Answer:
Speed of the boat is 9.4mph and the current is 15.4mph
Step-by-step explanation:
Rate= distance/ time
With current; rate= boat+ current= b+c
Against current; rate= boat - current = b- c
30=3(b+c)••••••••••••••eqn(1)
30=5(b-c)•••••••••••••••••eqn(2)
30=3b +3c••••••••••••••eqn(3)
30=5b-5c•••••••••••••••eqn(4)
Solve simultaneously
b=12mph
From eqn(3)
30=3b +3c
Divide both sides by 3, we have
10= b+c
If we make "b" the subject of the formula we have
b= (10-c)••••••••eqn(5)
Divide both side of eqn(4) by 5 we have
6=b-c••••••••eqn(7)
Substitute eqn(5) into 7
6= (10-c)-c
6= 10c-c^2
C^2-10c+6
C= 9.4 or 0.64
Substitute the highest value 9.4 into equation 7
6=b-9.4
b=6+9.4
b= 15.4
Speed of the boat is 9.4mph and the current is 15.4mph
Use base ten blocks or an area model to find the product. 2.1 x 1.5
Determine the intercepts of the line
X-intercept: (__ , __)
Y-intercept: (__, __)
Answer:
x-intercept: (-40, 0)
y-intercept: (0, 15)
Step-by-step explanation:
The x-intercept is the value of x when y = 0. By looking at the graph, you can tell when y = 0, x = - 40. The x-intercept is the point that crosses the x-axis.
The y-intercept is the value of y when x = 0. By looking at the graph, you can tell y = 15 when x =0. The y-intercept is the point that crosses the y-axis.
what is 3 + 2x = -6x + 4
Answer:
x = 1/8
Step-by-step explanation:
The sum of three consecutive odd integers is -75. What is the smallest number
Answer:
-27
Step-by-step explanation:
First, let's call the smallest number: n
Then, the next two consecutive odd numbers would be:
n+2 and n+4 (this is because it's only odd numbers so we add 2)
We know the sum of these is −75 so we can write this equation and solve for n:
n + (n + 2) + (n + 4) = -75
n + n + 2 + n + 4 = -75
n + n + n + 2 + 4 = -75
n + n + n + 6 = -75
1n + 1n + 1n + 6 = -75
3n + 6 = -75 Subtract 6 from each side, which cancels the 6 on the left.
3n + 6 - 6 = -75 - 6
3n = -75 - 6
3n = -81 Divide each side by 3
3n/3 = -81/3
n = -81/3
n = -27
n + 2 = -27 + 2 = -25
n + 4 = -27 + 4 = -23
The 3 consecutive odd integers would be:
-27, -25, -23
Let's check our work:
-27 + -25 + -23 = -75 We are correct!
The smallest number is -27
is it A B C D Pls tell me
20 is 1000 times of 0.02. Correct answer is option C.
What is Decimal ?Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.
Here, given value
0.02 = 002/100
= 2/100
On multiply numerator and denominator by 10, we get
0.02 = 20/1000
or 20 = 1000 X 0.02
Thus, 20 is 1000 times of 0.02.
Learn more about Decimal Number from:
https://brainly.com/question/4708407
#SPJ1
A small airplane flew 104 miles in 50 minutes. At this rate, how many miles can it fly in one hour? (50 minutes = 56 hour)
Answer:
124.8 miles
Step-by-step explanation:
104 divided by 5 equals 20.8, then 20.8 times 6 equals 124.8
Make 0.26 and a fraction
Answer:13/50
Step-by-step explanation:
Answer: 26/100 or 13/50
Step-by-step explanation: 0.26 means in word form 26 hundreths. so you put 26 over 100. its your choice if you want to simplify though
how does the graph below change between point A and point B?
I am not able to solve this because there is no graph shown.
Round 3 487 to the nearest thousands place.
Answer:
3,000
Step-by-step explanation:
Answer:
3,000
Step-by-step explanation:
Since 4 is less than 5, the digit must not change. Meaning its 3,000
hoped i helped and hopefully i didnt sound confusing
Hahaha A little help? Plss
Answer:
Step-by-step explanation:
6/58=3/29
Answer:
3/29
Step-by-step explanation:
put -3, 1 3/4, -0.5 and 3 least to greatest to least.
Answer:
-3, -0.5, 1 3/4, 3
Step-by-step explanation: in a number line negative is always less than positive so the bigger the negative number the more is goes down on the number line so that's why -3 is smaller then -0.5 because -0.5 is closer to positive than -3
put the steps for the deriving for the area of a triangle in the correct order
Answer:
See Below.
Step-by-step explanation:
Steps:
1) Draw the altitude of the triangle from Vertex B to side CA and label it h.
2) Find [tex]\sin(C)[/tex] of the triangle.*
3) [tex]\displaystyle \sin(C)=\frac{h}{a}[/tex]
4) Solve for h.
5) [tex]h=a\sin(C)[/tex]
6) Substitute expression for h into traditional formula for area of a triangle,[tex]\displaystyle A=\frac{1}{2}bh[/tex].
7) [tex]\displaystyle A=\frac{1}{2}ba\sin(C)=\frac{1}{2}ab\sin(C)[/tex]
(We acquire two right triangles after drawing h since it is an altitude. We will use the smaller of the two.)
Madison's checking account had a balance of - $45. Then she wrote a check to pay her utility bill for $34. Write an expression to represent Madison's situation.
What is this simplified step by step
(-2k^3-7k^2+5k) + (6k^2+3k)
Answer:
-2k³+6k²+k+9
Step-by-step explanation:
please helphejejjwjwjw
Answer:
B
Step-by-step explanation:
3x -2
Which number line expression shows how to find the distance from 2 to -5?
Answer:
5+2=7
Step-by-step explanation:
Please I need some answers one or two are fine
Answer:
A. 10,000
B. 1,000,000
C. 10,000,000,000
D. 1,000,000,000,000
Step-by-step explanation:
10,000/ 10∧4 = 1
1,000,000/ 10∧6 = 1
10,000,000,000/ 10∧10 = 1
1,000,000,000,000/ 10∧12 = 1
Hope this helps! Good luck!
Point J is between H and K on line segment HK. Use the given information to solve for X. Also find the length of line segment HJ.
HK = 33
HJ = 3x-4
JK = 2x+7
X= ?
The length of line segment HJ= ?
Answer:
x=-3, so now u plug it in, 3(-3)-4=?
answer: HJ is -13.
Using line segments concepts, it is found that:
The value of x is 6.The length of line segment HJ is 14.-------------------------------
Point J is between H and K in a line segment HK, thus:[tex]HK = HJ + JK[/tex]
-------------------------------
We are given that:
[tex]HK = 33[/tex][tex]HJ = 3x - 4[/tex][tex]JK = 2x + 7[/tex]Thus, replacing into the equation, it is possible to solve for x.
-------------------------------
[tex]HK = HJ + JK[/tex]
[tex]33 = 3x - 4 + 2x + 7[/tex]
[tex]5x + 3 = 33[/tex]
[tex]5x = 30[/tex]
[tex]x = \frac{30}{5}[/tex]
[tex]x = 6[/tex]
The value of x is 6.
-------------------------------
The length of line segment HJ is:
[tex]HJ = 3x - 4 = 3(6) - 4 = 18 - 4 = 14[/tex]
A similar problem is given at https://brainly.com/question/24476050
Vaughn paints his porch floor and also the porch floors of 9 neighbors. Each floor is a rectangle that is 8.4 feet long and 6.9 feet wide.
Answer:
579.6 ft²
Step-by-step explanation:
10(8.4×6.9)
Answer:
521.64
Step-by-step explanation:
first you do 8.4 times 6.9 which gets you 57.96 and then you multiply that my 9 which gets you 521.64.
1)
If a bag contains 18 red, 6 yellow, 24 blue, and 8 white balloons, what is the part-to-whole ratio of white balloons to all balloons?
a
A)
1:5
B)
16
1:7
D)
1:8
E)
5:1
Answer:
E
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
8 white balloons
56 balloons in total
8:56 = 1:7
the set of letters in the word mathematics is finite?
Answer:
Yes
Step-by-step explanation:
What is 9.2568×10−3 written in standard form?
Answer:
80 9. 0.5 0.06 0.008 (89.568)
Step-by-step explanation:
9.2568x 10-3 would equal 89.568
The ratio of the weight of an object on Mars to the weight of an object on Earth is 0.4 to 1. How much will a 145 lb astronaut weigh on Mars?
A 145 lb astronaut will weight on Mars.
(Round to the nearest tenth.)
Answer:
58 lbs
Step-by-step explanation:
if it weighs 1 pounds on earth, it weighs 0.4 pounds on Mars. So multiply 145 by 0.4 to get the answer
3
d
Gulliver's Travels
11
10
9
8
Distance imesi
2
1 2 3 4 5 7 8 9 10
Time thous)
Given the graph of the function D(t) of Gulliver's Travels. The function d(t) represents Gulliver's
distance from home after t hours. What is the value of D(3)? *
(1 Point)
Answer: D(3) = 4 miles according to the graph.
Step-by-step explanation:
Look for the 3 on the time scale at the bottom of the graph. Follow the grid line straight up to where it meets the graphed line. Follow the grid line to the distance scale at the left to find the value at that point. It is 4 miles.
The surface area of a sphere with a diameter of 12 units is:
Answer:
452.39
Step-by-step explanation:
Using the formula
A=4pi r ^2
D=2r
A=pie r d^2
= pi. 12^2
=452.39
Of the 50 students in mr motchells classes 60% are girls on friday 20% of the girls in the classes wore jeans how mnay girls wore jeans
Answer:it would be 20
Step-by-step explanation:
Answer: 20.
Step-by-step explanation: 60% of 50 is 30 (students). 20% of it would be 20 (students).
how do you take the square root of a perfect square variable
QUESTION 1 Let’s say that an investigator is interested in the effects of caring for a person with ALS (Lou Gehrig’s disease) on physical and mental health. In particular, the researcher wants to know whether ALS caregivers suffer from clinically elevated levels of depression. They administer the Beck Depression Inventory (BDI) to 20 ALS caregivers. Scores on the BDI range from zero to 40. Scores at or above 25 are considered to reflect clinically significant levels of depression. The mean depression score for the 20 caregivers in the sample is 28. The standard deviation for this sample is 3.0. Do these data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25? This example is not a perfect example of a "true experiment," so the independent and dependent variable are not as clearly identifiable as some other examples. In this example, what is the dependent/outcome variable? Beck Depression Inventory scores How many ALS caregivers there are in the study Whether the caregivers are taking care of someone who has ALS vs. cancer The ALS caregivers vs. the national norms for adults
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25
dependent/outcome variable
Generally the dependent variable is Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers
Step-by-step explanation:
From the question we are told that
The sample size is n = 20
The population mean is [tex]\mu = 25[/tex]
The sample mean is [tex]\= x = 28[/tex]
The standard deviation is [tex] s = 3.0[/tex]
The null hypothesis is [tex]H_o : \mu = 25[/tex]
The alternative hypothesis is [tex]H_a : \mu > 25[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]z= \frac{ 28 -25 }{ \frac{3.0}{\sqrt{20 } } }[/tex]
=> [tex]z= 4.47[/tex]
Generally the probability of z from the z- table is
[tex]p-value = P(Z > 4.47) = 0.000[/tex]
From the values obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the data support the hypothesis that the mean depression score for ALS caregivers is significantly higher than the cutoff score for depression of 25
Generally the dependent variable is Beck Depression Inventory (BDI) scores because the score are dependent on the ALS caregivers
when your cousin was born, she was 21 4/5 inches long. when your friends was born he was 21 3/4 inches long. who was longer at birth? how much longer?
cousin
1/20 inches
Step-by-step explanation:Hi there !
cousin
21 4/5 = (21×5+4)/5 = 109/5
friend
21 3/4 = (21×4+3)/4 = 78/4
lcm(4 ; 5) = 20
⁴⁾109/5 = 436/20 (cousin)
⁵⁾87/4 = 435/20 (friend)
436/20 > 435/20
cousin > friend
436/20 - 435/20 = 1/20 inches longer (cousin)
Good luck !