Answer:
Amount that Brian has after 2 years = £6932.53
Step-by-step explanation:
To find, the amount that Brian will have after 2 years:
Formula for amount where compound interest is applicable:
[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]
Where A is the amount after t years time
P is the principal.
R is the rate of interest.
In the question, we are given the following details:
Principal amount,P = £6300
Rate of interest,R = 4.9%
Time,t = 2 years
Putting the values in formula:
[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]
Hence, Amount that Brian has after 2 years = £6932.53
Answer:
THE ANSWER IS ABOVE
Step-by-step explanation:
hahahaha
NEED HELP ASAP!!! a hexagon-based pyramid has a height of 54cm. The volume of the pyramid is 1080cm3. What is the area of the base?
Answer:
32
Step-by-step explanation:
If a graph of y=-9x+ 3 were changed to a graph of y=-9x + 1, how would the
y-intercept change?
Answer:
y-intercept decreased by 3-1= 2 points
Step-by-step explanation:
y=-9x+ 3 ⇒ y-intercept= 3
y=-9x + 1 ⇒ y-intercept= 1
y-intercept decreased by 3-1= 2 points = the line shifted down by 2 points
Answer:
Hello!
Answer: y-intercept decreased by 2 points because 3-1=2
I hope I was of help. If not, please let me know! Thanks!
Step-by-step explanation:
Write an equation of a line that is parallel to the line 3y=-x+6 and passes through the point (6,2).
Answer:
y = x+2
y =-x+2 shows 0
We want to show 1 both sides
2y = x+2 shows 2
y = x+2 shows 0 as explained below.
Step-by-step explanation:
3y−x=6
Solve for y.
y=2+x3
Rewrite in slope-intercept form.
y=13x+2.
Use the slope-intercept form to find the slope and y-intercept.
Slope: 13 y-intercept: 2
Any line can be graphed using two points. Select two
x values, and plug them into the equation to find the corresponding y values.
xy 02, 33
Graph the line using the slope and the y-intercept, or the points.
Slope:
13y-intercept: 2x y (0,2) (3,3)
At a gas station, 50% of the customers use regular gas, 30% use mid-grade gas and 20% use premium gas. Of those customers using regular gas, only 30% fill their tanks. Of those customers using mid-grade gas, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. If the next customer fills the tank, what is the probability that he uses premium gas
Answer:
The probability is 0.2326 or 23.26%.
Step-by-step explanation:
The probability that a random customer fills their tank with premium gas is:
[tex]P( prem\ \&\ fill) = 0.2*0.5=0.10[/tex]
The probability that a random customer fills their tank is given by:
[tex]P(fill)=P( reg\ \&\ fill)+P( mid\ \&\ fill)+P( prem\ \&\ fill)\\P(fill) = 0.5*0.3+0.3*0.6+0.2*0.5\\P(fill) = 0.43[/tex]
Therefore, the probability that a customer used premium gas given that hey have filled their tank is:
[tex]P(prem| fill) = \frac{P( prem\ \&\ fill) }{P(fill)} \\P(prem| fill) =\frac{0.10}{0.43}=0.2326[/tex]
The probability is 0.2326 or 23.26%.
Indicate in standard form equation of the line passing through the given 
Answer:
x + y = 6
Step-by-step explanation:
slope is rise/run so -6/6 = -1
y = -x+b
solve for b by plugging in any point
6 = 0 + b -> b = 6
y = -x+6
x + y = 6
YOU KNOW THE DRILL 2.0
Answer:
#1
Step-by-step explanation:
The four yellow boxes represent x so together they are 4 * x or 4x. The blue boxes seem to represent -1 and since there are three of them together they are -1 * 3 = -3. 4x + (-3) = 4x - 3.
A flexible cable always hangs in the shape of a catenary curve y = c + a cosh(x/a), where cand a are constants, a > 0. Suppose a telephone line hangs between two poles 18 meters apart, in the shape of the catenary y = 30 cosh(x/15) - 4, where x and y are measured in meters. a. (3 pts.) Find the slope of this curve where it meets the right pole. (Round to 3 decimal places.] b. (3 pts.) Find the angle between the line and the right pole. [Give your answer in degrees, rounded to the nearest hundredth.) Expert Answer
Answer:
The slope of this curve where it meets the right pole is 1.130
The angle between the line and the right pole is 41.51 °
Step-by-step explanation:
Given that ;
[tex]y = 30 \ cos h (\dfrac{x}{15} - 4)[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{30}{15} sinh(\dfrac{x}{15})[/tex]
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{x}{15})[/tex]
x = 9 m;( i.e half of the distance of the two poles at 18 meters apart.
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{9}{15})[/tex]
= 1.130
The slope of this curve where it meets the right pole is 1.130
The angle between the line an the right rope can be determined by using the tangent of the slope .
tan ∝ = 1.130
∝ = tan⁻¹ (1.130)
∝ = 48.49°
The angle is θ; so
θ = 90 - ∝
θ = 90 - 48.49°
θ = 41.51 °
Thus; the angle between the line and the right pole is 41.51 °
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
When x is 2, y is 16
Step-by-step explanation:
If y is 48 and x is 6, then y is 8 when x is 1.
Because of this, when x is 2, y will be 16.
Please mark Brainliest
Look at the row of numbers. What number should come next?
8, 4, 2, 1, 1/2, 1/4, ?
Answer:
1/8
Step-by-step explanation
Every time the number is divided by 2 like 8 divided by 2 is 4 and 4 divided by 2 is 2 and so on so if you divide 1/4 by 2 it would be 0.125 and that in fraction would be 1/8.
What’s the correct answer for this question?
Answer:
Arc EF = 11.30
Step-by-step explanation:
For Circle A
S = r∅
18.08=(8)∅
Where ∅ is the angle subtended by the Arc
So
∅ = 18.08/8
∅ = 2.26 (in radians)
Now
For Circle C
S = r∅
S = (5)(2.26)
S = 11.30
Which linear function has initial value 4?
a. y = 3x - 4
b. y = - 3x + 4
c. y = 4x - 3
d. y = 4x + 3
Answer:
y = -3x+4
Step-by-step explanation:
An initial value of 4 would be the y intercept
The only function with a y intercept of 4
(y = mx+b where b is the y intercept)
is y = -3x+4
Given that f(x) = x² + 4x, evaluate f(-2).
Answer:
-4
Step-by-step explanation:
Find w and y, will give brainliest for the correct answer
Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
What is the slope of the line?
A door wedge is 5 cm tall. Its has 3.7 cm high triangular bases with 2 congruent 5 cm sides and a 4 cm side. What is its surface area?
Answer:
Surface Area = 84.8 cm²
Step-by-step explanation:
This wedge is simply a triangular prism.
We are given;
Height of door wedge; H = 5 cm
Height of triangular base;h = 3.7 cm
Congruent sides; S2 = S3 = 5cm
base of triangular side;b = S1 = 4 cm
Now, formula for surface area of triangular prism is;
SA = bh + (s1 + s2 + s3)H
Thus, plugging in the relevant values, we have;
SA = (4 x 3.7) + (4 + 5 + 5)5
SA = 14.8 + 70
SA = 84.8 cm²
What is the graph of 3x+5y=15
Answer: y= -15 - 3x/5 is the answer.
Step-by-step explanation:
Answer:
The second graph
Step-by-step explanation:
Cheeseburgers to go has advertised for counter help. If you take the job, you will be working 18 hours
a week for $69.20 per week. How much would you make an hour?
Answer:
about $3.84
Step-by-step explanation:
you do 69.20 divided by 18
what is the solution for this equation [3y+7]=13
Answer:2
Step-by-step explanation:
3y+ 7= 13
3y= 13 - 7
3y= 6
Y = 6/3
Y= 2
What’s the correct answer for this question?
Answer:
B:
Step-by-step explanation:
According to theorem, "the angle in a semi-circle is a right angle" So,
<O = 90°
<M = 54
<K = 180-90-54
<OKM = 36°
The function f(x)=2x2−x+4; f ( x ) = 2 x 2 − x + 4 is defined over the domain 0 ≤ x ≤ 3 Find the range of this function. A. 4 < f(x) < 7 B. 4 < f(x )< 19 C. 4 ≤ f(x) ≤ 19 D. 4 ≤ f(x) ≤ 25
Answer:
C. 4 ≤ f(x) ≤ 19 . . . . . . best of bad answer choices
Step-by-step explanation:
When looking for the range of a function on an interval, one must check the function values at the ends of the interval, along with any local maxima or minima.
Here, the function values at the interval ends are ...
f(0) = 4
f(3) = 2·3² -3 +4 = 19
The axis of symmetry is located at ...
x = -b/(2a) = -(-1)/(2(2)) = 1/4
This is a value in the interval, so will be the location of the minimum value of the function.
f(1/4) = 2(1/4)² -1/4 +4 = 3.875
The range of f(x) on the interval [0, 3] is [3.875, 19]:
3.875 ≤ f(x) ≤ 19
__
All of the answer choices are incorrect. Please discuss question this with your teacher.
List the four possible results of the combinations of decisions and true states of nature for a test of hypothesis. Which of the following lists the four possible results of the combinations of decisions and true states of nature for a test of hypothesis? A. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H 0H0 when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true B. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true; reject Upper H Subscript aHa when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true C. Reject Upper H 0H0 when Upper H Subscript aHa is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H Subscript aHa when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true D. Reject Upper H 0H0 when Upper H 0H0 is true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true; reject Upper H 0H0 when Upper H Subscript aHa is true; accept Upper H Subscript aHa when Upper H 0H0 is true
Answer:
A
Step-by-step explanation:
The combinations of decisions and true states of nature for a test of hypothesis is given below:
When [tex]H_o[/tex] is True, Accept [tex]H_o[/tex]When [tex]H_o[/tex] is True, Reject [tex]H_o[/tex] (Type I Error)When [tex]H_o[/tex] is False, Accept [tex]H_o[/tex] (Type II Error)When [tex]H_o[/tex] is False, Reject [tex]H_o[/tex]Note that when [tex]H_o[/tex] is False, then the Alternate Hypothesis, [tex]H_a[/tex] is True.
Therefore Option A gives the possible combinations.
The possible choices in Option A are ordered below to correspond to the results above.
Insufficient evidence to reject [tex]H_o[/tex] when [tex]H_o[/tex] is true; Reject [tex]H_o[/tex] when [tex]H_o[/tex] is true; Type 1 Error Insufficient evidence to reject [tex]H_o[/tex] when [tex]H_a[/tex] is true -Type II Error Reject [tex]H_o[/tex] when [tex]H_a[/tex] is true;Question 14
For the following system of equations, determine how many solutions there are.
6x + y = -1 and -6x - 4y = 4
Answer:
The system of equations has a one unique solution
Step-by-step explanation:
To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:
1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or
2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or
3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)
So we write them in slope -intercept form:
First equation:
[tex]6x+y=-1\\y=-6x-1[/tex]
second equation:
[tex]-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1[/tex]
So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.
Please answer this correctly
Answer:
540
Step-by-step explanation:
Since the surface area is 408, we can set up the equation
2*9*6 + 2*r*9 + 2*r*6 = 408
108 + 30r = 408
30r = 300
r = 10
The volume is length * width * height
9*6*10 = 540
13. Carla drew two acute non-overlapping
angles that share a ray and labeled them
ZJLK and Z KLM. The two angles have
different measures. Carla says
ZILM is
greater than a right angle.
An acute angle is open
less than a right angle.
Answer:
An acute angle is open
Step-by-step explanation:
An acute angle is an angle that is less than [tex]90^{0}[/tex]. Two or more acute angles are set to be complementary if their sum equals a right angle.
Clara's diagram involves two acute angles JLK and KLM with both sharing the side LK.
If the acute angles are complementary angles, then JLM would be a right angle.
If the acute angles are not complementary angles, then JLM would be less than a right angle.
So the appropriate choice to select is an acute angle is open. Which implies that JLM may be a right angle or not depending on the degrees of the acute angles involved.
When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation for each option. Graph each line and use the graph to answer the question. You will need to upload a picture or screenshot of your graphs.
Answer:
it´s b
Step-by-step explanation:
The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
Answer:
2.5
Step-by-step explanation:
[tex]9(u-2)+1.5u=8.25 \\\\9u-18+1.5u=8.25\\\\10.5u-18=8.25\\\\10.5u=26.25\\\\u=2.5[/tex]
Hope this helps!
When converting measurements in the metric system, you can move the decimal point to the left or to the right. Why? Select all that apply. A. When converting from smaller to larger units, you are dividing by a power of 10. B. Moving a decimal point is the same as adding or subtracting. C. The metric system is based on powers of 10. D. When converting from larger to smaller units, you are multiplying by a power of 10.
Answer:
This has multiple answers, A, C, And D
Step-by-step explanation:
Answer:
It is definitely A, C, and D.
Step-by-step explanation:
I just answered this question and got it right. I hope this helps and please mark brainliest!
A science club has 16 members. How many ways can a president, a Vice President, and a treasurer be selected from the members?
Answer:
3,360
Step-by-step explanation:
We calculate the number of permutations for this problem where the order in which we accommodate people matters to us as follows:
[tex]P=\frac{n!}{(n-r)!}[/tex]
where n is the total number of options we have; the total number of members: [tex]n=16[/tex]
and r is the number of places or positions we are considering which in this case are the President position, the Vice president position and the treasurer position ⇒ 3 positions in total ⇒ [tex]r=3[/tex]
substituting n and r in the formula:
[tex]P=\frac{16!}{(16-3)!} \\\\P=\frac{16!}{13!} \\\\P=3,360[/tex]
A president, a Vice President, and a treasurer can be selected from the members in 3,360 ways
A) Divide 160km in the ratio 10:9:13
B) divide 66 in the ratio 6:15:1
Answer:
A) 50 km : 45 km : 65 km
B) 18:45:3
Step-by-step explanation:
A) 160 km in the ratio 10:9:13
10x+9x+13x= 16032x= 160x= 510:9:3 ⇔ 50 km : 45 km : 65 km
B) 66 in the ratio 6:15:1
6x+15x+x= 6622x=66x=36:15:1 ⇔ 18:45:3
The probability that a freshman at a certain college takes an introductory statistics class is 0.21. What is the probability that a randomly selected freshman from this college does not take an introductory statistics class
Answer:
[tex] P(A) = 0.21[/tex]
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
[tex] P(A')=1-0.21= 0.79[/tex]
Step-by-step explanation:
For this problem we know that the probability that a freshman at a certain college takes an introductory statistics class is 0.21, let's define of interest as A and we can set the probability like this:
[tex] P(A) = 0.21[/tex]
We want to find the probability that a randomly selected freshman from this college does not take an introductory statistics class, so then we can use the complement rule given by:
[tex] P(A') = 1-P(A)[/tex]
Where A is the event of interest (a freshman at a certain college takes an introductory statistics class) and A' the complement (a freshman at a certain college NOT takes an introductory statistics class) and then replacing we got:
[tex] P(A')=1-0.21= 0.79[/tex]
