Answer:
Answer = 72.46
Answer: 72.46
Step-by-step explanation:
Nearest hundredth is second place to the right of decimal point
- 72.46387
- The second place to the right of decimal point is 6.
Look at the place after 6 to determine whether or not to move up.
- The next place is 3, and 3 is less than 5, so we keep the place.
72.46
Hope this helps!! :)
Please let me know if you have any question or need further explanation
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Answer:
Area = 13.15 square units
Step-by-step explanation:
Let the given vertices be represented as follows:
A(2, -1, 1) = 2i - j + k
B(5, 1, 4) = 5i + j + 4k
C(0, 1, 1) = 0i + j + k
D(3, 3, 4) = 3i + 3j + 4k
(i) Let's calculate the vectors of all the sides:
[tex]\\[/tex]AB = B - A = (5i + j + 4k) - (2i - j + k)
AB = 5i + j + 4k - 2i + j - k [Collect like terms]
AB = 3i + 2j + 3k
BC = C - B = (0i + j + k) - (5i + j + 4k)
BC = 0i + j + k - 5i - j - 4k [Collect like terms]
BC = -5i + 0j - 3k
CD = D - C = (3i + 3j + 4k) - (0i + j + k)
CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]
CD = 3i + 2j + 3k
DA = A - D = (2i - j + k) - (3i + 3j + 4k)
DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]
DA = -i - 4j - 3k
AC = C - A = (0i + j + k) - (2i - j + k)
AC = 0i + j + k - 2i + j - k [Collect like terms]
AC = -2i + 2j
BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)
BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]
BD = -2i + 2j
(ii) From the results in (i) above, we can deduce that;
AB = CD This implies that AB || CD [AB is parallel to CD]
AC = BD This implies that AC || BD [AC is parallel to BD]
(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram
Now let's calculate the area
To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.
In this case, we'll choose AB and AC
Area = |AB X AC|
Where;
[tex]AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right][/tex]
AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)
AB X AC = - 6i - 6j + 10k
|AB X AC| = [tex]\sqrt{(-6)^2 + (-6)^2 + (10)^2}[/tex]
|AB X AC| = [tex]\sqrt{172}[/tex]
|AB X AC| = 13.15
Area = 13.15 square units.
PS: ACBD is also a parallelogram. The diagram has also been attached to this response.
3. Kirk bought a bag of candy and took 10
pieces. He split the rest evenly among 12
friends. Each friend received 5 pieces. Letc
represent the number of pieces in a bag.
Equation:
Solve it to find how many pieces of candy were in the bag.
Type here
Show your work
Write and solve the equation
-6 < 2x - 4<4
Solve the inequality
Use the Well-Ordering Principle to prove that given a > 0, a^n > 0 for every positive integer n
Answer:
Following are the answer to this question:
Step-by-step explanation:
Given value:
[tex]\to x > 0[/tex]
[tex]\to S= { n\varepsilon N : x^n \leq 0 } \\\\ s \neq \phi \\\\ \to x^n \leq 0\\[/tex]
[tex]\to x^{n-1} x\leq 0\\\\ \to x>0 = x^{n-1} \leq 0 \\\\\to n-1 \varepsilon s \\ \ \ _{where} \ \ n-1 < n \\\\\to s= \phi \\\\\to \hence x^n > 0 \\[/tex]
Given the original number n. Multiply the number by 8. Add 136. Divide this sum by 8. Subtract the original number, n, from the quotient.
Answer:
8
Step-by-step explanation:
n×8=8n
8n+136=144n
144n÷8=18n
18n-n = 18
When two straight lines cross, it is found that the angles opposite each other are the same size. They are known as .............
Answer:
Step-by-step explanation:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.
Answer:
When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal. Adjacent angles are angles that come out of the same vertex.
Step-by-step explanation:
Adjacent angles are angles that come out of the same vertex.
If you use a 0.10 level of significance in a two-tail hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean equals 500 if you use the Z test
Answer:
If the value of our test statistics is less than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
If the value of our test statistics is more than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Step-by-step explanation:
We are given that the population mean equals 500 and we use a 0.10 level of significance in a two-tail hypothesis test.
Let [tex]\mu[/tex] = population mean.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 500
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 500
Here, the null hypothesis states that the population mean is equal to 500.
On the other hand, the alternate hypothesis states the population mean is different from 500.
Now, firstly we should note that for the two-tailed test, the level of significance to be taken is ([tex]\frac{\alpha}{2}=\frac{0.10}{2}[/tex]) = 0.05 or 5%.
So, the decision rule for rejecting a null hypothesis is given by;
If the value of our test statistics is less than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.If the value of our test statistics is more than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.3 packs of soda cost $10 less than 5 packs of soda. Write an equation and solve to find the cost of one pack of soda *
1 point
Answer:
3s = 5s - 10
Step-by-step explanation:
20+x= (-15)
what does x eqaul?
Answer:
x= -35 because you have tk get x alone. so you subtract 20 from -15
Answer:
x = -35
Step-by-step explanation:
20 + x = -15
(20 + x) - 20 = -15 - 20
x = -35
g The critical value changes as ____ changes. All of the choices in this question are correct The Alpha Level The Obtained Statistic The Population Mean
Answer:
The Alpha Level
Step-by-step explanation:
The critical value is obtained by applying the alpha value to an area. For example if we choose the alpha level of 0.05 the critical value would be 1.96 for a two tailed test. But if the alpha is 0.1 the critical value would be 1.645 and similarly the critical value would be 2.58 for 0.01 alpha level.
The critcal value depends on the alpha level and is set accordingly depending on one tailed or tailed test. It does not involve the use of The Obtained Statistic or The Population Mean.
what is 1/16 times 1/4 as a fraction?
Answer:
[tex]\frac{1}{16}[/tex] x [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]
multiply 16 by 4 to get the denominator
The fraction 1/16 times 1/4 is equal to 1/64.
To find the product of 1/16 and 1/4, we can multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
1/16 x 1/4
= (1 x 1) / (16 x 4)
The product of the numerators is 1 x 1 = 1, and the product of the denominators is 16 x 4 = 64.
So, the result is:
1/16 x 1/4 = 1/64
Therefore, 1/16 times 1/4 is equal to 1/64.
Learn more about fraction here:
https://brainly.com/question/29019463
#SPJ6
Two different red-light-running signal systems were installed at various intersection locations with the goal of reducing angle-type crashes. Red-Light-Running System A resulted in 60% angle crashes over a sample of 720 total crashes. Red-Light-Running System B resulted in 52% angle crashes over a sample of 680 total crashes. Was there a difference between the proportions of angle crashes between
Complete Question
Two different red-light-running signal systems were installed at various intersection locations with the goal of reducing angle-type crashes. Red-Light-Running System A resulted in 60% angle crashes over a sample of 720 total crashes. Red-Light-Running System B resulted in 52% angle crashes over a sample of 680 total crashes. Was there a difference between the proportions of angle crashes between the two red-light-running systems installed? Use an alpha of 0.10.
Answer:
Yes there is a difference between the proportions of angle crashes between the two red-light-running systems installed
Step-by-step explanation:
From the question we are told that
The first sample proportion is [tex]\r p_ 1 = 0.60[/tex]
The second sample proportion is [tex]p_2 = 0.52[/tex]
The first sample size is [tex]n_1 = 720[/tex]
The second sample size is [tex]n_2 = 680[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \r p_1 - \r p_2 = 0[/tex]
The alternative hypothesis is [tex]H_a : \r p_1 - \r p_2 \ne 0[/tex]
Generally the pooled proportion is mathematically represented as
[tex]p_p = \frac{(\r p_1 * n_1 ) + (\r p_2 * n_2)}{n_1 + n_2 }[/tex]
=> [tex]p_p = \frac{(0.6 * 720) + ( 0.52 * 680)}{720 +680 }[/tex]
=> [tex]p_p = 0.56[/tex]
Generally the test statistics is evaluated as
[tex]t = \frac{ ( \r p_1 - \r p_2 ) - 0 }{ \sqrt{ (p_p (1- p_p) * [ \frac{1}{n_1 } + \frac{1}{n_2 } ])} }[/tex]
[tex]t = \frac{ (0.60 - 0.52 ) - 0 }{ \sqrt{ (0.56 (1- 0.56) * [ \frac{1}{720} + \frac{1}{680 } ])} }[/tex]
[tex]t = 3.0[/tex]
The p-value obtained from the z-table is
[tex]p-value = P(Z> t ) = 0.0013499[/tex]
From the question we see that [tex]p-value < \alpha[/tex] so the null hypothesis is rejected
Hence we can conclude that there is a difference between the proportions
-5x-6(-6+3x)=105 what is the answer
Answer:
x = -3
Step-by-step explanation:
expand -23x + 36 = 105
subtract 36 from both sides -23x +36 -36 = 105 - 36
Simplify -23x = 69
Divid both sides by -23: -23x / - 23 = 69 / -23
x = -3
Write the equation of the line that passes through (3,-2) and has a slope of 4 in point-slope form. (2 points)
A)y + 2 = 4(x - 3)
B)y- 3 = 4(x + 2)
C)X - 3 = 4(y + 2)
D)x + 2 = 4(y - 3)
Plz explain just a bit how you got the answer. Will give brainliest!!
Answer:
[tex]A)y + 2 = 4(x - 3)[/tex]
log(16x+2) - log(4x+2)= log(2x+4)
Same as my answer last time:
Answer:
NO solution
Step-by-step explanation:
log(16x+2) - log(4x+2) = log((16x+2)/(4x+2)).
remove log
(16x+2)/(4x+2) = 2x + 4
multiply both sides by 2x + 1
8x + 1 = (2x + 4)(2x + 1)
distribute
8x + 1 = 4x^2 + 10x + 4
move to one side
4x^2 + 2x + 3 = 0
factor
but you can't
so you try to use quadratic formula, but you find that the discriminate is less than zero.
So there is no solution when x is a real number.
Which option is an example of an experiment
Answer: Testing the effectiveness of a mouthwash by allowing one group to use it and comparing the results with those of a group that doesn't use it.
Step-by-step explanation: It's the most effective
If x+y=8 and xy=24,
Fnd the value of x and y
Answer:
No solution
Step-by-step explanation:
I hope it helps
Answer:
You'll find out once you go through the steps below.
Step-by-step explanation:
First look at x and y being multiplied. You'll get an idea of what are the possible pair of numbers that multiply together. So in this case they could be 6 and 4 but it cant be possible since they will add and become 10 but we need eight. We now know that the answer is in a decimal. I hope these steps were helpful. Have a nice day. :)
Kyle is renewing his subscription to his favorite computer magazine . The cost is $24 for 12 issues. What is the cost of each issue
Answer:
$2
Step-by-step explanation:
$24 ÷ 12 issues = $2 per issue
Answer:
$2 / issue
Step-by-step explanation:
We want to find the cost of each issue. We need to find the unit rate.
Divide the cost by the number of issues.
cost / issues
It costs $24 for 12 issues.
cost = $24
issues = 12 issues
$24 / 12 issues
Divide 24 by 12
$2 / issue
It costs $2 per issue.
given the points (0,2) and (8,4) , what's the slope of the line?
To find the slope of this line, let's use the slope formula.
m = y2 - y1 / x2 - x1
m = 4 - 2 / 8 - 0 ⇒ 2/8 ⇒ 1/4
So m = 1/4.
what is the simplest form of fraction
Answer:
A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers. To simplify a fraction: divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).
FOR EXAMPLE
5/10 = 1/2
HERE 1/2 IS THE SIMPLEST FRACTION
How much fencing would you need to fence in a rectangular storage that measures 40 feet x 20 feet?
Answer:
Ammount of fencing required = perimeter of the rectangular storage.
Perimeter of a rectangle = 2(l+b), where l = length, b = breadth.
so perimeter = 2(40+20) = 2(60) = 120 feet
so fencing required = 120 feet
HOPE IT WAS HELPFUL!
Answer:
[tex]\Huge \boxed{\mathrm{120 \ feet}}[/tex]
Step-by-step explanation:
The length of the rectangular storage is 40 feet.
The width of the rectangular storage is 20 feet.
The length of fencing is needed to fence the entire rectangular storage.
The perimeter of the rectangle is required.
[tex]P=2l+2w \\ \\ \sf P=perimeter \\ l=length \\ w=width[/tex]
[tex]P=2(40)+2(20) \\ \\ P=80+40 \\ \\ P=120[/tex]
120 feet of fencing is needed to fence the rectangular storage.
PLEASE HELP ME, I DON'T UNDERSTAND THIS! :( Multiply.
Hey there! I'm happy to help!
First, let's multiply the numerators. We will put q+5 in parentheses so we can multiply it by 4q.
4q(q+5)
We use the distributive property to undo the parentheses.
First, we multiply 4q by q.
4q×q=4q²
And we multiply 4q and 5.
4q×5=20q
So, our numerator right now is 4q²+20q.
Now, for the denominators.
2(q+4)
We do 2 by q.
2×q=2q
And 2×4, which is 8.
So, our denominator is 2q+8.
Right now, our fraction is [tex]\frac{4q^2+20}{2q+8}[/tex], and this is your correct answer. However, we can simplify it a bit more. We can divide the 4 by 2, q² by q, and simplify the 20 and the 8.
4/2=2
q²/q=q
20/8=5/2
Now, our final product is (2q+5)/2
But, mark down your answer as [tex]\frac{4q^2+20}{2q+8}[/tex] because that is technically correct.
Have a wonderful day! :D
100 is deposited into an investment account on January 1, 1998. You are given the following information on investment activity that takes place during the year:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
The amount in the account on January 1, 1999 is 115. During 1998, The annual effective dollar weighted yield is 0%, and the annual effective time weighted yield is y. Calculate y.
Answer:
y = - 0.681 % ≈ -0.7 %
Step-by-step explanation:
Given:
April 19,1998 October 30, 1998
Value immediately prior to deposit 95 105
Deposit 2X X
amount in the account on January 1, 1999 = 115
effective dollar weighted yield = 0%
annual effective time weighted yield = y
To find:
Calculate y
Solution:
Given that the dollar weighted return is 0%
100 is deposited into investment account on January 1, 1998. So, add 100 to the deposits 2X X
100 + 2x + x = 115
3x = 115 - 100
3x = 15
x = 15/3
x = 5
Compute y
1 + y = (95/100)(105/105)(115/110)
1 + y = 0.95 * 1 * 1.045
1 + y = 0.99318
y = 0.99318 - 1
y = - 0.0068 * 100
y = - 0.681 % ≈ -0.7 %
y = -0.7 %
Polygon B is a scaled copy of Polygon A.
What is the scale factor from Polygon A to Polygon B?
Hey There!!
The answer to this is: 25 times larger. The scale factor is 5, so each side length of the polygon was multiplied by 5.
Key Idea
If the length of a figure scales by x, then area of the figure scales by x^{2}
The Polygon B is created with a scale factor of 5. So, the area of Polygon B scales by 5^{2}
5^{2} = 5 × 5=25
The area of Polygon B is 25 times larger than the area of Polygon A
Hope It Helped!~ ♡
ItsNobody~ ☆
Both the Galapagos Islands and the island of Naura are on the Equator, but the Galapagos Islands are at 90.30◦W whereas the island of Nauru is at 166.56◦E. How far is it from the Galapagos Islands to Nauru traveling over the Pacific ocean along the Equator, correct to the nearest km ?
Answer:
11,481 km
Step-by-step explanation:
Longitude 90.30° W is equivalent to 360° -90.30° = 269.70° E. Then the difference in longitude of the islands is ...
269.70° -166.56° = 103.14°
The circumference of the earth at the equator is 40,075 kilometers. Hence the distance will be 103.14/360 times that distance:
(103.14/360)(40,075 km) = 11,481 km
_____
Additional comment
As always with global distance measures, the result of a calculation depends on the assumptions you make. Attached is another take on the question. Apparently, the distance depends on precisely where in the islands you're measuring from/to. The distance computed above differs from the one below by 136 km. The extent of the Galapagos Islands is on the order of 265 km. So, the number we have computed is at least approximately correct.
A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer:
(a) the new angle the ladder makes with the ground is [tex]32.7^o[/tex]
(b) the ladder slipped back about 5 meters
Step-by-step explanation:
Notice that the ladder doesn't change its length in the process.
So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:
[tex]sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m[/tex]
therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.
Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:
[tex]sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o[/tex]
To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:
[tex]cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m[/tex]
Now fro the new position of the bottom of the ladder relative to the wall:
[tex]cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m[/tex]
then the difference in between those two distances is what we need:
8.4 m - 3.4 m = 5 m
Question 1 (1 point)
Danny wants to buy a truck in 4 years. He is going to put away $2,500.00 into his savings account that will pay him 6.75% interest compounded
monthly. How much will he have when he withdraws the funds to give a down payment?
Answer:
Amount after 4 years = $3274.125
Step-by-step explanation:
Time t= 4 years
Principal amount p= $2500
Interest rate R= 6.75%
Number of times compounded n= 4*12
Number of times compounded n= 48
Amount A = p(1+r/n)^(nt)
A= 2500(1+0.0675/48)^(48*4)
A= 2500(1+0.001406)^(192)
A= 2500(1.001406)^192
A= 2500(1.30965)
A= 3274.125
Amount after 4 years = $3274.125
Translate from algebra to English: 14 < 21.
Answer:
14 is less than 21
Scarlett purchased 20 shares of ad stock at $43 per share. she told the 20 shares at $52 per share. how much money did Scarlett make on her investment?
Answer: $180
Step-by-step explanation:
If she purchased 20 shares of ad stock for $43 per share then multiply 20 by 43 to find the total amount of money.
20 * 43 = $860 which means that she spent a total of $860 for the 20 shares.
If she then sold the 20 stocks for $52 each then you will multiply 20 by 52 and subtract 860 from it to find the total amount she made.
20 * 52 = 1040
$ 1040 - $860 = $180
A Gardener makes a new circular flower bed. The bed is ten feet in diameter. Calculate the circumference and the area of the circular flower bed
Answer:
The circumference is 31.42 and the area is 78.54
Step-by-step explanation:
For circumference you use the formula
C=2 r
R= radius and = 3.14
For area use the formula
A= r^2
I hope this helps