Answer:
.
Step-by-step explanation:
1. Lilly has two cousins. One of the cousins is 7 years older than Lilly. The other cousin is 3 years younger than Lilly. The product of Lilly’s cousins' ages is 24. How old is Lilly?
2. Jackie is building a rectangular football field that has an area of 6000 square yards. The football field must be 40 yards longer than its width. Determine the width of the football field, in yards.
3. James is reading a book and noticed the page numbers are consecutive integers whose product is 1640. What is the value of the larger page number?
Answer: a. 5 years
b. 60 yards
c. 41
Step-by-step explanation:
1. Let Lily's age be x.
One of the cousins is 7 years older than Lilly. The age will be = x + 7
The other cousin is 3 years younger than Lilly. The age will be = x - 3
Therefore, (x + 7)(x - 3) = 24
x² - 3x + 7x - 21 = 24
x² + 4x - 21 - 24 = 0
x² + 4x - 45 = 0
x² + 9x - 5x - 45 = 0
(x² + 9x) - (5x - 45) = 0
x(x + 9) - 5(x + 9) = 0
(x - 5)(x + 9) = 0
(x - 5) = 0
x = 0 + 5
x = 5
Therefore, Lily is 5 years
2. Let the width be represented by x
Therefore, length will be x + 40.
Area = length × width
6000 = x(x + 40)
x² + 40x = 6000
x² + 40x - 6000 = 0
x² + 100x - 60x - 6000 = 0
x(x + 100) - 60(x + 100) = 0
(x - 60)(x + 100) = 0
x - 60 = 0
x = 0 + 60 = 60
Therefore, the width is 60 yards
3. Let the consecutive numbers be x and x+1.
Therefore, x(x + 1) = 1640
x² + x = 1640
x² + x - 1640 = 0
x² + 41x - 40x - 1640 = 0
x(x + 41) - 40(x + 41) = 0
(x - 40) = 0
x = 0 + 40
x = 40
Larger number = x + 1 = 40 + 1 = 41
Without properly working spark plugs, a vehicle will not run. For a specific vehicle, the spark plugs are supposed to have a gap between 3.9mm and 4.3mm. Any spark plugs with gaps larger or smaller than this will fail inspection and be discarded. At the factory, the machine that sets the gap follows a normal distribution with a mean of 4.1mm and standard deviation of 0.075mm. What is the probability that a randomly selected spark plug passes inspection
Answer:
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = 0.9922
Step-by-step explanation:
Step(i):-
Given that the mean of the Normal distribution = 4.1mm
Given that the standard deviation of the Normal distribution = 0.0075mm
Let 'X' be the random variable in a normal distribution
Given that X₁ = 3.9mm
[tex]Z_{1} = \frac{X_{1} -mean}{S.D}[/tex]
[tex]Z_{1} = \frac{3.9 -4.1}{0.075} = -2.666[/tex]
Given that X₂ = 4.3mm
[tex]Z_{2} = \frac{X_{2} -mean}{S.D}[/tex]
[tex]Z_{1} = \frac{4.3 -4.1}{0.075} = 2.666[/tex]
Step(ii):-
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = P(-2.666≤Z≤2.666)
= P(Z≤2.666)-P(Z≤-2.666)
= 0.5 +A(2.666) - (0.5-A(2.666)
= 2 × A(2.666)
= 2×0.4961
= 0.9922
Final answer:-
The probability that the spark plugs are supposed to have a gap between 3.9mm and 4.3mm.
P(3.9≤X≤4.3) = 0.9922
2(1/5m-2/5)+3/5 Combine like terms to create and equivalent expression, please help :).
Answer:
Step-by-step explanation:
First, carry out the indicated multiplication. We get:
2m/5 - 4/5 + 3/5, which condenses to
2m - 1
2m/5- 1/5 or ---------------
5
I need this please.Give the right answer.It’s a huge grade that I NEED!
Answer:
Line 2 will be the best fit for the data
Step-by-step explanation:
hope it helps...
have a great day!!
What fraction of the students are wearing either a white or blue shirt?
PLX HELP THIS TEST IS 20 PERCENT OF MY FINALE GRADEEEEE
On Friday,
3/10
of the students at school were wearing white shirts and
5/12
of the students were wearing blue shirts.
select the fraction of students wearing either a white shirt or a blue shirt.
Answer:
43/60
3/10 x 12 = 36/120
5/12 x 10 = 50/120
50/120 + 36/120 = 86/120
Simplified we get 43/60
** 20 points ! find the surface area, in square inches :)
Answer:
Surface area
103.109in²
Step-by-step explanation:
Hope this helps! I would appreciate if you make me brainliest!
please HELPL I WILL MARK BRAINLIST FOR FIRST AND CORRECT ANSWER
Help me plz ………………?…;
Answer:
9.04ft
Step-by-step explanation:
This will help you
Solve: Four more than a number is more than 13
Inequality :
Solution :
Answer:
x + 4 > 13
x > 9
Step-by-step explanation:
In this equation, the value of the "number" is unknown, so I used a variable (x) to represent the unknown value.
FOUR more than x would mean addition.
x + 4.
According to this word problem, four more than x is larger than thirteen, so a greater than symbol was used.
Like this,
x + 4 > 13.
We can find the solution to 'x' by subtracting 4 from 13.
Like this,
13 - 4 = 9
Therefore, the solution is x > 9
And, the inequality is x + 4 > 13.
15. What is the volume of a rectangular prism with a length 8 cm, width 5 cm and height 3 cm?
Answer:
120cm³
Step-by-step explanation:
V=w·h·l=5·3·8=120cm³
Answer: i hope it help u
Step-by-step explanation:
Expand -2/10(1-2x + 2
Answer:
[tex]\frac{2x}{5} - \frac{3}{5}[/tex]
Help please! I'll mark you as Brainliest!
Answer:
c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Since we are working with tenths all we have to do is add the numerators of each fraction.
4 + 3 + 1 + 1 = 9
9/10
A pet store advertises
a 30% off sale or dog crates.
What is the regular price of a
large crate that costs $85.50
on sale?
Answer:
the answer is 1.99 I think im not sure I guessed
Step-by-step explanation:
Which graph represents a quadratic function with a negative discriminant?
Choice 1
Choice 2
Choice 3
Choice 4
Answer:
Choice 4
Step-by-step explanation:
#4 because the graph does not intersect the x-axis
The graph that represents a quadratic function with a negative discriminant is graph 4.
What is a Discriminant?The part in the formula of a quadratic equation that helps us to know the nature of the roots of a quadratic equation is known as a discriminant.
D = b2 - 4ac,
If the value of the discriminant is greater than zero then the roots of the equation are real and distinct,If the value of the discriminant is equal to zero then the roots of the equation are real and same, andIf the value of the discriminant is less than zero then the roots of the equation are imaginary.Since for the value of the discriminant to be negative, the roots of the quadratic equation should be imaginary. Also, imaginary never intersects the x-axis of the graph.
Now, in the group of the graphs the only graph that does not intersect the x-axis of the graph or have imaginary roots is graph 4.
Hence, the correct option is graph4 (Bottom Right).
Learn more about the Discriminant here:
https://brainly.com/question/15884086
#SPJ2
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Olivia sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 144 visitors purchased no costume. 182 visitors purchased exactly one costume. 9 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase no more than one costume as a decimal to the nearest hundredth.
Answer:
There is a 54.328% probability that the next person will purchase no more than one costume.
Step-by-step explanation:
Since in a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance, and Olivia sets up a website where players can buy and sell these costumes online, and information about the number of people who visited. the website and the number of costumes purchased in a single day states that 144 visitors purchased no costume, 182 visitors purchased exactly one costume, and 9 visitors purchased more than one costume, to determine, based on these results, the probability that the next person will purchase no more than one costume as a decimal to the nearest hundredth, the following calculation must be performed:
144 + 182 + 9 = 335
335 = 100
182 = X
182 x 100/335 = X
18,200 / 335 = X
54,328 = X
Therefore, there is a 54.328% probability that the next person will purchase no more than one costume.
what is 5 2/3 divided by 3/2
Answer:
≈3.8
Your Welcome!
Joan is planning a party. She wanted to serve nachos as an appetizer dish for her guests. Joan went to Costco and found a huge can of pre-made nacho cheese. When she got home, she wondered, "how much cheese is in this giant can?" So, she grabbed a ruler, measured the can, and concluded that it is 12-inches tall with a diameter of 6-inches. Continue Joan's calculation and find the amount of space inside that nacho cheese can.
Answer:
339.29
Step-by-step explanation:
V=πr²h
Solve using suitable property
-2/3 x 5/7 x -9/16 x 14/25
Given:
The given expression is:
[tex]\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-9}{16}\times \dfrac{14}{25}[/tex]
To find:
The value of the given expression.
Solution:
We have,
[tex]\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-9}{16}\times \dfrac{14}{25}[/tex]
It can be written as:
[tex]=\dfrac{-2}{3}\times \dfrac{5}{7}\times \dfrac{-3\times 3}{2\times 2\times 2\times 2}\times \dfrac{2\times 7}{5\times 5}[/tex]
[tex]=\dfrac{-2\times 5\times (-3)\times 3\times 2\times 7}{3\times 7\times 2\times 2\times 2\times 2\times 5\times 5}[/tex]
Cancel out the common factors.
[tex]=\dfrac{-(-3)}{2\times 2\times 5}[/tex]
[tex]=\dfrac{3}{20}[/tex]
Therefore, the value of given expression is [tex]\dfrac{3}{20}[/tex].
if x=9.6 , y=3.60 and z=5 , find the percentage error in the calculation of
x+y/2 giving your answer to three significant figures.
formula for percentage error is (actual value /absolute error)
X+y/2
9.6+3.60/2 = 11.4,,
The length of a living room is 12ft and it's width is 10 1/2 ft. The length of the living room is being expanded by X feet? Choose an expression to represent the new area of the living room in square feet and the expanded fotm of the expression? Select all that apply
Answer:
C. 10.5(12 + x) square feet
E. (126 + 10.5x) square feet
Step-by-step explanation:
A. 10.5(12x) square feet
B. (10.5 + 12 + x) square feet
C. 10.5(12 + x) square feet
D. 126x square feet
E. (126 + 10.5x) square feet
F. (22.5 + x) square feet
length of a living room = 12ft
width = 10 1/2 ft
The length of the living room is being expanded by X feet
New length of a living room = 12ft + x feet
new area of the living room = length × width
= 12ft + x feet × 10 1/2 ft
= (12 + x) 10 1/2
Note: 10 1/2 is equivalent to 10.5
= (12 + x) 10.5
= (126 + 10.5x) square feet
Options that applies
C. 10.5(12 + x) square feet
E. (126 + 10.5x) square feet
Help me please I am struggling with this question
Answer:
a: 153
Step-by-step explanation:
Do cross multiplication.
Which histogram represents the times from team are on the obstacle course
Answer:
Image attached
Step-by-step explanation:
If y=−3, then
4y
4+y
=
Answer:
4y4+y is 4x-3x4+-3 so the answer is -51
Step-by-step explanation:
4 times -3 is -12
-12 times 4 is -48
-48 plus -3 is -51
hope this is right lm.ao
Answer:
4 x -3 + 4 = 5
4 x -3= 1
4 + -3 =1
Step-by-step explanation:
I checked the calculator (Sorry if I’m wrong)
An angle measures 162º more than the measure of its supplementary angle. What is the
measure of each angle?
Answer:
there is only one straight angle which measures 180°
Step-by-step explanation:
if an angle is 162° then its supplementary angle is 18°
Find the value of x.
Please help me
To wash a window that is 12 feet off the ground, Mason leans a 20-foot ladder against the side of the building. To reach the window, how far away from the building should Mason place the base of the ladder?
Answer:
by clumbing the ladder
Step-by-step explanation:
The base of the ladder should be placed so that it is one foot away from the building for every four feet of hight to where the ladder rests against the building. This is known as the 4 to 1 rule.
0
1
N
3 4 5 6 7
8 9 10
Number of Snacks
What is the median of the data values?
Answer: it would be 5
Step-by-step explanation:
0,1,2,3,4,5,6,7,8,9,10 the middle #is 5
find the missing measurement
9514 1404 393
Answer:
4.2 km
Step-by-step explanation:
The altitude of the triangle can be found using the triangle area formula:
A = 1/2bh
22.7 km² = 1/2(10.8 km)h
h = (22.7 km²)/(5.4 km) ≈ 4.2037... km
The missing measurement is about 4.2 km.
Mrs. Williamson had 18 students in her homeroom at the beginning of the school year and 24 students at the end of the year. What was the approximate percent increase in the number of students in Mrs. Williamson’s homeroom?
25%
33%
57%
75%
Answer:
25%
Step-by-step explanation:
An easy way to figure this out is just by dividing the initial amount of students (18) by the current amount of students (24), and then subtracting 1.
So, 18/24 = 0.75 (aka 75%), and 1 - 0.75 = 0.25 (aka 25%)
A person is standing 215 feet above the ocean
watching a ship come in. Initially the angle of elevation
from the boat to the person is 31 degrees. After
traveling towards the person for a few minutes, then
angle is 48 degrees. How far did the boat travel
between the two points? Round to the nearest foot.
Answer:
Step-by-step explanation: I don’t know I just want my extra points
Answer: 164 ft
Step-by-step explanation:
tan 48=215/x
-> x.tan48=215
->x =215/tan 48
->x = 193.6
tan 31=215/y
-> y.tan31 = 215
-> y= 215/ tan 31
-> y= 357.82
BC= y-x
= 357.82-193.6
= 164.22 = 164 ft