Answer:
The bearing is N 55.62° W
Step-by-step explanation:
ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.
It then turns 90° towards the south after one hour.
Still maintain the same speed and direction for two hours.
The bearing is just the angle difference from the ship current location to where it started.
Let the speed be km/h
Distance covered in the first round
= 15*1
= 15km
Distance covered in the second round
=15*2
= 30 km
Angle at C = (90-80)+90
Angle at C = 10+90= 100
Let the distance between the port and the ship be c
C²= a² + b² -2abcos
C²= 15²+30²-2(15)(30)cos 100
C²= 225+900+156.28
C²= 1281.28
C= 35.8 km
Using sine formula
30/sin x= 35.8/sin 100
30/35.8 * sin 100 = sinx
0.838*0.9848= sin x
0.8253= sin x
Sin ^-1 0.8253 = x
55.62° = x
The bearing is N 55.62° W
find x on the lines plz and thanks
Answer:
x = 9
this is a ratio problem. You can see that 12/6 = 2, so you can also take 18/2 to get 9.
Answer:
the answer is 6
Step-by-step explanation:
Because 6 and x are corresponding angle so that means no matter what ( if u want the answer to how long the line is or what degree the angle is ) the answer is always going to be the same as the one above ( which is 6 )
Hop this helpssss
what is a negative number that has an absolute value greater than 3?
Answer:
x > -3
Step-by-step explanation:
Any negative number greater than -3 will have an absolute value greater than 3.
Complete the pattern ___ 8,579 ____85.7 8.57____
Answer:
the next one is .857 I hope this helps you :)
What are the coordinates of the point (2,-4) under the dilation D-2?
A) (8,-4)
B) (4,-8)
C) (-8,4)
D) (-4,8)
Answer:
D) (-4,8)
Step-by-step explanation:
Multiply both coordinates by -2
Answer:
(-4,8)
Step-by-step explanation:
I found a school pdf with the answer key to this exact equation and thats the answer
Picking a card and spinning a spinner are independent events.
True
False
Answer:
True
Step-by-step explanation:
Both happened in different times and are seprate events
Which of these functions could have been the graph shown below?
Answer:
B
Step-by-step explanation:
we take the only point we know
(0,20)
in A when x =0
[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]
in B when x=0
[tex]f(x)=20e^x=20e^0=20*1=20[/tex]
fits
in C
[tex]f(x)=20^x=20^0=1[/tex]
in D
[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]
so the only choice is B
What does the tape measure say Measurement # 4 is?
Answer:
It looks like 6 and one eighth of an inch.
Find the value of a and YZ if Y is between X and Z. XY = 7a, YZ = 5a, XZ = 6a + 24 = YZ =
[tex]\\ \sf\longmapsto XY+YZ=XZ[/tex]
[tex]\\ \sf\longmapsto 7a+5a=6a+24[/tex]
[tex]\\ \sf\longmapsto 12a=6a+24[/tex]
[tex]\\ \sf\longmapsto 12a-6a=24[/tex]
[tex]\\ \sf\longmapsto 6a=24[/tex]
[tex]\\ \sf\longmapsto a=\dfrac{24}{6}[/tex]
[tex]\\ \sf\longmapsto a=5[/tex]
YZ=5a=5(5)=25Value of a is 4 and value of YZ is 20 units
Step-by-step explanation:
Given:
Y is between point X and Z
Value of line XY = 7a
Value of line YZ = 5a
Value of line XZ = 6a + 24
Find:
Value of "a" and line YZ
Computation:
We know that
XY + YZ = XZ
So,
7a + 5a = 6a + 24
12a = 6a + 24
6a = 24
a = 4
Value of a = 4
So,
Value of line YZ = 5a
By putting value of a
Value of line YZ = 5(4)
Value of line YZ = 20 units
Learn more;
https://brainly.com/question/18983323?referrer=searchResults
Assuming that the loss of ability to recall learned material is a first-order process with a halflife of 35 days. Compute the number of days required to forget 90% of the material that you have learned today. Report to 1 decimal place.
Answer:
5.3 days
Step-by-step explanation:
Let us assume the loss of ability to recall a learned material = 100%
Formula to calculate number of days = time(t) =
t = t½ × Log½(Nt/No)
Nt = Ending Amount
No = Beginning Amount
t½ = Half life
t = Time elapsed
Therefore, we have the following values from the questions:
Half life (t½)= 35 days
Initial or beginning amount = 100%
Ending amount = 90%
t = t½ × Log½ (Nt/No)
t = 35 × Log ½(90/100)
t = 5.3201082705768 days
Approximately = 5.3 days
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
https://brainly.com/question/5453159
Solve the following system of equations.
2x + y = 3
x = 2y-1
ANSWER: ______
plz help me
(1,1) is your answer.
Work is shown below.
Any questions? Feel free to ask.
Answer: (1,1)
Step-by-step explanation:
Solve for x step by step:
2(4x-3)-8=4+2x
Answer:
3
Step-by-step explanation:
2(4x-3)-8=4+2x
8x - 6 - 8 = 4 + 2x
8x - 2x = 4 + 6 + 8
6x = 18
x = 18/6
x = 3
Answer:
[tex]2(4x - 3) - 8 = 4 + 2x \\ 2 \times 4x + 2 \times - 3 - 8 = 4 + 2x \\ according \: to \: bodmas \: first \: \times then + or - \\ so \\ 8x - 6 - 8 = 4 + 2x \\ 8x - 14 = 4 + 2x \\ 8x - 2x = 4 + 14 \\ 6x = 18 \\ x = \frac{18}{6} \\ x = 3 \\ thank \: you[/tex]
One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?
Answer:
The [tex]L_{ACL}[/tex] of the player is [tex]L_{ACL} = 56.82 \ mm[/tex]
Step-by-step explanation:
From the question we are told that
The relationship between the length [tex]L_{ACL}[/tex] to the height is
[tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]
The height of the basketball player is [tex]h = 2.13 \ m = 2130 \ mm[/tex]
Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is
[tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]
[tex]L_{ACL} = 56.82 \ mm[/tex]
Please help me I will mark brainliest! The ratio of the number of boys to the number of girls in a school is 3:4. One-third of the boys and three-eighths of the girls wear spectacles, If there are 612 pupils who do not wear spectacles, a)find the total number of the pupils in the school, and b) how many more girls than boys are there in the school
Answer:
a) 952
b) 136
Step-by-step explanation:
Ratio of b:g = 3:4, based on this we have:
Number of boys = 3xNumber of girls = 4xTotal number of pupils = 3x+4x = 7xNumber of spectacle wearers:
1/3*3x + 3/8*4x = x + 3/2x = 2.5xNumber of those not wearing spectacles:
7x - 2.5x= 4.5xAnd this number equals to 612, then we can find the value of x:
4.5 x = 612x= 612/4.5x= 136a) Total number of pupils:
7x = 7*136 = 952b) The difference in the number of boys and girls:
4x-3x= x = 136Answer:
total number of students: 952
number of girls more than boys :136 more girls
Step-by-step explanation:
1/3 of boys +3/8 girls= spectacles
612 people do not wear spectacles
3:4= boys: girls
total number of students
3+4=7
boys + girls = total ratio
7= total ratio
1/3×3=1 3/8×4=3/2
1+3/2=5/2
7-5/2=9/2 9/2=612 students
If 9/2=612 Then 7=?
7= 7÷ 9/2×612
=952 people
Girls more than boys
if 7= 952
3= 3/7 × 952=408 boys
if 7 = 952
4= 4/7 ×952=544girls
Girls - boys
544- 408 = 136 girls
The graph below represents the function f.
f(x)
if g is a quadratic function with a positive leading coefficient and a vertex at (0,3), which statement is true?
А.
The function fintersects the x-axis at two points, and the function g never intersects the x-axis.
B
The function fintersects the x-axis at two points, and the function g intersects the x-axis at only one point.
c.
Both of the functions fand g intersect the x-axis at only one point.
D
Both of the functions fand g intersect the x-axis at exactly two points.
Answer: А.
The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
In the graph we can see f(x), first let's do some analysis of the graph.
First, f(x) is a quadratic equation: f(x) = a*x^2 + b*x + c.
The arms of the graph go up, so the leading coefficient of f(x) is positive.
The vertex of f(x) is near (-0.5, -2)
The roots are at x = -2 and x = 1. (intersects the x-axis at two points)
Now, we know that:
g(x) has a positive leading coefficient, and a vertex at (0, 3)
As the leading coefficient is positive, the arms go up, and the minimum value will be the value at the vertex, so the minimum value of g(x) is 3, when x = 0.
As the minimum value of y is 3, we can see that the graph never goes to the negative y-axis, so it never intersects the x-axis.
so:
f(x) intersects the x-axis at two points
g(x) does not intersect the x-axis.
The correct option is A.
Answer:
The answer is A.) The function f intersects the x-axis at two points, and the function g never intersects the x-axis.
Step-by-step explanation:
I took the test and got it right.
(4x - 3) × (x + 2)=0
Hi,
AxB = 0 means A=0. or B=0
so 2 solutions :
4x-3= 0
4x=3
x = 3/4
and x+2 = 0.
x= -2
solutions are : -2 +and 3/4
2 answers
1) -2
2) -3/4
Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboard from which she cuts out - squares from each corner. The length of the original piece of cardboard is more than the width. If the volume of the box is , determine the dimensions of the original piece of cardboard.
Question is not complete, so i have attached it.
Answer:
Length = 30 inches
Width = 22 inches
Step-by-step explanation:
Let the width of rectangular sheet be x inches.
Let the length of the sheet be (x + 8) inches.
Now, after she cuts 4 inches squares from each corner, she will get a box of length: x + 8 - 4 - 4 = x inches , width: (x - 8) inches and height 4 inches.
Now, volume of a cube is;
V = lwh
Thus;
V = x(x - 8)(4)
We are told that the volume of the box is 2640 in³
Thus;
x(x - 8)(4) = 2640
Divide both sides by 4 to get;
x(x - 8) = 660
x² - 8x - 660 = 0
Using quadratic formula, we have;
x = 30 or - 22.
We will use x = 30 as the other one is negative.
Since we earlier deduced that she will get a box of will get a box of length: x inches , width: (x - 8) inches
Thus,
Length = 30 inches
Width = 30 - 8 = 22 inches
Consider the function below. (If an answer does not exist, enter DNE.) f(x) = x3 − 27x + 3 (a) Find the interval of increase. (Enter your answer using interval notation.)
Answer:
(-∞,-3) and (3,∞)
Step-by-step explanation:
f(x) = x³ − 27x + 3
1. Find the critical points
(a) Calculate the first derivative of the function.
f'(x) = 3x² -27
(b) Factor the first derivative
f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)
(c) Find the zeros
3(x + 3) (x - 3) = 0
x + 3 = 0 x - 3 = 0
x = -3 x = 3
The critical points are at x = -3 and x = 3.
2. Find the local extrema
(a) x = -3
f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57
(b) x = 3
f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51
The local extrema are at (-3,57) and (3,-51).
3, Identify the local extrema as maxima or minima
Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)
f'(-4) = 3x² -27 = 3(4)² - 27 = 21
f'(0) = 3(0)² -27 = -27
f'(4) = 3(4)² - 27 = 51
The function is increasing on the intervals (-∞,-3) and (3,∞).
The graph below shows the critical points of your function.
In 2014, the population of India1 was 1.236 billion people and increasing at a rate proportional to its population. If the population is measured in billions of people and time is measured in years, the constant of proportionality is 0.0125. Define P to be the population of India, in billions of people, in the year t, where t represents the number of years since 2014. (a) Write a differential equation to describe the relationship.\
Answer: i don’t kno I’m 6 years old
Step-by-step explanation:
A researcher was interested in whether a new sports drink could change people's running endurance. For one week, 6 participants continued with their normal routine and then their endurance was measured. The following week, the same participants were instructed to drink the new sports drink an hour before their endurance was measured. Below are your data.
Week I 90 100 110 110 85 95
Week 2 100 110 110 120 95 95
What type of analysis would be used on the above data?
a. Z-test
b. One sample t-test
c. Independent samples t-test
d. Dependent samples t-test
Answer:
The correct option is (d).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have 2 measurements on the same item, person or thing. We should also use this test if we have 2 items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case, the same participants are selected for both the trials.
And the difference between the endurance before and after the usage of the new sports drink are noted.
Thus, the analysis that would be used on the data is the Dependent samples t-test.
Suppose you finance a home in the amount of $425,000 at 4.3% compounded monthly for 30 years. Calculate your payment.
Answer: $1,540,194.30 .
Step-by-step explanation:
The formula to calculate the accumulated amount earned on principal (P) at rate of interest (r)[ in decimal] compounded monthly after t years :
[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex]
Given: P= $425,000
r= 4.3% = 0.043
t= 30 years
[tex]A=425000(1+\dfrac{0.043}{12})^{12(30)}\\\\=425000(1.003583)^{360}\\\\=425000\times3.62398657958\approx1540194.30[/tex]
Hence, the payment would be $1,540,194.30 .
As part of an enterprise day, Guramar and Gurnam baked 4 cakes. They gave 1/2 of one cake away to the staff. In the morning they sold 2 1/3 cakes and in the afternoon they sold 1 1/8. How much cake did they have left?
9514 1404 393
Answer:
1/24 of a cake
Step-by-step explanation:
The remaining amount of cake was ...
4 -1/2 -2 1/3 -1 1/8 = 4 -12/24 -2 8/24 - 1 3/24 = (4 -2 -1) -(12 +8 +3)/24
= 1 -23/24 = 1/24
1/24 of a cake was left
_____
Basically, crumbs.
An online polling site posed this question: "How much stock do you put in long-range weather forecasts?" Among its Web site users, 38, 528 chose to respond Complete parts (a) through (c) below.
a. Among the responses received, 3% answered with "a lot". What is the actual number of responses consisting of "a lot"?
b. Among the responses received, 18, 566 consisted of "very little or none". What percentage of responses consisted of "very little or none"?
c. Because the sample size of 38, 528 is so large, can we conclude that about 3% of the general population puts "a lot" of stock in long-range weather forecasts? Why or why not?
A. No, because the sample is a voluntary response sample, so the sample is not likely to be representative of the population.
B. Yes, because the sample is so large, the margin of error is negligible.
C. No, because even though the sample size is so large, there is still a margin of error.
D. Yes, because the sample size is large enough so that the sample is representative of the population.
Answer:
(a) 1155.84
(b) 48.2%
(c) D
Step-by-step explanation:
The number of total responses is, N = 38,528.
(a)
It is provided that 3% answered with "a lot".
Compute the actual number of responses consisting of "a lot" as follows:
n (a lot) = N × P (a lot)
= 38528 × 0.03
= 1155.84
Thus, the actual number of responses consisting of "a lot" is 1155.84.
(b)
The number of responses consisting of "very little or none" is,
n (very little or none) = 18,566
Compute the percentage of responses consisted of "very little or none" as follows:
[tex]P(\text{very little or none})=\frac{n(\text{very little or none})}{N}[/tex]
[tex]=\frac{18566}{38528}\\\\=0.481883\\\\\approx 0.482[/tex]
The percentage is: 0.482 × 100% = 48.2%.
Thus, the percentage of responses consisted of "very little or none" is 48.2%.
(c)
As the sample size increases the sample statistic value gets closer and closer to the actual population parameter value.
Thus, making the sample statistic an unbiased estimator of the population parameter.
And proving that the sample is a true representative of the population.
Thus, the correct option is (D).
Could someone help me pls! And could you explain if possible? Thanks you
Answer:
3%
Step-by-step explanation:
1. Set up the equation
6(0.18) + 12x = 18(0.08)
2. Simplify
1.08 + 12x = 1.44
3. Solve
12x = 0.36
x = 0.03
0.03 = 3%
1) Given P(A) = 0.3 and P(B) = 0.5, do the following.
(a) If A and B are mutually exclusive events, compute P(A or B).
(b) If P(A and B) = 0.2, compute P(A or B).
2) Given P(A) = 0.4 and P(B) = 0.2, do the following.
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.7, compute P(A and B).
Answer:
1) a) 0.8
b) 0.6
2) a) 0.08
b) 0.14
Step-by-step explanation:
1) Given
[tex]P(A) = 0.3[/tex] and [tex]P(B) = 0.5[/tex]
Let us learn about a formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\OR\\P(A\cup B) = P(A) +P(B) -P(A\cap B)[/tex]
(a) If A and B are mutually exclusive i.e. no common thing in the two events.
In other words:
[tex]P(A\ and\ B)[/tex] = [tex]P(A \cap B)[/tex] = 0
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0 = \bold{0.8}[/tex]
(b) P(A and B) = 0.2
Using above formula:
[tex]P(A\ or\ B) = P(A) +P(B) -P(A\ and\ B)\\\Rightarrow P(A\ or\ B) = 0.3 + 0.5 -0.2 = \bold{0.6}[/tex]
*************************************
1) Given
[tex]P(A) = 0.4[/tex] and [tex]P(B) = 0.2[/tex]
Let us learn about a formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B)[/tex] for dependent events
[tex]P(A\ and\ B) = P(A) \times P(B)[/tex] for independent events.
(a) If A and B are independent events :
Using the above formula for independent events:
[tex]P(A\ and\ B) = 0.4 \times 0.2 = \bold{0.08}[/tex]
(b) [tex]P(A / B) = 0.7[/tex]
Using above formula:
[tex]P(A\ and\ B) = P(B) \times P(A/B) = 0.2 \times 0.7 = \bold{0.14}[/tex]
given the vector with a manitude of 9m at an angle a of -80 degrees, decompose this vector into two vector components oarallel to the x axis with a slope of
Answer:
We have the magnitude, M, and the angle A.
(The angle is always measured from the +x-axis)
Then we have that:
x = M*cos(A)
y = M*sin(A)
in this case:
M = 9m
A = -80°
x = 9m*cos(-80°) = 1.562
y = 9m*sin(-80) = -8.86m
Now, the component parallel to the x axis is:
x = 9m*cos(-80°) = 1.562 m
And the slope of something parallel to the x-axis is always zero, as this is a constant line.
Find the missing side or angle.
Round to the nearest tenth.
Answer:
[tex] b = 2.7 [/tex]
Step-by-step explanation:
Given:
< C = 53°
< B = 80°
a = 2
Required:
Find b
Solution:
The question given suggests we are given measures for a ∆.
To find side b, which corresponds to angle B, first, we'd find angle A, which corresponds to side a, then apply the Law of sines to find side b.
=> A = 180 - (53 + 80) = 47°
Law of Sines: [tex] \frac{a}{sin(A} = \frac{b}{sin(B} [/tex]
Plug in the values into the formula
[tex] \frac{2}{sin(47} = \frac{b}{sin(80} [/tex]
Cross multiply
[tex] 2*sin(80) = b*sin(47) [/tex]
Divide both sides by sin(47) to make b the subject of formula
[tex] \frac{2*sin(80)}{sin(47} = b [/tex]
[tex] 2.69 = b [/tex]
[tex] b = 2.7 [/tex] (nearest tenth)
Keith tabulated the following values for time spent napping in minutes of six of his friends: 23, 35, 17, 30, 20, and 19. The standard deviation is 7.043 Keith reads that the mean nap is 22 minutes. The t-statistic for a two-sided test would be __________. Answer choices are rounded to the hundredths place. 1.39 or 1.43 or 2.88 or 0.70
Answer:
The t-statistic is [tex]t = 0.6956[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 22 \ minutes[/tex]
The standard deviation is [tex]s = 7.043[/tex]
The given data is 23, 35, 17, 30, 20, and 19.
Generally the sample mean is mathematically evaluated as
[tex]\= x = \frac{23+ 35+17+ 30+ 20+ 19 }{6}[/tex]
[tex]\= x =24[/tex]
The t-statistic is mathematically evaluated as
[tex]t = \frac{ \= x - \mu }{\frac{s}{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 24 - 22 }{\frac{ 7.043}{ \sqrt{6} } }[/tex]
=> [tex]t = 0.6956[/tex]
Answer: 0.70
Step-by-step explanation:
The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?
There are 2229 students in a school district. Among a sample of 452 students from this school district, 163 have mathematics scores below grade level. Based on this sample, estimate the number of students in this school district with mathematics scores below grade level.
a. 804
b. 844
c. 884
d. 0.36
Answer:
A. 804Step-by-step explanation:
Given the total number of students in the school to be 2229 students. If among a sample of 452 students from this school district, 163 have mathematics scores below grade level, then we can determine the number of students in this school district with mathematics scores below grade level based on the sample scores using ratio.
Let the number of students in this school district with mathematics scores below grade level be x. The ratio of the students with math score below grade level to total population will be x:2229
Also, the ratio of the sample students with math score below grade level to sample population will be 163:452
On equating both ratios, we will have;
x:2229 = 163:452
[tex]\dfrac{x}{2229} = \dfrac{163}{452}\\ \\cross\ multiplying;\\\\\\452*x = 2229*163\\\\x = \dfrac{2229*163}{452}\\ \\x = \frac{363,327}{452}\\ \\x = 803.8\\\\x \approx 804[/tex]
Hence the estimate of the number of students in this school district with mathematics scores below grade level based on the sample is 804