Answer:
4/5
Step-by-step explanation:
t + b = 2.50
t = b+1.50
Substitute
b+1.50+ b = 2.50
Combine like terms
2b + 1.50=2.50
2b =1
b = .5
t = b+ 1.5
t = .5+ 1.5
t = 2
The fraction of the total price
t/2.50
2/2.50
20/25
4/5
Answer:
80% of the total price is torch.
Step-by-step explanation:
Let
t=cost of torch
b=cost of battery
A torch and battery cost £2.50 altogether.
t+b=2.5
The torch costs £1.50 more than the battery.
t-b=1.5
Keep in mind:
When equations of the form
a+b = Sum
a-b = Diff
then the solution is immediately
a=(Sum+Difference)/2
b=(Sum-Difference)/2
and apply the rule,
t=(2.5+1.5)/2 = £2
b=(2.5-1.5)/2 = £1
Torch / total
= 2/2.5
= 80%
What is the sum of the measures, in degrees, of the interior angles of an 18-
sided polygon?
A. 2880
B. 3600
C. 3240
D. 3060
Answer:
Option (D)
Step-by-step explanation:
Sum of interior angles of a polygon is represented by the expression,
Sum of interior angles = n(n - 1)×180°
Here n is the number of sides of a polygon
If n = 18,
Sum of 18 sided polygon = (18 - 1) × 180°
= 7 × 180°
= 3060°
Therefore, sum of interior angles of a 18 sided polygon will be 3060°.
Option (D) will be the answer.
Answer:
2880
Step-by-step explanation:
SUM=_-2=
18-2=16
16*180 = 2880 OR
18*160 = 2880 degrees
1. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
2. Find the perimeter of a circle whose radius is 3.5cm. (Take pi = 22/7)
3. The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
4. What is the coefficient of b in the expression b² - 5b +18
5. Expand (x +2) (9 - x)
7. Find x and y in the simultaneous equations. x + y = 4 3x + y = 8
8. Factorize a² +3ab - 5ab - 15b²
9. The bearing of a staff room from the assembly ground is 195degrees, what is the bearing of the assembly ground from the staff room?
Step-by-step explanation:
68$53++83(-$(7(3($++$
Help ASAP please .
Which expression represents the volume of the sphere,
in cubic units?
3/4pi(6)^2
4/3pi(6)^3
3/4pi(12)^2
4/3pi(12)^3
Answer:
second option
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ( where r is the radius )
Here r = 6 , thus
V = [tex]\frac{4}{3}[/tex]π(6)³
Answer:
Second option
Step-by-step explanation:
Volume of a sphere = [tex]\frac{4}{3}*\pi *r^{3}[/tex]
→ Substitute in the value of radius
Volume of a sphere = [tex]\frac{4}{3}*\pi *6^{3}[/tex]
Find the values for a and b that would make the equality true.
-3(2x2 + ax + b) = –6x2 + 12x – 15
a =
b=
Answer:
a = - 4, b = 5
Step-by-step explanation:
Expand the left side and compare the coefficients of like terms on the right side.
- 3(2x² + ax + b)
= - 6x² - 3ax - 3b
Comparing like terms with - 6x² + 12x - 15
x - term → - 3a = 12 ( divide both sides by - 3 )
a = - 4
constant term → - 3b = - 15 ( divide both sides by - 3 )
b = 5
The sum of three numbers is 180. If the first number is (2 x minus 11), and the second is (x minus 4) which expression represents the third number? 165 minus 3 x 187 minus x 195 minus x 195 minus 3 x
Answer:
The third number is 195-3x
Step-by-step explanation:
Given:
sum of three numbers, a, b, c is 180.
a=2x-11
b=x-4
c= ?
Solution:
a+b+c = 180
2x-11 + x-4 + c = 180
c = 180 - (2x-11) - (x-4)
= 180 -2x+11 - x+4
= 180 + 11 + 4 -2x -x
= 195 -3x
Answer:
D
Step-by-step explanation:
pllllllease help me asap
Answer & Step-by-step explanation:
When we see the phrase "rate of change" then it means that we are looking for the slope. So, we will need to know the formula for finding slope or the rate of change.
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Now, let's use this equation to solve for the rate of change of each question.
Problem 1:
[tex]Slope=\frac{2-\frac{4}{3}}{0-(-1)}\\\\Slope=\frac{\frac{2}{3}}{1}\\\\Slope=\frac{2}{3}[/tex]
The rate of change of this equation is 2/3
Problem 2:
[tex]Slope=\frac{4-2}{1-0}\\\\Slope=\frac{2}{1}\\\\Slope=2[/tex]
The rate of change for this equation is 2
Problem 3:
[tex]Slope=\frac{10-4}{2-1}\\\\Slope=\frac{6}{1}\\\\Slope=6[/tex]
The rate of change for this equation is 6
Find the value of x in each case:
Answer:
45
Step-by-step explanation:
From the figure given, TV and RS are parallel.
Therefore, angle VTS and angle RST equal (Alternate angles)
Thus, angle VTS = angle RST = x
Angle T + angle S + angle R = 180° (sum of angles in a triangle)
2x + x + x = 180
4x = 180
Divide both sides by 4 to solve for x
x = 180/4
x = 45
The value of x in each case is 45
If we input 45 as a value of x in the angles in the triangle, the sum of what we have will give us 180°.
Answer:45
Step-by-step explanation:
Circle A has radius 5, and Circle B has radius 2. If CD = 12 and is a common
tangent, what is AB?
Answer:
[tex]3\sqrt{17}$ or \approx 12.37$ Units[/tex]
Step-by-step explanation:
In the attached diagram
CA=CO+OA
CO=DB
Therefore:
5=2+OA
OA=3 Units
The angle between a tangent line and a radius is 90 degrees. therefore triangle OAB is a right triangle with:
OB=12 units
OA=3 units
Using Pythagoras theorem
[tex]AB=\sqrt{3^2+12^2}\\ =\sqrt{153}\\=3\sqrt{17}$ or \approx 12.37$ Units[/tex]
El número de lados de un polígono de 4690,44 cm² de área, 38,7 cm de apotema y cuya longitud de su lado es 12,12 cm.
Answer:
su respuesta sería 21521.3
the base of a triangle is x cm and its height is (x-7) Write down the expression of the triangle
Step-by-step explanation:
if you mean the area of the triangle then it is S = 1/2*x(x-7)
Answer:
Step-by-step explanation:
b= x cm
h = (x - 7) cm
Area of triangle = [tex]\frac{1}{2}*x*(x-7)\\\\[/tex]
[tex]\frac{x*x-x*7}{2}\\\\=\frac{x^{2}-7x}{2}[/tex] square cm
Predict the number of pancakes that would have 48 chocolate chips
A prism has a volume of 405 cubic inches. A prism has a length of 15 inches, height of h, and width of 4.5 inches. Which is the correct substitution for finding the height of the prism? V = l w h. 405 = 15 + 4.5 + h. V = l w h = 15 times 4.5 times 405 V = l w h = 15 times 4.5 times 15 V = l w h. 405 = 15 times 4.5 times h
Answer:
d) 405 = 15 times 4.5 times h
The height of the prism 'h' = 6 inches
Step-by-step explanation:
Explanation:-
Given Volume of prism
V = 405 cubic inches
Given length of the prism
L = 15 inches
Given width of the prism
W = 4.5 inches
The volume of the prism
V = l w h
405 = 15 ×4.5× h
405 = 67.5 h
Dividing '67.5' on both sides , we get
h = 6 inches
Final answer:-
The height of the prism 'h' = 6 inches
Answer: V = l w h. 405 = 15 times 4.5 times h
Step-by-step explanation:
Given the following :
Volume of prism = 405 in^3
Length = 15 inches
Height = h
Width = 4.5 inches
Recall :
The volume of a prism is the product of the Base and the height.
That is;
Volume = Base × height
However, Base of prism is given by the area of the base shape of the prism.
From our parameters Base shape of the prism is a rectangle.
Therefore, Area of rectangle = Length × width
= 15 inches × 4.5 inches = 67.5 inch^2 = Base of prism
Therefore, Volume of prism equals ;
Volume = 15 × 4.5 × h
Volume = 405in^3
Volume = Base × height
405 = 15 × 4.5 × h
A line goes through points (0, 3) and (6, 12). What would be the slope of this line's perpendicular bisector?
Answer:
the slope of the perpendicular bisector is -2/3
Step-by-step explanation:
The slope of the line joining the two points P1(0,3), P2(6,12) is given by
m1 = (y2-y1) / (x2-x1) = (12-3) / (6-0) = 9/6 = 1.5
The slope m2 of a line perpendicular to the previous line is given by
m1*m2 = -1
solving
m2 = -1/m1 = -1/ (3/2) = -2/3
THerefore the slope of the perpendicular bisector is -2/3
A marble is randomly selected from a bag. The probability of selecting a marble with dots on it is 0.2. The probability of selecting a marble that is both purple and has dots on it is 0.1. What is the probability of selecting a purple marble given that the marble has dots on it? Enter your answer as a decimal in the box.
Answer:
0.5
Step-by-step explanation:
Let D be the event of selecting a marble with dots.
Let P be the event of selecting a purple marble.
The probability of selecting a marble with dots, P(D)=0.2
The probability of selecting a marble that is both purple and has dots, [tex]P(D \cap P)=0.1[/tex]
We want to determine the probability of selecting a purple marble given that the marble has dots on it, P(P|D)
By the definition of conditional probability:
[tex]P(P|D)= \dfrac{P(P \cap D)}{P(D)} \\= \dfrac{0.1}{0.2}\\ =0.5[/tex]
The probability of selecting a purple marble given that the marble has dots on it is 0.5.
Pls answer this question....
Answer:
2310cm³
Step-by-step explanation:
volume= πr²h
22/7× radius of circle × height
circumference= πd
44cm=22/7×d, diameter= 7 cm, radius= 3.5cm
v= 22/7× 3.5× 21 = 2310cm³
The windows of a downtown office building are arranged so that each floor has 6 fewer windows than the floor below. If the ground floor has 52 windows, how many windows are on the 8th floor?
Answer:
10
Step-by-step explanation:
This is an arithmetic sequence. The common difference is -6, and the first term is 52.
a = 52 − 6(n − 1)
When n = 8:
a = 52 − 6(8 − 1)
a = 52 − 42
a = 10
(04.03 MC)
Choose a system of equations with the same solution as the following system:
6x + 2y = -6
3x – 4y = -18
Answer:
x = -2 and y = 3
{y = -3 x - 3, y = (3 x)/4 + 9/2} = x = -2 and y = 3
Step-by-step explanation:
Solve the following system:
{6 x + 2 y = -6
3 x - 4 y = -18
Express the system in matrix form:
(6 | 2
3 | -4)(x
y) = (-6
-18)
Solve the system with Cramer's rule:
x = -6 | 2
-18 | -4/6 | 2
3 | -4 and y = 6 | -6
3 | -18/6 | 2
3 | -4
Evaluate the determinant 6 | 2
3 | -4 = -30:
x = -6 | 2
-18 | -4/(-30) and y = 6 | -6
3 | -18/(-30)
Simplify -6 | 2
-18 | -4/(-30):
x = -1/30 -6 | 2
-18 | -4 and y = 6 | -6
3 | -18/(-30)
Simplify 6 | -6
3 | -18/(-30):
x = -(-6 | 2
-18 | -4)/30 and y = -1/30 6 | -6
3 | -18
Evaluate the determinant -6 | 2
-18 | -4 = 60:
x = (-1)/30×60 and y = -(6 | -6
3 | -18)/30
(-1)/30×60 = -2:
x = -2 and y = -(6 | -6
3 | -18)/30
Evaluate the determinant 6 | -6
3 | -18 = -90:
x = -2 and y = (-1)/30×-90
(-1)/30 (-90) = 3:
Answer: x = -2 and y = 3
___________________________________________
Solve the following system:
{y = -3 x - 3
y = (3 x)/4 + 9/2
Express the system in standard form:
{3 x + y = -3
-(3 x)/4 + y = 9/2
Express the system in matrix form:
(3 | 1
-3/4 | 1)(x
y) = (-3
9/2)
Write the system in augmented matrix form and use Gaussian elimination:
(3 | 1 | -3
-3/4 | 1 | 9/2)
Add 1/4 × (row 1) to row 2:
(3 | 1 | -3
0 | 5/4 | 15/4)
Multiply row 2 by 4/5:
(3 | 1 | -3
0 | 1 | 3)
Subtract row 2 from row 1:
(3 | 0 | -6
0 | 1 | 3)
Divide row 1 by 3:
(1 | 0 | -2
0 | 1 | 3)
Collect results:
Answer: {x = -2 , y = 3
Fernando is playing hide-and-seek with Darnel and Joy. Darnel is hiding 5 meters south of Fernando, and Joy is hiding due east of Darnel. If Fernando is 8 meters from Joy, how far apart are Darnel and Joy? If necessary, round to the nearest tenth.
Answer:
6.2 metres apartStep-by-step explanation:
Find attached a diagram for proper elucidation of the question. The resulting shape is a right angled triangle with hypotenuse FJ, and the other two sides DF and DJ respectively.
Using Pythagoras theorem to get the side DJ which is the distance between Daniel and Joy. According to the theorem, the square of the hypotenuse of a right angled triangle is equal to the sum of the other two sides.
FJ² = DF² + DJ²
From the diagram, FJ = 8 and DF = 5. Substituting this values into the theorem above to get DJ;
8² = 5²+DJ²
DJ² = 8²-5²
DJ² = 64 -25
DJ² = 39
DJ = √39
DJ = 6.2 (to the nearest tenth)
This shows that Darnel is 6.2 metres away from Joy
Create a list of steps, in order, that will solve the following equation.
3(x + 1)2 = 108
Solution steps:
- Add 1 to both sides
- Divide both sides by 3
- Multiply both sides by 3
- Subtract 1 from both sides
- Square both sides
- Take the square root of both sides
PLSS HELP!!
you roll a 6-sided die with faces numbered 1 through 6, and toss a coin what is the probability of rolling a 2 or getting heads
Answer:
2/3
Step-by-step explanation:
You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.
Add 1/2 and 1/6 to get 2/3
Plz help urgently ❤️Plz
Answer:
1st fig ans=12x ^2-7x-21.
2nd fig ans
i) ( x-15)(x+2)
ii) 2(x+7)(x-9)
iii) -3x(2x+1)(5x-3)
Hope it will help uh....
Answer:
1C 2 D 3 c
Step-by-step explanation:
1, X^2-13x-30
X^2-15x+2x-30
X(x-15)+2(x-15)
(X+2)(x-15)
2, 2x^+4x-126..... Simplified As
(2x-14)(x+9)
3, -30x^3+3x^2+9x ..... Simplified as
-3x(2x+1)(5x-3)
an elastic band. which is 72cm
Initial length = 72 cm
Stretched length = 90 cm
Find the increased in length:
increase = 90 - 72 = 18
Find the percentage increase:
Percentage increase = change/original x 100
Percentage increase = 18/72 x 100 = 25%
Answer: The elastic band's length is increased by 25%
A study of an association between which ear is used for cell phone calls and whether the subject is left-handed or right-handed began with a survey e-mailed to 5000 people belonging to an otology online group, and 717 surveys were returned. (Otology relates to the ear and hearing.) What percentage of the 5000 surveys were returned? Does that response rate appear to be low? In general, what is a problem with a very low response rate? Of the 5000 surveys, nothing% were returned. This response rate ▼ appears does not appear to be low.
Answer:
Of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
Step-by-step explanation:
Given:
Total sample collected = 5000
Survey returned = 700
i) What percentage of the 5000 surveys were returned?
To find percentage returned, we have:
[tex] = \frac{700}{5000} * 100 = 14 percent [/tex]
Percentage returned = 14%
ii) Does that response rate appear to be low?
Yes, the response is significantly low as only 14% is returned out of expected 100%
iii) In general, what is a problem with a very low response rate?
The problem with in low response rate in general is that it causes the result to be biased as biased samples of those interested in a particular aspect may have been gotten.
Therefore, of the 5000 surveys, 14% were returned. This response rate APPEARS to be low.
The graph of f(x) =7x is reflected across the x-axis. write a function g(x) to describe the new graph. G(x)=___
To reflect a function across the x axis, we just stick a negative in front. This will make all point's y coordinates to go from positive to negative or vice versa. If the original function already has a negative out front, then remove it.
1. Who conducted the study described in the article?
A. a
group of
parents
B. Yale University
C. the U.S. government
McDonald's
- 2 = 2+v/4 solve for the variable
Hey there! :)
Answer:
v = -16.
Step-by-step explanation:
Given:
-2 = 2 + v/4
Subtract 2 from both sides:
-2 -2 = 2 - 2 + v/4
-4 = v/4
Multiply both sides by 4:
-4 · 4 = v/4 · 4
-16 = v
There are 100 sophomores at a school. 85% of them are good students. What would the percent of good students be at school if (round the answer up to the nearest ones) ten “F” students would come to this school?
Answer: subtract 85 with a hundred because you are trying to see how many students out of 100% are good students after that you should get your answer
Step-by-step explanation:
Answer:
77% (rounded)
Step-by-step explanation:
1. Find 85% of 100
100 x 0.85 = 85
SO 85 students out of 100 students are good students.
2. Add the 10 more students to the total number.
100 + 10 = 110 total students
3. Find the percent of good students in the total number of current students.
85/110 = 0.77 * 100 (to convert to percent) = 77%
A study is performed involving two remedies for midwest farm crops who experienced the worst drought in years. In the midwest, 450 crop fields were given randomly one of two remedies. Specifically, 220 were given Remedy A and 230 were given Remedy B. A total of 74 of the 450 crop fields were salvageable, 35 from Remedy A group and 39 from Remedy B group. A significance test was performed for the following hypotheses and resulted in a p-value of 0.3822: H0: Salvage rates are the same for Remedy A and B Ha: Remedy B has a greater salvage rate Part A: Interpret the p-value in terms of the context. (3 points) Part B: Using a significance level of α = 0.05, what can you conclude from the context of this study? (4 points) Part C: Based on your conclusion in part B, which type of error—Type I or Type II—could have been made? What is one potential consequence of this error? (3 points)
Answer:
Explained below.
Step-by-step explanation:
(A)
The p-value is well defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
The p-value of the test was, p = 0.3822.
That is the probability that Remedy B has a greater salvage rate than A is 0.3822, given that rates are the same for Remedy A and B.
(B)
The significance level of the test is: α = 0.05.
A small p-value (typically ≤ 0.05) specifies strong evidence against the null hypothesis (H₀), so you discard H₀. A large p-value (> 0.05) specifies fragile proof against the H₀, so you fail to discard H₀.
The p-value of the test is very large. The null hypothesis will not be rejected.
Concluding that salvage rates are the same for Remedy A and B.
(C)
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false.
In this case a type II error could have been made as the null hypothesis was not rejected.
The type II error could have been made because of the following reasons:
The sample size selected is too small. Significance level of the test must be small.As the sample selected is quite large, the only potential consequence of this error is that the significance level of the test must be small.
Which of the following expressions are equivalent to -9/6?
the correct answer is:
A. 9/-6
Which expression is equivalent to 2 (a + 2 b) minus a minus 2 b?
Answer:
a -2b
Step-by-step explanation:
2 (a + 2 b) - a - 2 b
Distribute
2a +4b -a-2b
Combine like terms
2a-a +4b-2b
a -2b
Answer:
a
Step-by-step explanation: