Answer: (a) When he turns 68 , the account will have = $1,179,415.39
(b) $ 288,000
Step-by-step explanation:
Formula: Future value of annuity =[tex]P[\dfrac{(1+r)^n-1}{r}][/tex], where P+ periodic payment, r = rate of interest per period, n= number of periods.
As per given, we have
P= $1800
rate of interest = 6% = 0.06
(a) n= 68-28 = 40
Rate per period : r= [tex]\dfrac{0.06}{4}=0.015[/tex]
Number of periods: n = 4x 40 =160
Now, Future value of amount when Mr. Pink turns 28 years = [tex]1800(\dfrac{(1+0.015)^{160}-1}{0.015})[/tex]
[tex]=1800(\dfrac{10.8284615777-1}{0.015})\\\\=1800\times\dfrac{9.8284615777}{0.015}\\\\\approx\$1179415.39[/tex]
Hence, when he turns 68 , the account will have = $1,179,415.39
(b) Total contribution = P × n
=1800 × 160
=$ 288,000
Hence, Total contribution =$ 288,000
the price of apples at three different stores is shown below. Store R sells apples for $1.20 per pound. Store S sells 4 pounds of apples for $5.00. Store T sells 3 pounds of apples for $3.48.
which of these is a true statemnt
Store R sells apples at the lowest rate
Store T sells apples at the lowest rate
Store s charges a lower rate than Store T
Store t charges the same rate as Store R
Store T sells apples at the lowest rate
Step-by-step explanation:
1st We need to make every statement in order of 1 pound. Then We will easily find the lowest rate of apple.
i) R sell 1.20 $ per pound.
ii) S sell 4 pounds for 5$
i.e S sell 1 pound for 5/4 = 1.25$
iii) T sell 3 pound for 3.48$
i.e T sell 1 pound for 3.48/3 = 1.16$
Analysing the above data I get,
Store T sells apples at the lowest rate
Which set of integers does NOT represent the lengths of the sides of a triangle? A. {6,6,11} B. {9,10,11} C. {4,8,12} D. {4,7,9}
Answer:
C
Step-by-step explanation:
I suppose you have learned that for the sides of a triangle to work, it has to be a + b > c, the 4 is the a, the 8 is the b, the 12 is the c.
So: 4 + 8 > 12; however this is not true, they are equal so the triangle wont be a triangle, it would be lines that never connect.
Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 64 + x2 − y2 R = {(x, y): x2 + y2 ≤ 64}
The area of the surface above the region R is 4096π square units.
Given that:
The function: [tex]f(x, y) = 64 + x^2 - y^2[/tex]
The region R is the disk with a radius of 8 units [tex]x^2 + y^2 \le 64[/tex].
To find the area of the surface given by z = f(x, y) that lies above the region R, to calculate the double integral over the region R of the function f(x, y) with respect to dA.
The integral for the area is given by:
[tex]Area = \int\int_R f(x, y) dA[/tex]
To evaluate this integral, we need to set up the limits of integration for x and y over the region R, which is the disk cantered at the origin with a radius of 8 units.
Using polar coordinates, we can parameterize the region R as follows:
x = rcos(θ)
y = rsin(θ)
where r goes from 0 to 8, and θ goes from 0 to 2π.
Now, rewrite the integral in polar coordinates:
[tex]Area =\int\int_R f(x, y) dA\\Area = \int_0 ^{2\pi} \int_0^8(64 + r^2cos^2(\theta) - r^2sin^2(\theta)) \times r dr d \theta[/tex]
Now, we can integrate with respect to r first and then with respect to θ:
[tex]Area = \int_0^{2\pi} \int_0^8] (64r + r^3cos^2(\theta) - r^3sin^2(\theta)) dr d \theta[/tex]
Integrate with respect to r:
[tex]Area = \int_0^{2\pi}[(32r^2 + (1/4)r^4cos^2(\theta) - (1/4)r^4sin^2(\theta))]_0^8 d \theta\\Area = \int_0^{2\pi} (2048 + 256cos^2(\theta) - 256sin^2(\theta)) d \theta[/tex]
Now, we can integrate with respect to θ:
[tex]Area = [2048\theta + 128(sin(2\theta) + \theta)]_0 ^{2\pi}[/tex]
Area = 2048(2π) + 128(sin(4π) + 2π) - (2048(0) + 128(sin(0) + 0))
Area = 4096π + 128(0) - 0
Area = 4096π square units
So, the area of the surface above the region R is 4096π square units.
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which is greater 7.955 or 7.95
Answer:
[tex]\boxed{7.955>7.95}[/tex]
Step-by-step explanation:
7.95 can also be written as 7.950 .
So, we'll compare 7.955 and 7.950.
All the digits in ones, tenths, hundredths place are equal so we'll look at the thousandths place.
5 is in the thousandths place of 7.955 and 0 is in the thousandths place of 7.950. Since 5 is greater than 0 so 7.955 is greater than 7.95. It can also be written as:
7.955 > 7.950
Refer to the following wage breakdown for a garment factory:
Hourly Wages Number of employees
$4 up to $7 18
7 up to 10 36
10 up to 13 20
13 up to 16 6
What is the class interval for the preceding table of wages?
A. $4
B. $2
C. $5
D. $3
Answer:
The class interval is $3Step-by-step explanation:
The class interval is simply the difference between the lower or upper class boundary or limit of a class and the lower or upper class boundary or limit of the next class.
In this case for the class
$4 up to $7 18 and
$7 up to $10 36
The lower class boundary of the first class is $4 and the lower class boundary of the second class is $7
Hence the class interval = $7-$4= $3Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xey + yez + zex, (0, 0, 0), v = 4, 3, −1
Answer: 6 / √26
Step-by-step explanation:
Given that f(x, y, z) = xe^y + ye^z + ze^x
so first we compute the gradient vector at (0, 0, 0)
Δf ( x, y, z ) = [ e^y + ze^x, xe^y + e^z, ye^z + e^x ]
Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]
Now we were also given that V = < 4, 3, -1 >
so ║v║ = √ ( 4² + 3² + (-1)² )
║v║ = √ ( 16 + 9 + 1 )
║v║ = √ 26
It must be noted that "v" is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)
so
⊆ = ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]
therefore by equation D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆
D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]
= ( 1×4 + 1×3 -1×1 ) / √26
= (4 + 3 - 1) / √26
= 6 / √26
What is the area of this triangle on a Coordinate Grid?
Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2), is drawn inside a rectangle
Answer: 8.5 sq. units.
Step-by-step explanation:
Formula:
Area of triangle : [tex]\dfrac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]
Given: Triangle IJK, with vertices I(3,-7), J(7,-4), and K(4,-2)
Then, Area of triangle IJK = [tex]\dfrac{1}{2}|3(-4-(-2))+7(-2-(-7))+4(-7-(-4))|[/tex]
[tex]\dfrac{1}{2}|3(-2)+7(5)+4(-3)|\\\\=\dfrac{1}{2}|-6+35-12|\\\\=\dfrac{1}{2}(17)\\\\=8.5\text{ sq. units}[/tex]
Hence, the area of this triangle IJK on a Coordinate Grid = 8.5 sq. units.
12. What is m∠GEA?
Answer:
90°
Step-by-step explanation:
Circumcenter of a triangle is obtained by drawing perpendicular bisectors of the sides of a triangle. Hence GE is perpendicular to AC.
Therefore, m∠GEA = 90°
Of the following points, name all that lie on the same horizontal line? (1,-2) (-1,2) (-2,1) (2,-1)
Hey there!
If a line is horizontal, the entire line is at the same elevation. On a line, the elevation is the y-value. So, all of the points with the same y-value are on the same horizontal line.
We see that all of these points have different y-values so none of them would be on the same horizontal line.
I hope that this helps! Have a wonderful day!
In randomized, double-blind clinical trials of Prevnar, infants were randomly divided into two groups. Subjects in group 1 received Prevnar, while subjects in group 2 received a control vaccine. Aft er the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect. After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect. Does the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the αα=0.05 level of significance?
Answer:
Step-by-step explanation:
From the summary of the given data;
After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as a side effect.
Let consider [tex]p_1[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_1[/tex] = [tex]\dfrac{137}{452}[/tex]
[tex]p_1[/tex] = 0.3031
After the second dose, 31 of 99 subjects in the control group (group 2) experienced drowsiness as a side effect.
Let consider [tex]p_2[/tex] to be the probability of those that experience the drowsiness in group 1
[tex]p_2[/tex] = [tex]\dfrac{31}{99}[/tex]
[tex]p_2[/tex] = 0.3131
The objective is to be able to determine if the evidence suggest that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2 at the α=0.05 level of significance.
In order to do that; we have to state the null and alternative hypothesis; carry out our test statistics and make conclusion based on it.
So; the null and the alternative hypothesis can be computed as:
[tex]H_o :p_1 =p_2[/tex]
[tex]H_a= p_1<p_2[/tex]
The test statistics is computed as follows:
[tex]Z = \dfrac{p_1-p_2}{\sqrt{p_1 *\dfrac{1-p_1}{n_1} +p_2 *\dfrac{1-p_2}{n_2}} }[/tex]
[tex]Z = \dfrac{0.3031-0.3131}{\sqrt{0.3031 *\dfrac{1-0.3031}{452} +0.3131 *\dfrac{1-0.3131}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *\dfrac{0.6969}{452} +0.3131 *\dfrac{0.6869}{99}} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{0.3031 *0.0015418 +0.3131 *0.0069384} }[/tex]
[tex]Z = \dfrac{-0.01}{\sqrt{4.6731958*10^{-4}+0.00217241304} }[/tex]
[tex]Z = \dfrac{-0.01}{0.051378 }[/tex]
Z = - 0.1946
At the level of significance ∝ = 0.05
From the standard normal table;
the critical value for Z(0.05) = -1.645
Decision Rule: Reject the null hypothesis if Z-value is lesser than the critical value.
Conclusion: We do not reject the null hypothesis because the Z value is greater than the critical value. Therefore, we cannot conclude that a lower proportion of subjects in group 1 experienced drowsiness as a side effect than subjects in group 2
In 2015, the CDC analyzed whether American adults were eating enough fruits and vegetables. Let the mean cups of vegetables adults eat in a day be μ. If the CDC wanted to know if adults were eating, on average, more than the recommended 2 cups of vegetables a day, what are the null and alternative hypothesis? Select the correct answer below: H0: μ=2; Ha: μ>2 H0: μ>2; Ha: μ=2 H0: μ=2; Ha: μ<2 H0: μ=2; Ha: μ≠2
Answer:
H0: μ=2; Ha: μ>2
Step-by-step explanation:
The null hypothesis is the default hypothesis while the alternative hypothesis is the opposite of the null and is always tested against the null hypothesis.
In this case study, the null hypothesis is that adults were eating, on average, the recommended 2 cups of vegetables a day: H0: μ=2 while the alternative hypothesis is adults were eating, on average, more than the recommended 2 cups of vegetables a day Ha: μ>2.
find the equation of a straight line joining the points (6,9) and (4,7). Please help im bad at mathematic :( and please do a calculation too.
Answer:
y = x+3
Step-by-step explanation:
First step is to find the slope
m = ( y2-y1)/(x2-x1)
= ( 7-9)/(4 - 6)
= -2 / -2
= 1
The we can put is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = 1x+b
Putting in one of the points
9 = 1*6+b
Subtracting 6
9-6 = b
3=b
y = 1x+3
y = x+3
Answer:
[tex]\boxed{y=x+3}[/tex]
Step-by-step explanation:
Solve for slope first.
The slope can be found through 2 points.
[tex]slope=\frac{change \: in \: y}{change \: in \: x}[/tex]
[tex]slope=\frac{7-9}{4-6}[/tex]
[tex]slope=\frac{-2}{-2}[/tex]
[tex]slope=1[/tex]
Using slope-intercept form.
[tex]y=mx+b\\m=slope\\b=y \: intercept[/tex]
[tex]y=1x+b[/tex]
Let x = 6 and y = 9.
[tex]9=1(6)+b[/tex]
[tex]9-6=b[/tex]
[tex]3=b[/tex]
[tex]y=1x+3[/tex]
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures. (Note: Researchers can match subjects by matching particular characteristics, or, in some cases, matched subjects are naturally paired, such as siblings or married couples.)
You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.
The design described ___________a, b, or c_________________________.
a. uses a related sample - repeated measures
b. uses a related sample - matched subjects
c. does not use a related sample
John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people.
The design described ______a, b, or c_________________________.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)
Answer:
a. uses a related sample - repeated measures
c. uses a related sample (matched subjects)
Step-by-step explanation:
A) You are interested in a potential treatment for compulsive hoarding. You treat a group of 50 compulsive hoarders and compare their scores on the Hoarding Severity scale before and after the treatment. You want to see if the treatment will lead to lower hoarding scores.
The design described uses a related sample - repeated measures because the scores were compared on the Hoarding Severity scale before and after the treatment.
B) John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample of lonely people to the sleep quality of a random sample of nonlonely people.
The design described uses a related sample (matched subjects)
The rule r_y-axis ° R_0,90 (x,y) is applied to ABC. Which triangle shows the final image?
a. 1
b. 2
c. 3
d. 4
Answer: 4
Step-by-step explanation:
Simply rotate the graph 1-turn to the left to see where the triangle lands. The x-axis will be the horizontal line and the y-axis will be the vertical line.
The attachment shows the graph rotated 1-turn to the left (90°).
Notice it is in the exact same position as #4.
The following data values represent a sample. What is the variance of the
sample? X = 8. Use the information in the table to help you.
х
12
9
11
5
3
(x; - x)²
16
1
9
9
25
Answer:
The variance of the data is 15.
σ² = 15
Step-by-step explanation:
The mean is given as
X = 8
х | (x - X) | (x - X) ²
12 | 4 | 16
9 | 1 | 1
11 | 3 | 9
5 | -3 | 9
3 | -5 | 25
The variance is given by
[tex]\sigma^2 = \frac{1}{n-1} \sum (x - X)^2[/tex]
[tex]\sigma^2 = \frac{1}{5 - 1} (16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} ( 16 + 1 + 9 + 9 +25) \\\\\sigma^2 = \frac{1}{4} (60) \\\\\sigma^2 = 15[/tex]
Therefore, the variance of the data is 15.
Determine by inspection whether the vectors are linearly independent. Justify your answer.
[4 1], [3 9], [1 5], [-1 7]
Choose the correct answer below.
A.The set is linearly dependent because at least one of the vectors is a multiple of another vector.
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
C. The set is linearly dependent because there are four vectors but only two entries in each vector.
D. The set is linearly independent because there are four vectors in the set but only two entries in each vector.
Answer:
B. The set is linearly independent because at least one of the vectors is a multiple of another vector.
Step-by-step explanation:
A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.
WHY CAN'T ANYONE HELP ME? :( Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $106. Two adults and three children must pay $75. Find the price of the adult's ticket and the price of a child's ticket.
Answer:
Children: $13
Adults: $18
Step-by-step explanation:
Well for both sets we can set up the following system of equations,
[tex]\left \{ {{3a + 4c = 106} \atop {2a + 3c = 75}} \right.[/tex]
So first we need to solve for a in the first equation.
3a + 4c = 106
-4c to both sides
3a = -4c + 106
Divide 3 by both sides
a = -4/3c + 35 1/3
Now we plug in that a for a in 2a + 3c = 75.
2(-4/3c + 35 1/3) + 3c = 75
-8/3c + 70 2/3 + 3c = 75
Combine like terms
1/3c + 70 2/3 = 75
-70 2/3 to both sides
1/3c = 4 1/3
Divide 1/3 to both sides
c = 13
Now we can plug in 13 for c in 3a + 4c = 106,
3a + 4(13) = 106
3a + 52 = 106
-52 to both sides
3a = 54
Divide 3 by both sides.
a = 18
Thus,
an adult ticket is $18 and a children's ticket is $13.
Hope this helps :)
Answer:
Adults pay $18 and children pay $13.5
Step-by-step explanation:
Hello!
You need to calculate the price of the tickets for adults and children for the group trip to New York.
If X represents adult and Y represents children, then you can express the given information as two equations with two unknown values:
Three adults and four children must pay $106. ⇒ 3X + 4Y= $106
Two adults and three children must pay $75. ⇒ 2X + 3Y= $75
I) First step, in one of the equations you have to clear one of the unknown values, I'll clear the value of Y:
3X + 4Y= 106
4Y= 106 - 3X
[tex]Y= \frac{106-3X}{4}[/tex]
II) Second step you have to replace it in the second equation:
2X + 3Y= 75
[tex]2X + 3(\frac{106-3X}{4} )= 75[/tex]
[tex]2X + \frac{3}{4}(106-3X)= 75[/tex]
[tex]2X + (\frac{3}{4}*106 - \frac{3}{4}*3X )= 75[/tex]
[tex]2X + 79.5 -\frac{9}{4}X =75[/tex]
[tex]2X - \frac{9}{4}X= 75 - 79.5[/tex]
[tex]-\frac{1}{4} X= -\frac{9}{2}[/tex]
[tex]X= -\frac{9}{2} * -4= 18[/tex]
The price for adult tickets is $18.
III) Third step, using the calculated value of X, you replace it on the formula obtained in I) yo calculate the price for the children Y:
[tex]Y= \frac{106-3X}{4}= \frac{106-(3*18)}{4} = \frac{27}{2}= 13.5[/tex]
The ticket price for children is $13.5
I hope this helps!
If a pair of dice are rolled,
what is the probability that at least
one die shows a 5?
Answer:
11/36
Step-by-step explanation:
Find the probability that neither dice shows a 5 (also means the dice can show any number except 5- where there are 5 possible choices out of 6):
= 5/6 x 5/6
=25/36
If we subtract the probability that neither dice shows a 5, we can obtain the probability that at least 1 dice shows a 5- (either one of them is 5, or both of them is 5)
1- 25/36
=11/36
What is the range of the function F(x) graphed below?F(x)= -(x+2)^2+3
Answer:
range of the function F(x) is (-infinity, 3)
Step-by-step explanation:
I do not see the graph function F(x), so will assume that it is a graph of the function F(x) over the complete domain (-inf,inf).
As you can see from the attached graph, the function reaches a maximum at y=+3, and extends all the way to -infinity.
So the range of the function F(x) is (-infinity, 3)
what is the length of a rectangle with width 12 inches and an area of 66 inches^2
Answer:
The length is 5.5 inches
Step-by-step explanation:
The area of a rectangle is
A = lw
66 = l * 12
Divide each side by 12
66/12 = l
5.5 = l
The length is 5.5 inches
Answer:
5.5 inches
Step-by-step explanation:
Length times width is the area so
12*width =66
same as
66/12=5.5 inches
Ask more questions in the comments if you are still confused.
123=0
4235=0
656=2
5390=2
8890=6
1001=2
19235=1
What is 123456789?
Answer:
4
Step-by-step explanation:
I suppose this is a trick question.
The answer is equal to the "circular hole" in the numbers. (except 4, which does not contain circular hole).
So by counting the holes,
123456789 = 4
Answer:
4
Step-by-step explanation:
This is a trick/pattern
We have to count the number of holes in each number
1-0
2-0
3-0
4-0
5-0
6-1
7-0
8-2
9- 1
1+2+1 =4
prove that 1/3 root2 is irrational
Step-by-step explanation:
Let us assume that 1/2+root 3 is rational . So 1/2+root 3 = a/b where a and b are irrationals. since rhs is a rational number root 3 should be also rational .
Verify the Cauchy-Schwarz Inequality and the triangle inequality for the given vectors and inner product.
p(x)=5x , q(x)= -2x^2+1, (p,q)= aobo+ a1b1+ a2b2
Required:
a. Compute (p,q)
b. Compute ||p|| and ||q||
Answer:
To verify the Cauchy-Bunyakovsky-Schwarz Inequality, (p,q) must be less than (or equal to) ||p|| • ||q||
(1,1,1) is not equal to (-10,5)
Step-by-step explanation:
a°b° + a^1b^1 + a^2b^2 < 5x (-2x^2 + 1)
Any algebra raised to the power of zero is equal to 1.
a°b° = 1 × 1 = 1
1 + ab + a^2b^2 < -10x^3 + 5x
The vectors:
(1,1,1) < (-10,5)
This verifies the Cauchy-Schwarz Inequality
Triangle Inequality states that for any triangle, the sum of the lengths of two sides must be greater than or equal to the length of the third side.
Solve : 1 − | 0.2(m−3)+ 1/4| =0
Answer:
1-{0.2(m-3)+¼}=0
1{0.2m-0.6+¼}=0
1-{(0.8m-2.4+1)/4}=0
1-(0.8m-1.4)/4=0
lcm
(4-0.8m-1.4)/4=0
(2.6-0.8m)/4=0
cross multiply
2.6-0.8m=0
m=2.6/0.8
m=3.25
The solution of the expression are,
⇒ m = 3.25
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Expression is,
⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0
Now, We can simplify as;
⇒ 1 - | 0.2m - 0.6 + 1/4| = 0
⇒ 1 - |0.2m - 0.6 + 0.25| = 0
⇒ 1 - |0.2m - 0.35| = 0
⇒ 1 = 0.2m + 0.35
⇒ 1 - 0.35 = 0.2m
⇒ 0.2m = 0.65
⇒ m = 3.25
Thus, The solution of the expression are,
⇒ m = 3.25
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You are selling your product at a three-day event. Each day, there is a 60% chance that you will make money. What is the probability that you will make money on the first two days and lose money on the third day
Answer:
The required probability = 0.144
Step-by-step explanation:
Since the probability of making money is 60%, then the probability of losing money will be 100-60% = 40%
Now the probability we want to calculate is the probability of making money in the first two days and losing money on the third day.
That would be;
P(making money) * P(making money) * P(losing money)
Kindly recollect;
P(making money) = 60% = 60/100 = 0.6
P(losing money) = 40% = 40/100 = 0.4
The probability we want to calculate is thus;
0.6 * 0.6 * 0.4 = 0.144
what is the surface area of a cylinder height is 4 cm and diameter is 5 cm
Answer:
20cm it's is the answers
Step-by-step explanation:
5*4=20
What is the horizontal distance from the end of the ramp to the back of the truck?
Answer:
134.4 centimetersStep-by-step explanation:
Given,
Hypotenuse ( h ) = 158 cm
Perpendicular ( p ) = 83
Base ( b ) = ?
Now, Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]
Plug the values
[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]
Evaluate the power
[tex] {b}^{2} = 24964 - 6889[/tex]
Calculate the difference
[tex] {b}^{2} = 18075[/tex]
[tex]b = \sqrt{18075} [/tex]
Calculate
[tex]b = 134.4 \: cm[/tex]
Hope this helps..
Best regards!!
Solve the equation 1/3 (x + 1) +2x =2
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Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
Step 1: Simplify both sides of the equation.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)
[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]
[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)
[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]
Step 2: Subtract 1/3 from both sides.
[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]
Step 3: Multiply both sides by 3/7.
[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]
So the answer is : [tex]x = \frac{5}{7}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
Given: ∠N ≅ ∠S, line ℓ bisects at Q. Prove: ∆NQT ≅ ∆SQR Which reason justifies Step 2 in the proof? If two lines are parallel, then the corresponding angles formed are congruent. If two lines are parallel, then the alternate interior angles formed are congruent. Vertical angles are congruent. If two lines are parallel, then the same-side interior angles formed are congruent.
Answer:
Vertical angles are congruent.
Step-by-step explanation:
Vertical angles are opposite angles formed by intersecting lines, and are always congruent.
The automatic opening device of a military cargo parachute has been designed to open when the parachute is 155 m above the ground. Suppose opening altitude actually has a normal distribution with mean value 155 and standard deviation 30 m. Equipment damage will occur if the parachute opens at an altitude of less than 100 m. What is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes
Answer:
the probability that one parachute of the five parachute is damaged is 0.156
Step-by-step explanation:
From the given information;
Let consider X to be the altitude above the ground that a parachute opens
Then; we can posit that the probability that the parachute is damaged is:
P(X ≤ 100 )
Given that the population mean μ = 155
the standard deviation σ = 30
Then;
[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]
[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]
[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]
[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]
From standard normal tables
[tex]P(X \leq 100 ) = 0.0334[/tex]
Hence; the probability of the given parachute damaged is 0.0334
Let consider Q to be the dropped parachute
Given that the number of parachute be n= 5
The probability that the parachute opens in each trail be p = 0.0334
Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334
The probability mass function is:
Q [tex]\sim[/tex] B(5, 0.0334)
Similarly; the event that one parachute is damaged is :
Q ≥ 1
P( Q ≥ 1 ) = 1 - P( Q < 1 )
P( Q ≥ 1 ) = 1 - P( Y = 0 )
P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )
P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]
P( Q ≥ 1 ) = 1 - 0.8437891838
P( Q ≥ 1 ) = 0.1562108162
P( Q ≥ 1 ) [tex]\approx[/tex] 0.156
Therefore; the probability that one parachute of the five parachute is damaged is 0.156