]a = {( \frac{7}{2}) }^{2} [/tex]
[tex]a = \frac{49}{4} [/tex]
HOPE IT HELPS....
BRAINLIEST PLEASE ;-)The complete equation will be x^2+7x+49/4=(x+7/2)2
Given the quadratic function x^2 + 7x + ?
In order to complete the square using the completing the square method, we will add the square of the half of coefficient of x to both sides of the expression.
Coefficient of x = 7
Half of the coefficient = 7/2
Taking the square of the result = (7/2)² = 49/4
The constant that will complete the equation is 49/9. The equation becomes x^2 + 7x + (7/2)² = (x+7/2)²
Hence the complete equation will be x^2+7x+49/4=(x+7/2)2
Learn more here: https://brainly.com/question/13981588
The distance between two cities on a map is 4 centimeters. If the scale is 0.5 cm:1 km, how many kilometers apart are the actual cities?
Answer:
8 km
Step-by-step explanation:
1 km
4 cm x -------- = 8 km
0.5 cm
The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The distance between two cities on a map = 4 centimeters.
Also, the scale
0.5 cm = 1 km
To find actual distance between cities, use ratio properly,
0.5 cm = 1 km
1 cm = 2 km
4 cm = 8 km
The distance between the actual cities is 8 km.
To learn more about Ratio on :
https://brainly.com/question/13419413
#SPJ2
Each power smoothie that Theo makes has 3 scoops of mango, 1 scoop of strawberries, and 1 scoop of spinach. If Theo makes 7 power smoothies, how many scoops will he use in all?
Answer: 35 scoops total!
Step-by-step explanation: FIrst, you would add the number of scoops in total which is 3+1+1=5 scoops.
Now you would do 7*5=35
Therefore, Theo uses 35 scoops in all. I hope this helps you!
this person made an error. what is it, and what is the right answer?
Answer:
Base area (B) should not be added.
Step-by-step explanation:
Base area should not be added as cone is not solid. Only Lateral surface area is sufficient in order to find the required paper.
