Answer:
w=6
l=14
Step-by-step explanation:
Area of rectangle = l*w
So:
[tex]w*(w+8)=84[/tex]
Then, just find w, and w+8.
[tex]w^2+8w=84\\w^2+8w-84=0\\(w-6)(w+14)=0\\w-6=0, w=6\\w+14=0, w=-14[/tex]
Length cannot be negative, so the width is 6.
Length = width + 8 = 6+8=14
Is the point (3, -2) a solution to the following system of equations? How do you know?
y=−3x+7
y=2x−8
Answer:
YES
Step-by-step explanation:
Any straight line can be represented by an equation of the form
Y = mX + b
where m is the slope and b is the Y intercept, so these two equations are lines. The only solution is where the two lines cross, so must satisfy both equations. Plugging in 3 for X and -2 for Y we get
Y = -3X + 7
-2 = -3(3) + 7
-2 = -9 + 7
-2 = -2 True
AND,
Y = 2X - 8
-2 = 2(3) - 8
-2 = 6 - 8
-2 = -2 True
So since both are true, yes (3, -2) is the solution.
When you roll two number cubes, what are the odds, in simplest form, in favor of getting two numbers less than 3?
Answer:
1/3
Step-by-step explanation:
there are 4 numbers total that are less than 3 and there are 12 sides total
so 4/12 would be the total and 1/3 would be simplified
(3)
8.
The normal price of a denim shirt at a shop is £9.60
On Special Offer Day, there is 1/3 off the normal price.
Billy has £13
Has he enough money to buy two denim shirts on
Special Offer Day? You must show all your working.
Special Offer Day
1
off normal prices
Answer:
Yes, Billy will have enough money to buy two denim shirts.
Step-by-step explanation:
£9.60 × (1/3)
= £3.20
On the special offer day, a denim shirt will cost £3.20.
£3.20×2 = £6.40
Two shirts will cost £6.40
Billy has £13, which will be enough for him to buy two shirts and will have a remaining balance of £6.60
ames has 268 cookies to put into bags. Each bag holds 8 cookies.
If James uses as many of the cookies as possible, how many bags can he make, and how many cookies are left over?
Enter your answers in the boxes.
Step-by-step explanation:
Total amount of cookies= 268
One bag can hold 8 cookies
268 / 8 = 33 (remainder 4)
He can make as many as 33 bags, and there are 4 cookies left over.
The City of Irvine upgraded a bicycle lane in a section of road to have a physical barrier between the cyclists as opposed to just a painted white line on the road. They now want to do a study to see if the bicycle lane upgrades have encouraged more people to utilize the bike lane. Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25. Test the hypothesis at the 0.05 significance level.
Answer:
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Step-by-step explanation:
Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.
At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So
[tex]H_0: \mu = 350[/tex]
At the alternate hypothesis, we test if this mean increased, that is:
[tex]H_1: \mu > 350[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
350 is tested at the null hypothesis:
This means that [tex]\mu = 350[/tex]
After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.
This means that [tex]n = 35, X = 405, s = 25[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]
[tex]t = 13.02[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.
Using a t-distribution calculator, this probability is of 0.
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Please help me with this
Answer:
–x² + 12x + 5
Step-by-step explanation:
x² + 3x
–2x² + 9x + 5
The sum of the above expression can be obtained as follow:
.... x² + 3x
+ –2x² + 9x + 5
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
–x² + 12x + 5
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Thus, the sum of x² + 3x and –2x² + 9x + 5 is –x² + 12x + 5
Find the surface area of the triangular prism.
Answer: 125.6
Step-by-step explanation:
Write an equation that represents a perpendicular line to y=-3x+5
Answer:
Example
Step-by-step explanation:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 3 3 . The equation of a perpendicular line to y=3x−5 y = 3 x - 5 must have a slope that is the negative reciprocal of the original slope.
Drag tiles to match each fraction, decimal, or percent to an equivalent fraction, decimal, or percent.
Answer:
...
Step-by-step explanation:
1. 0.002
2. 308%
3. 2 6/10
HELP ME ASAP
I NEED YOUR HELP PLS
I NEED AN ANSWER NOW
Answer:
N=21 Degrees M=122 Degrees L= 37 Degrees X=21 Degrees
Step-by-step explanation:
Add all them up then make them equal 180 degrees
9x-9 = 180
Solve
9x=180 +9
9x= 189
9x/9= 189/9
x=21
Then plug in x to find each Angle.
N (x) Degrees
N=21 Degrees
M = 6x - 4
M = 6(21) - 4
M = 126 - 4
M = 122 Degrees
L = 2x - 5
L = 2(21) -5
L = 42 - 5
L = 37 Degrees
Math number 8.
Find the value of x
Answer:
8
Step-by-step explanation:
By intersecting chords theorem:
[tex]14(2x + 2) = 12(2x + 5) \\ \\ 28x + 28 = 24x + 60 \\ \\ 28x - 24x = 60 - 28 \\ \\ 4x = 32 \\ \\ x = \frac{32}{4} \\ \\ x = 8[/tex]
Steven and his family ordered a meal the cost 136.50. Steven paid 14% sales tax and left a 20% tip on 136.50. What was the total cost
Answer:
The total cost was $182.91.
Step-by-step explanation:
Tax formula:
tax=tax percentage×amount
Tip formula:
tip=tip percentage×amount
solve
First find the tax. Write 14% as the decimal 0.14 before using it in the equation.
tax
= tax percentage×amount
= 0.14×136.50
= 19.11
The tax was $19.11.
Now find the tip. Write 20% as the decimal 0.20 before using it in the equation.
tip
= tip percentage×amount
= 0.20×136.50
= 27.3
The tip was $27.30.
Finally, find the total cost.
total cost
= cost + tax+tip
= 136.50+19.11+27.30
= 182.91
Answer:
182.91
Step-by-step explanation:
A:45
B:60
C:90
D:180
Answer:
90
Step-by-step explanation:
When you have Triangles, you have to divide your answer by two. So first, Multiply 3 x 5, which is 15. But you need to divide by two, so 15 ÷ 2 is 7.5. Then, Multiply 7.5 x 12, and now you have 90. Hope this helps!
What is the least common multiple of 3, 10, and 15?
Answer:
30
Step-by-step explanation:
30/3 = 10
30/10 = 3
30/15 = 2
Hope this helps!
Question
A bottle of medicine contained 300 mL. Convert this to liters.
Provide your answer below:
L
Answer:
0.3L
Step-by-step explanation:
1000mL = 1L
300mL = 0.3L
write down the coordinates of a point which lies in the second quadrant and 6 units far from both the axes
Answer:
(-6, 6)
Step-by-step explanation:
The product of two positive integer numbers is 40 and the sum of the same two numbers is 13.
9514 1404 393
Answer:
5 and 8
Step-by-step explanation:
Factor pairs that make 40 are ...
40 = 1×40 = 2×20 = 4×10 = 5×8
The pair that has a sum of 13 is 5 and 8.
Graph the ordered pair(4,6) and its reflection over the y-axis name the coordinates for the reflection
The new point after a reflection over the y-axis is (-4,6)
Help please i need this done i will mark brainlest and it will help me out a lot please
no links or images please just words!!!
Answer:
Perimeter is (width×height) but in this case it would be base×width & height...
First find the with of the triangle,by measureing the points with the base.
Second to find the base simply look equilateral and the half circle. and see how the lines in between it and the triangle collide. and count the spaces to find the base.
Third measure the height with the best estimate.
And finally, multiply by (h×w) and divide by the base.
After following these steps the answer I have come to is: 45
Step-by-step explanation:
I'm sorry if this is wrong I tried my best ❤️Good luck! and have a great day or night!
Answer:
42,84
Step-by-step explanation:
Remark
Two of the sides are 12 inches. The third side is also 12 but it serves as a diameter of the semicircle.
The circumference of the semi circle is 2*pi*r /2 = pi * r
The total perimeter is pi * r + 2*12
r = d/2
r = 12/2
r = 6
Perimeter = 6*pi + 24 might be you answer.
Perimeter = 42.84
I don't know which answer to use. It all depends how other questions have been answered. Sometimes you take the decimal answer and sometimes you take the answer in terms of pi. I think the latter is what I would try first.
Solve the inequality
J+7>3j-4
Answer:
E. j<5.5
Step-by-step explanation:
Step by step explanation
Find Sin S, sin R, cos S, and cos R
Answer:
18/26
16/26
16/26
18/26
Step-by-step explanation:
Assume that the probability of a defective computer component is 0.02. Components arerandomly selected. Find the probability that the first defect is caused by the seventh componenttested. Find the expected number and variance of the number of components tested before adefective component is found.
Answer:
0.0177 = 1.77% probability that the first defect is caused by the seventh component tested.
The expected number of components tested before a defective component is found is 50, with a variance of 0.0208.
Step-by-step explanation:
Assume that the probability of a defective computer component is 0.02. Components are randomly selected. Find the probability that the first defect is caused by the seventh component tested.
First six not defective, each with 0.98 probability.
7th defective, with 0.02 probability. So
[tex]p = (0.98)^6*0.02 = 0.0177[/tex]
0.0177 = 1.77% probability that the first defect is caused by the seventh component tested.
Find the expected number and variance of the number of components tested before a defective component is found.
Inverse binomial distribution, with [tex]p = 0.02[/tex]
Expected number before 1 defective(n = 1). So
[tex]E = \frac{n}{p} = \frac{1}{0.02} = 50[/tex]
Variance is:
[tex]V = \frac{np}{(1-p)^2} = \frac{0.02}{(1-0.02)^2} = 0.0208[/tex]
The expected number of components tested before a defective component is found is 50, with a variance of 0.0208.
what percentage of simple interest returest reture must a firm get on their deposit if it wants its birr 25000 to grow to birr 26500 in 6 months?
Answer:
0.9759%
Step-by-step explanation:
26500 = 25000x^6
solve for x
x = 1.009759
This means it increases by 0.009759 which is 0.9759%
On a piece of graph paper, graph the line that passes through point (-2,3) with a slope of 2/3. Give me the coordinates of a first quadrant point that lies on this line, and has integer coordinates.
Answer:
Pic po nasan???????Step-by-step explanation:
-_-A rectangular barn door needs to be painted. The door is 81 inches high and
50 inches wide. What is the area of the front of the door?
А
8,100 square inches
B
1,620 square inches
524 square inches
D 4,050 square inches
Unit 1: Geometry Basics Homework 3: Angle Relationships
Answer:
juicy no no square
Step-by-step explanation:
The value of x = z = 73 degrees and y = 107degrees
3) Geometry is a branch of mathematics that deals with the measurement of lines and angles.
From the diagram shown, we can see that the two lines intersect at a point. The following is therefore true:
y = 107° (vertically opposite angle)The sum of z and 107 is supplementary. Hence;
z + 107 = 180z = 180 - 107z = 73degreesAlso, the sum of x and y is also supplementary. This shows that:
x + y = 180x + 107 = 180x = 180 - 107x = 73dgreesFrom the calculations, hence x = z = 73 degrees and y = 107degrees
Learn more on lines and angles here: https://brainly.com/question/19023162
big help someone clutch up for me.TIMED!!
Answer:
B. 5
Step-by-step explanation:
Given expression;
n(n - x) = 25
From the given expression, x = 0
Substitute the value of x into the given equation and solve for n;
n(n - 0) = 25
this equation reduces to;
n(n) = 25
simplifying further to obtain the value of n;
n² = 25
n = √25
n = 5
Therefore, the correct option is B.
Which expression is equivalent to 4 (3n - 5)?
On - 20
7-9
12n - 5
12n - 20
Done -
The ratio of blue cars to red cars in a garage is 9:7. If there are 49 red cars in the garage then how many blue cars must be in the
garage?
Answer:
Blue cars, B = 63 cars
Step-by-step explanation:
Let the blue cars be B.
Let the red cars be R.
Given the following data;
Ratio of B:R = 9:7 = 9 + 7 = 16
Red cars, R = 49
To find the number of blue cars;
First of all, we would determine the total number of cars using the expression;
R = 7/16 * x = 49
7x = 49 * 16
7x = 784
x = 112 cars
Now, we can find the number of blue cars;
B = 9/16 * 112
B = 1008/16
Blue cars, B = 63 cars
PLS HWLP ME, I REALLY NEED IT
Answer:
E. 3×3×3×3
part b:
3×3×3×3
9×9
81