Answer:
A=108 cm²
Step-by-step explanation:
length (l)=3w
perimeter=2l+2w
P=2(3w)+2w
48=6w+2w
width=48/8
w=6
l=3w=3(6)=18
l=18 cm , w=6 cmArea=l*w
A=18*6
A=108 cm²
Two brothers, Tom and Allen, each inherit $39000. Tom invests his inheritance in a savings account with an annual return of 2.9%, while Allen invests his inheritance in a CD paying 5.7% annually. How much more money than Tom does Allen have after 1 year?
Answer:
Tom:
initial money = $ 39000
% increased per annum = 2.9%
money gained per annum = 39000 * 2.9/100 = $1131
Allen:
initial money = $ 39000
% increased per annum = 5.7 %
money gained per annum = 39000 * 5.7/100 = $2223
Allen has $ (2223 - 1131) = $ 1192 more than Tom
A ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° toward the south. After 2 hours, maintain the same speed. What is the bearing to the ship from port?
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
Solve the system by graphing y=-4x-2 -2x+y=-2 Plot both lines and point of intersection by moving the dots to the correct location
Answer:
The point of intersection is (0,-2).
Step-by-step explanation:
Equation 1: [tex]y=-4x-2[/tex]
Equation 2 : [tex]-2x+y=-2[/tex]
Plot the lines on the graph
Refer the attached figure
Equation 1: [tex]y=-4x-2 ---- Red[/tex]
Equation 2 : [tex]-2x+y=-2 ---- Blue[/tex]
Point of intersection : A point where both the lines intersect is called point of intersection.
So, Both lines intersect at point (0,-2)
So, Point of intersection is (0,-2)
Hence The point of intersection is (0,-2).
A vector has a magnitude of 43
meters at an angle (0). If the
Y-component of the vector is 30
meters, what is the X-component?
[?]m
30.8 m
Step-by-step explanation:
Given: [tex]V = 43\:\text{m}[/tex], [tex]V_y = 30\:\text{m}[/tex]
The x-component of vector [tex]\vec{\text{V}}[/tex] is
[tex]V_x = \sqrt{V^2 - V_y^2} = \sqrt{(43)^2 - (30)^2} = 30.8\:\text{m}[/tex]
The x- component of the vector is 30.8meters.
What is the magnitude and direction of vector?If [tex]v = < a. b >[/tex] be a position vector then the magnitude of vector v is found by [tex]|v| =\sqrt{a^{2}+b^{2} } }[/tex] , where a and b are the x and y component respectively.
And the direction is equals to the angle formed x- axis or y axis.
According to the given question
We have
Magnitude of the vector, |v| = 43meters
Y- component of the vector, b = 30meters
Since, we know that
[tex]|v| =\sqrt{a^{2} +b^{2} }[/tex]
Substitute the value of |v| = 43 and b = 30 in the above formula of magnitude.
⇒ [tex]43 = \sqrt{a^{2}+30^{2} }[/tex]
⇒ [tex]43 = \sqrt{a^{2}+900 }[/tex]
⇒ [tex]43^{2} =a^{2} + 900[/tex]
⇒ [tex]1849 = a^{2} + 900[/tex]
⇒ [tex]1849-900=a^{2}[/tex]
⇒ [tex]949=a^{2}[/tex]
⇒ [tex]a =\sqrt{949}[/tex]
⇒ [tex]a = 30.8[/tex]
Hence, the x- component of the vector is 30.8meters.
Learn more about magnitude and direction of a vector here:
https://brainly.com/question/13134973
#SPJ2
The perimeter of a rectangle is 80 cm. Find the lengths of the sides of the rectangle giving the maximum area.Enter the answers for the lengths of the sides in increasing order.
Answer:
The lengths of the sides are 20 cm and 20 cm
Step-by-step explanation:
Given
Perimeter, P = 80cm
Represent the length and width with L and W, respectively;
[tex]P= 2*(L + B)[/tex]
Substitute 80 for P
[tex]80 = 2 * (L + B)[/tex]
Divide through by 2
[tex]40 = L + B[/tex]
[tex]L + B = 40[/tex]
Make L the subject of formula
[tex]L = 40 - B[/tex]
Area of a rectangle is calculated as thus;
[tex]Area = L * B[/tex]
Substitute 40 - B for L
[tex]Area = (40 - B) * B[/tex]
Express this as a function
[tex]A(B) = (40 - B)* B[/tex]
[tex](40 - B)* B = A(B)[/tex]
Set A(B) = 0 to determine the roots
Hence;
[tex](40 - B)* B = 0[/tex]
[tex]40 - B = 0[/tex] or [tex]B = 0[/tex]
[tex]40 = B[/tex] or [tex]B = 0[/tex]
[tex]B = 40[/tex] or [tex]B = 0[/tex]
The maximum area of a rectangle occurs at half the sum of the roots;
So;
[tex]B= \frac{B_1 + B_2}{2}[/tex]
[tex]B= \frac{40+0}{2}[/tex]
[tex]B= \frac{40}{2}[/tex]
[tex]B = 20[/tex]
Recall that [tex]L = 40 - B[/tex]
[tex]L = 40 - 20[/tex]
[tex]L = 20[/tex]
Hence the lengths of the sides are 20 cm and 20 cm
5. If W(-10, 4), X(-3,-1), and Y(-5, 11) classify AWXY by its sides. Show all work to justify your
answer.
Answer:
an isosceles right triangle
Step-by-step explanation:
The square of the length of a side can be found from the distance formula:
d^2 = (x2-x1)^2 +(y2-y1)^2
The square of the length of WX is ...
WX^2 = (-3-(-10))^2 +(-1-4)^2 = 49+25 = 74
The square of the length of XY is ...
XY^2 = (-5-(-3))^2 +(11-(-1))^2 = 4 +144 = 148
The square of the length of YW is ...
YW^2 = (-10-(-5))^2 +(4 -11)^2 = 25 +49 = 74
The sum of the squares of the short sides is equal to the square of the long side, so this is a right triangle. The squares of the short sides are equal, so this is an isosceles right triangle.
Jayden, who burns 345 calories in 45 min
while hiking is preparing for a 6 hour hike.
He uses a special supplement beverage
pack that provides water, needed
electrolytes, and 310 calories. The goal is to
replace roughly 1/3 of the calories burned
while carrying as light a load as possible.
How many packs should he take?
This question is solved using proportions.
First, we find how many calories he will burn in the hike.Then, we find how many calories he will need to replace, and the number of packs needed.Doing this, we get that he should take 3 packs.
How many calories he burns in the hike?
In 45 minutes, he burns 345 calories. How many calories in 6*60 = 360 minutes?
45 minutes - 345 calories
360 minutes - x calories
Applying cross multiplication:
[tex]45x = 345*360[/tex]
[tex]x = \frac{345*360}{45}[/tex]
[tex]x = 2760[/tex]
He burns 2760 calories in the hike.
How many calories he wants to replace?
Roughly 1/3, so he have to find one third of 2760, that is:
[tex]\frac{2760}{3} = 920[/tex]
How many packs?
One pack recovers 310 calories, how many packs for 920 calories?
1 pack - 310 calories
x packs - 920 calories
Applying cross multiplication:
[tex]310x = 920[/tex]
[tex]x = \frac{920}{310}[/tex]
[tex]x = 2.97[/tex]
Rounding up, he should take 3 packs.
A similar question is found at https://brainly.com/question/14426926
FIND THE AREA OF THE SHAPE BELOW
PLEASE HELP I HAVE BEEN STUCK ON THIS FOREVERRRR!!
THANK YOU
Answer:
Is answer 22 units sqaure ?
What should be added to 9x to get 15x ?
with formal
Answer:
15x-9x=6x
please mark me as brainliest
Answer:
6x.
Step-by-step explanation:
15x - 9x = 6x.
Choose the inequality that represents the following graph.
Answer:
option a
Step-by-step explanation:
give person above brainliest :)
What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex]a + bi[/tex]
Required
Determine the type of number in that form
Numbers written in [tex]a + bi[/tex] are referred to as complex numbers
Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]
Note that a and b can either integers or non integers and a and be can also be positive or negative
The following are valid examples of complex numbers
[tex]2 + 3i[/tex]
[tex]2.4 - 5i[/tex]
[tex]-3 - i[/tex]
and lots more..
In the number 5,794,032,861, which digit is in the ten millions place?
09
0 5
o 7
0 4
The count in a bacteria culture was 900 after 15 minutes and 1100 after 35 minutes. Assuming the count grows exponentially,
What was the initial size of the culture?
Answer:
300
Step-by-step explanation:
1100 = 900 [tex]e^{k*20}[/tex]
1.222222 = [tex]e^{k*20}[/tex]
ln(1.222) = 20k ln(e)
k = ln(1.222)/20
k = .2004
900 = x [tex]e^{15* .20004}[/tex]
900/x = [tex]e^{15* .20004}[/tex]
[tex]e^{15*.2004} = 900/x[/tex]
x = 900/ [tex]e^{15*.2004}[/tex]
x = 300
A class of 40 students visits a farm they tour the farm in group of 5 how many groups of 5 can they make?
Answer:
8
Step-by-step explanation:
40 grouped into 5 = 40/5 = 8
Divide and check by multiplying the quotation by the divisor 8m^4+12m^3 over 4m
Answer:
2m^3 + 3m^2
Step-by-step explanation:
8m^4+12m^3
---------------------
4m
2m^3 + 3m^2
Check
4m(2m^3+3m^2)
8m^4 + 12 m^3
The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?
Answer:
The answer for this question is 5
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of .
Answer:
The zero 1 has a multiplicity of 1.
The zero -2 has a multiplicity of 2.
Hope this clears up any confusion :)
Step-by-step explanation:
Answer:
The zero 1 has a multiplicity of 1.
The zero −2 has a multiplicity of 2 .
Step-by-step explanation:
A bag contains 12 blue marbles, 5 red marbles, and 3 green marbles. Jonas selects a marble and then returns it to the bag before selecting a marble again. If Jonas selects a blue marble 4 out of 20 times, what is the experimental probability that the next marble he selects will be blue? A. .02% B. 2% C. 20% D. 200% Please show ALL work! <3
Answer:
20 %
Step-by-step explanation:
The experimental probability is 4/20 = 1/5 = .2 = 20 %
A manager from a certain well known department store found out the money their customers carry into the store is normally distributed with a mean of $258 dollars and a standard deviation of $35. In a sample of 76 Americans who walked into that store find the probability that a random customer will have more than $260 in his or her wallet
Answer:
0.30924
Approximately ≈ 0.3092
Step-by-step explanation:
To solve for this question, we use the formula:
z = (x - μ)/σ
where x is the raw score
μ is the sample mean
σ is the sample standard deviation.
From the question,
x is the raw score = 260
μ is the sample mean = population standard deviation = 258
σ is the sample standard deviation
= σ/√N
N = 76 samples
σ = Population standard deviation
= 35/√76
= 4.0146919966
Hence,
z = (x - μ)/σ
= 260 - 258/ 4.0146919966
= 0.4981702212
Approximately = 0.498
We find the Probability using z score table for normal distribution
P(x = z) = P( x = 260)
= P( z = 0.498)
= 0.69076
The probability that a random customer will have more than $260 in his or her wallet is calculated as:
P(x>Z) = 1 - P( z = 0.498)
P(x>Z) = 1 - 0.69076
P(x>Z) = 0.30924
Approximately ≈ 0.3092
perform the following division (-2/3) ÷ (4/7)
Answer:
-7/6
Step-by-step explanation:
-2/3 x 7/4 = -14/12 = -7/6
Answer: -7/6
Step-by-step explanation: (-2/3) ÷ (4/7) can be rewritten as (-2/3) · (7/4).
Remember that dividing by a fraction is the same thing
as multiplying by the reciprocal of the fraction.
Before multiplying however, notice that we
can cross-cancel the 2 and 4 to 1 and 2.
So multiplying across the numerators and denominator and
remembering our negative in the first fraction, we have -7/6.
evaluate the function f(x)=4x^2-7x+7 find f(7)
please I need the answer soon!
9514 1404 393
Answer:
f(7) = 154
Step-by-step explanation:
The basic idea is you put 7 where x is and do the arithmetic.
Polynomial evaluation is sometimes easier if you rewrite it to Horner form.
f(x) = (4x -7)x +7
f(7) = (4·7 -7)(7) +7 = 21(7) +7 = 147 +7
f(7) = 154
Which of the following is a correct interpretation of the expression -4 - (-7)?
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex]-4-(-7)[/tex]
First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:
[tex]-4-(-7)\\=-4+7[/tex]
When adding on the number line, we move to the right.
Therefore, the correct interpretation is the value 7 digits to the right of -4.
D is the correct answer.
Answer:
D. the number that is 7 to the right of -4 on the number line
Step-by-step explanation:
interpret -4 - (-7)
= -4 +7
therefore
the number that is 7 to the right of -4 on the number line
so its D.
Figure ABCD is a square find the value of x
Answer:
x=3
Step-by-step explanation:
since its a square all sides equal each other
5x-2=x+10
4x -2 =10
4x=12
x = 3
(PLEASE HELP AGAIN SORRY)
Find x.
A) 11.53
B) 12.12
C) 16.45
D) 15.92
Answer:
x = 15.92
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan 53 = x / 12
12 tan 53 = x
x=15.92453
Rounding to the nearest hundredth
x = 15.92
Answer:
15.92
Step-by-step explanation:
Graph x^2/49+y+1^2/4=1
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Perhaps you want a graph of ...
x^2/49 +(y +1)^2/4 = 1
This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.
2. What is the length of AB? Round your
answer to the nearest hundredth.
Answer:
The required length of AB is 7.28 units.
Given that
[tex]\sqrt{2p-7}=3[/tex]
and
[tex]7\sqrt{3q-1}=2[/tex]
Evaluate
[tex]p + {q}^{2} [/tex]
Answer:
Below
Step-by-step explanation:
The two given expressions are:
● √(2p-7) = 3
● 7√(3q-1) = 2
We are told to evaluate p+q^2
To do that let's find the values of p and q^2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with p.
● √(2p-7) = 3
Square both sides
● (2p-7) = 3^2
● 2p-7 = 9
Add 7 to both sides
● 2p-7+7 = 9+7
● 2p = 16
Divide both sides by 2
● 2p/2 = 16/2
● p = 8
So the value of p is 8
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's find the value of q^2
● 7√(3q-1) = 2
Square both sides
● 7^2 × (3q-1) = 2^2
● 49 × (3q-1) = 4
● 49 × 3q - 49 × 1 = 4
● 147q - 49 = 4
Add 49 to both sides
● 147q -49 +49 = 4+49
● 147q = 53
Divide both sides by 147
● 147q/147 = 53/147
● q = 53/ 147
Square both sides
● q^2 = 53^2 / 147^2
● q^2 = 2809/21609
■■■■■■■■■■■■■■■■■■■■■■■■■
● p+q^2 = 8 +(2809/21609)
● p+q^2 = (2809 + 8×21609)/21609
● p+q^2 = 175681 / 21609
● p + q^2 = 8.129
Round it to the nearest unit
● p+ q^2 = 8
When comparing more than two treatment means, why should you use an analysis of variance instead of using several t tests?
Answer:
Because it increases the risk of Type 1 error
Step-by-step explanation:
ANOVA is the analysis of the variance .
When comparing more than two treatment means we use ANOVA because a t test increases the risk of type 1 error .
For example if we wish to compare 4 population means there will be 4C2 = 6 separate pairs and to test the null hypothesis that all four population means are equal would require six two sample t test. Similarly to test 10 population mean would require 45 separate two sample t test.
This has two disadvantages .
First the procedure is too lengthy and tediuos.
Second the overall level of significance greatly increases as the number of t- tests increases.
The analysis of the variance compares two different estimates of variance using the F distributionto determine whether the population means are equal.
True or false? induction is a kind of thinking you use to form general ideas and rules based on mathematical formuals
Answer:
Hey there!
True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.
Let me know if this helps :)
If f(x) =3x-2 and g(x) = 2x+1, find (f+g) (x)
Answer:
3x-2+2x+1+X
3x+2x+x-2+1
6x-1