Answer:
5 hr.
Step-by-step explanation:
this is because one car is moving at 30 miles an hour and the other at 30+20 miles an hour = 50mph. so after 1 hour one car would have gone 30 miles and the other 50 = 80 altogether not 400 yet. After 2 hours one car would have gone 60 miles and the other 100 = 160 not 400 yet. ECT... After five hours one car has gone 150 mile (30mph*5hr = 150miles) and the other 250miles (59mph*50hr = 250miles) = 400, since 150+250=400. Therefore it would take 5hr for the cars to meet. and crash ._.
Final answer:
The two cars traveling towards each other, one at 30 mph and the other at 50 mph, will meet after 5 hours, since their combined speed is 80 mph and they are 400 miles apart.
Explanation:
To solve the problem of when two cars moving towards each other will meet, we can use the concept of relative speed. The first car travels at 30 mph, and the second car travels at the faster speed of 50 mph (since it is 20 mph faster than the first car). The combined speed at which the two cars are moving towards each other is the sum of their individual speeds.
The formula for time is:
Time = Distance / Speed
Given that the two cars are 400 miles apart, and the combined speed is 30 mph + 50 mph = 80 mph, the time it takes for the two cars to meet is:
Time = 400 miles / 80 mph = 5 hours
Therefore, the cars will meet after 5 hours of travel.
select the equation of the line that passes through the point (3,-1) and is parallel to the line on the graph
ANSWER
y=-1
EXPLANATION
The given line in the graph has equation
[tex]y = 2.5[/tex]
This line is a horizontal line.
All horizontal line has a slope of 0.
Let the equation of the line that is parallel to this line be
[tex]y = mx + b[/tex]
The slope of this line must also be zero.
We substitute the slope, m=0 and the point (3,-1) into this equation to get:
[tex] - 1 = 0(3) + b[/tex]
[tex] \therefore \: b = 0[/tex]
Hence the required equation is
[tex]y = - 1[/tex]
ANSWER
y= -1
Step-by-step explanation:
The given line in the graph has equation
This line is a horizontal line.
All horizontal line has a slope of 0.
Let the equation of the line that is parallel to this line be
The slope of this line must also be zero.
We substitute the slope, m=0 and the point (3,-1) into this equation to get:
Hence the required equation is
How do you simplify the expression “3x (2/x + 5) +4”?
Answer:
15x + 10
Step-by-step explanation:
distribute the 3x to the 2/x and 5 inside the parentheses:
3x(2/x) + 3x(5) + 4
multiply:
6x/x + 15x +4
There is x in the numerator and the denominator of 6x/x, so the xs cancel:
6 + 15x + 4
15x + 10
Answer:
15x+10
Step-by-step explanation:
3x (2/x + 5) +4
Distribute the 3x
3x*2/x + 3x*5 +4
6x/x + 15x +4
6+15x+4
Combine like terms
15x+10
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A. 120 metres
B. 180 metres
C. 324 metres
D. 150 metres
Answer:
D. 150 metres
Step-by-step explanation:
speed = (60) times 5/18 = 50/3
lenght of the train = (speed x time)
lenght = 50/3 times (9)
= 150 m.
The mean of a data is 52.4 and the standard deviation is 11.8.What percent of the data is between 40.6 and 64.2?
A.50%
B.68%
C.95%
D.99.7%
Answer:
B. 68%
Step-by-step explanation:
Any number within 1 positive or negative deviation of the mean represents 68% of normally distributed data.
Math explanation:
52.4+11.8=64.2
52.4-11.8=40.6
Your answer is b, 68%
Trig: Which complex number's graph is shown?
ANSWER
[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]
EXPLANATION
The complex number shown has coordinates (2,-2)
or
[tex]z = 2 - 2i[/tex]
The modulus is
[tex] |z| = \sqrt{ {2}^{2} + {( - 2)}^{2} } [/tex]
[tex]|z| = \sqrt{ 8} = 2 \sqrt{2} [/tex]
The argument is
[tex] \theta= \tan^{ - 1} ( \frac{ - 2}{2} )[/tex]
[tex] \theta= \tan^{ - 1} ( -1) = \frac{7\pi}{4} [/tex]
The polar form is
[tex]2 \sqrt{2} ( \cos( \frac{7\pi}{4} + i \sin( \frac{7\pi}{4} ) ) [/tex]
The first option is correct.
Answer:
The first option (the one all the way at the top)
Step-by-step explanation:
a.pex
Sandy mixed together 9 gallons of one brand of juice and 8 gallons of a second brand of juice which contains 48% real fruit juice. Find the percent of real fruit juice in the first brand if the mixture contained 30% real fruit juice.
A) 18%
B) 140%
C) 180%
D) 14%
Answer:
D) 14%
Step-by-step explanation:
Let the percent of the real fruit in the first brand = x
Given that number of gallons of real fruit in the first brand = 9 gallons
Given that percent of the real fruit in the second brand = 48%
Given that number of gallons of real fruit in the second brand = 8 gallons
Given that percent of the real fruit in the mixture = 30%
then number of gallons of real fruit in the mixture = (9+8) = 17 gallons
Then we get equation:
[x% of 9 gallons] + [48% of 8 gallons] = [30% of 17 gallons]
9x+48(8)=30(17)
9x+384=510
9x=510-384
9x=126
x=126/9
x=14
Hence final answer is D) 14%
Answer:D
Step-by-step explanation:jus took test
The odometer of a new automobile functions improperly and registers only 2 miles for every 3 miles driven. If the odometer indicates 48 miles, how many miles has the automobile actually been driven?
Final answer:
The odometer reads 2 miles for every 3 actual miles driven. To find the actual distance when the odometer shows 48 miles, a proportion is used, leading to the calculation that the automobile has driven 72 actual miles.
Explanation:
The student is dealing with a proportion problem in mathematics where the automobile's odometer is inaccurate. Given that the odometer registers 2 miles for every 3 miles driven, we can set up a proportion to find the actual distance driven. If the odometer indicates 48 miles, we can write the proportion as follows:
2 miles (odometer) / 3 miles (actual) = 48 miles (odometer) / x miles (actual)
Cross-multiply to solve for x: 2x = 48 × 3
Calculate x: 2x = 144
Divide both sides by 2 to isolate x: x = 144 / 2
Find the value of x: x = 72 miles
Therefore, the automobile has actually been driven 72 miles.
4. Samantha went out to eat with her
friends on Monday, Tuesday, Wednesday,
and Friday. She spent $5.65 on Monday,
$7.50 on Tuesday, $9.75 on Wednesday,
and $5.95 on Friday. How much
more money did Samantha spend on
Wednesday and Friday than on Monday
and Tuesday?
$28.85 (just add it if u dont get it)
On Wednesday and Friday she spent, $9.75+$5.95=$15.70
On Monday and Tuesday she spent, $5.65+$7.50= $13.15
Its a subtraction problem so $15.70-$13.15=$2.55
The answer is $2.55
I apologize if this is not what you meant.
Andrew is paid $4 per hour for the first 30 hours he works each week. He makes $5 per hour for each hour he works over 30 hours per week. In other words, total wages = fixed wages for 30 hours + additional wages at $5 per hour. Apply function notation to answer the following questions about Andrew’s wages. Part A Write a function that gives Andrew’s total wages when he works more than 30 hours. Use the variables w for wages and h for hours.
Answer:
w = 120 + 5*(h-30)
Step-by-step explanation:
Part A;
We are informed that Andrew is paid $4 per hour for the first 30 hours he works each week and makes $5 per hour for each hour he works over 30 hours per week. This implies that the $4 per hour for the first 30 hours is fixed while the $5 per hour overtime depends on the number of extra hours worked.
If we let w denote the wage and h denote the hours worked per week, then;
$4 per hour for the first 30 hours; 4*30 = 120
The number of extra hours worked would be; h-30
w = 120 + 5*(h-30)
This is the function that gives Andrew’s total wages when he works more than 30 hours each week.
A set of quiz scores is shown in the histogram below. The mean of the data set is 20.2, and the (population) standard deviation is 2.4.
PLEASE PLEASE PLEASE How many numbers in the data set are within 1 standard deviation of the mean?
13
14
15
16
Answer:
[tex]13[/tex]
Step-by-step explanation:
As the mean is 20.2 and the standard deviation is 2.4
The range within the first standard deviation is
(17.8,22.6)
This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.
Within this range there are
[tex]2+3+4+3+1=13[/tex]
The standard deviation of the mean is 13.
Standard deviation of the meanAs the mean is 20.2 and the standard deviation is 2.4
The range within the first standard deviation is (17.8,22.6)
This means that we can safely use the range of (18,22) as we cannot confirm whether the other values fall within the range.
Within this range there are
2 + 3 + 4 + 3 + 1 = 13
Therefore, the correct answer is option (a) 13.
To learn more about the standard deviation of the mean
https://brainly.com/question/475676
#SPJ2
Leila has $360 in twenty-dollar bills. How many twenty-dollar bills does she have?
18 $20 Dollar Bills
5 Bills In 100
10 Bills In 200
15 Bills In 300
18 Bills In 360
-x^1 -10x -24 = 0 I’ll melt your popsicle
I don't have popsicle but I'm sure you will melt by this answer.
[tex]
-x^1-10x-24=0 \\
x+10x+24=0 \\
11x=-24 \\
\boxed{x=\frac{-24}{11}}
[/tex]
Hope this helps. (please don't melt)
r3t40
find the volume of the sphere. express your answer in term of Pie
Answer:
[tex]\large\boxed{36\pi}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
R - radius
We have R = 3 ?. Substitute
[tex]V=\dfrac{4}{3}\pi(3^3)=\dfrac{4}{3}\pi(27)=(4)\pi(9)=36\pi[/tex]
If the radius is 30, then the volume is:
[tex]V=\dfrac{4}{3}\pi(30^3)=\dfrac{4}{3}\pi(27,000)=(4)\pi(9,000)=36,000\pi[/tex]
If 30 is the length of diameter, then the radius R = 30 : 2 = 15.
Therefore the volume:
[tex]V=\dfrac{4}{3}\pi(15^3)=\dfrac{4}{3}\pi(3,375)=(4)\pi(1,125)=4,500\pi[/tex]
Find an equation for the nth term of the arithmetic sequence.
a10 = 32, a12 = 106 (2 points)
an = -301 + 37(n - 1)
an = -301 + 37(n - 2)
an = -301 + 37(n + 1)
an = -301 - 37(n + 1)
I hope this helps witb you.
Final answer:
To find the nth term of the arithmetic sequence, we calculated the common difference to be 37, and deduced the first term as -301. The equation for the nth term is an = -301 + 37(n - 1). Therefore, option a is correct answer.
Explanation:
To find an equation for the nth term of the arithmetic sequence given two terms, a10 = 32 and a12 = 106, we first need to determine the common difference. The common difference d in an arithmetic sequence is the consistent interval between consecutive terms, calculated by subtracting one term from the next. In this case:
d = a12 - a10
d = 106 - 32
d = 74
Since the terms are two positions apart, this common difference corresponds to two steps, meaning the common difference per step is 74 / 2 = 37.
Now, we know that the general formula for the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
Where a1 is the first term. To find a1, we can plug in the values for a10:
32 = a1 + (10 - 1)×37
32 = a1 + 9×37
32 = a1 + 333
a1 = 32 - 333
a1 = -301
Now, the equation for the nth term of the sequence is:
an = -301 + 37(n - 1)
Therefore, option a is correct answer.
20 points
Which expression is a polynomial?
A. 7/x^2
B. x - √ 7
C. 7/ √ x
D. √ 7x
Answer:
B.Step-by-step explanation:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
[tex]A.\ \dfrac{7}{x^2}=7x^{-2}\qquad\bold{NOT}\\\\B.\ x-\sqrt7\qquad\bold{YES}\\\\C.\ \dfrac{7}{\sqrt{x}}=7x^{-\frac{1}{2}}\qquad\bold{NOT}\\\\D.\ \sqrt{7x}=\sqrt7\cdot\sqrt{x}=\sqrt7 x^\frac{1}{2}\qquad\bold{NOT}[/tex]
For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?
for a rational expression the vertical asymptotes occur when the denominator equals 0, in this case that will be when x + a = 0.
now, if there were to be a vertical asymptote of x = 1, that simply means that
x = 1 ==> x - 1 = 0.
meaning that a = -1.
horizontal asymptotes occur when the denominator has a higher degree than the numerator OR when both have the same degree.
when the degree of the denominator is higher, then the only horizontal asymptote occurring is y = 0.
when the degrees are the same, then the horizontal asymptote occurs at the leading terms' coefficient fraction.
now, if this expression were to have a horizontal asymptote of y = 2, that simply means
[tex]\bf \cfrac{2x^m}{x+a}\implies \cfrac{2x^1}{1x^1+a}\implies \stackrel{\textit{horizontal asymptote}}{\cfrac{2}{1}\implies y=2}\qquad \textit{meaning m = 1}[/tex]
ANSWER
a=-1,m=1
EXPLANATION
The given function is
[tex]f(x) = \frac{2 {x}^{m} }{x + a} [/tex]
For this rational function to have a horizontal asymptote at y=2, the degree of the numerator must equal the degree of the denominator.
This implies that, we must have m=1.
For the function to have a vertical asymptote at x=1, then,
[tex]1 + a = 0[/tex]
This implies that,
[tex]a = 0 - 1[/tex]
[tex]a = - 1[/tex]
The correct choice is the third option.
A product costs $29.75 for 5 pounds. How much does it cost per ounce? (1 pound = 16 ounces)
Answer:
The product costs $0.37 per ounce.
Step-by-step explanation:
$29.75 for 5 pounds = x for 1 pound (Cross-Multiply)
5x/5 = $29.75/5
x = $5.95 per pound
$5.95 per pound/16 ounces = $0.37
$0.37 per ounce!
Answer:
$0.371875 does it cost per ounce.
Step-by-step explanation:
Use conversion:
1 pound = 16 ounces.
As per the statement:
A product costs $29.75 for 5 pounds.
In 5 pounds = product cost $ 29.75
then;
In 1 pound = [tex]\$\frac{29.75}{5}[/tex]
Using conversion we have;
In 16 ounces = [tex]\$\frac{29.75}{5}[/tex]
then;
in 1 ounces = [tex]\$\frac{29.75}{80} = \$0.371875[/tex]
Therefore, $0.371875 does it cost per ounce.
Find the value of each variable
Answer:
x=6.5
Step-by-step explanation:
This question is on intersecting cords and segments that intersect outside the circle
Forming an equation for this relation;
6(x+6)= 5(5+10)
6x+36=5(15)
6x+36=75.............................collect like terms
6x=75-36
6x=39...........................divide both sides by 6
x=6.5
can anybody help me solve this please?
Calculate the volume of each shape then add them together.
4 x 32 x 10 = 1280
12 x 16 x 10 = 1920
Total volume = 1280 + 1920 = 3,200 cubic in.
Is this a function, explain answer
No. There are two spots in the vertical line. (Vertical line test)
ANSWER
No, there are two points with the same x-coordinates.
EXPLANATION
The relation in the graph is not a function.
There are two points in the relation that have the same x-coordinates.
These points are (1,1) and (1,3).
As a result of this , a vertical line will intersect the graph of the relation at these two points.
Since the graph of the relation does not pass the vertical line test, it is not a function.
andre drinks 15 ounces of water, which is 3/5 of a bottle. How much does the bottle hold? Use x for the number of ounces of water the bottle holds.
Answer:
25 ounces of water
Step-by-step explanation:
3/5 = 15
Cross multiplying this:
1 = x
3/5 = 15
3/5x=15
x=25
Answer:
The bottle hold 25 ounces of water
Step-by-step explanation:
To find the amount of water the bottle hold, we will follow the steps below;
let x be the number of ounces of water the bottle holds
3/5 of x = 15 ounces
3/5 × x = 15
[tex]\frac{3X}{5}[/tex] = 15
Multiply both-side of the equation by 5
[tex]\frac{3X}{5}[/tex] × 5 = 15×5
At the left-hand side of the equation 5 will cancel-out 5 leaving us with 3x
3x = 75
Divide both-side of the equation by 3
[tex]\frac{3X}{3}[/tex] = [tex]\frac{75}{3}[/tex]
(On the left-hand side of the equation 3 at the numerator will cancel-out 3 at the denominator leaving us with x while on the right-hand side of the equation 75 will be divided by 3)
x = 25 ounce
help plz i dont know what to do
Answer:
The area of the irregular figure is 140 sq. ft.
Step-by-step explanation:
Triangle:
16-12=4
6 x 4 = 24
24 x 0.5 = 12
Triangle = 12
Rectangle:
16 x 8
= 128
Rectangle = 128
Total figure:
128+12
= 140
Plzz give me brainlist!!!
An Easter basket contains eggs of three different colors. Find the total number of eggs in the basket if 2 7 of all eggs are green, 1 4 of all are blue and the rest 26 eggs are red.
Answer:
Total number of eggs in basket = 56
Step-by-step explanation:
Let z be the total number of eggs
Green eggs = [tex]\frac{2}{7}[/tex] × z ........1
Blue eggs = [tex]\frac{1}{4}[/tex] × z .......2
Rest of eggs = 26 ........3
The addition of 1, 2 and 3 is equal to z
[tex]\frac{2}{7}[/tex] × z + [tex]\frac{1}{4}[/tex] + 26 = z
[tex]\frac{8z + 7 z}{28}[/tex] + 26 = z ∵GCF for 4 and 7 is 28
[tex]\frac{15z}{28}[/tex] + 26 = z
15z + (26 × 28) = 28z ∵ multiply both sides by 28
15z + 728 = 28z
28z - 15z = 728 .......... rearranging above equation
13z = 728 ⇒ z = [tex]\frac{728}{13}[/tex] ⇒ z = 56
Total number of eggs = z = 56
Answer: There are total 56 eggs in the basket.
Step-by-step explanation: Given that an Easter basket contains eggs of three different colors, out of which [tex]\dfrac{2}{7}[/tex] are green, [tex]\dfrac{1}{4}[/tex] are blue and rest 26 eggs are red.
We are to find the total number of eggs in the basket.
Let x be the total number of eggs in the Easter basket.
Then, according to the given information, we have
[tex]\dfrac{2}{7}\times x+\dfrac{1}{4}\times x+26=x\\\\\\\Rightarrow \dfrac{8x+7x}{28}+26=x\\\\\\\Rightarrow \dfrac{15x}{28}+26=x\\\\\\\Rightarrow x-\dfrac{15x}{28}=26\\\\\\\Rightarrow \dfrac{28x-15x}{28}=26\\\\\\\Rightarrow \dfrac{13x}{28}=26\\\\\Rightarrow x=\dfrac{26\times 28}{13}\\\\\Rightarrow x=56.[/tex]
Thus, there are total 56 eggs in the basket.
ASAP HELP PLEASE A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic centimeters?
A)
V = π(4.5h)2
B)
V = π(9h)2
C)
V = π(4.5)2h
D)
V = π(9)2h
Answer:
Option A, π(4.5)²
Step-by-step explanation:
Volume of a cylinder is-
V = πr²h
Substitute the value of the radius. (9 is the diameter of the base, so it needs to be half of it)
V = π(4.5)²h
Bring the "h" inside with 4.5
V = π(4.5h)²
Hope this helps
The volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and thus option c) [tex]\pi (4.5)^{2} h[/tex] is the correct option
Given: a cylinder of diameter 9 cm and height h cm
To find: equation to find the volume of the cylinder
We know that the volume of a cylinder can be calculate by using the formula:
[tex]\text{volume} = \pi r^{2} h[/tex]
where r is the radius of the cylinder and h is the height
It is given that the diameter of cylinder is 9 cm so radius of the cylinder will be half of the diameter:
[tex]\text{radius} = \frac{9}{2} = 4.5[/tex] cm
Now putting the values in the formula of volume:
[tex]\text{volume} = \pi (4.5)^{2} h[/tex]
Therefore, the volume of the cylinder is [tex]\pi (4.5)^{2} h[/tex] and the option that is same as our answer is option C. So, option C) [tex]\pi (4.5)^{2} h[/tex] is the correct answer
Pepper Jackie has 5.8 kg of rainbow sprinkles. If she divides them equally into 8 star containers, how much will be in each star?
Answer:
725 grams
Step-by-step explanation:
You divide 5.8 kg by 8 (the star containers)
and the final answer is 0.725 kg or 725 grams
7 example of independent event
8 pieces of fruit are drawn twice with replacement what is P
Answer:
7.
rolling two number cubes
8.
2/25
Step-by-step explanation:
7.
Events A and B are said to be statistically independent if the probability of A happening, P(A), in no way affects the probability of event B occurring, P(B);
P(A∩B) = P(A) P(B)
If A and B are independent the above equation is always true.
From the list given, rolling two number cubes is an example of independent events since the outcome from the first cube does not affect the outcome of the second cube.
8.
We are informed the bag contains 4 apples, 1 plum, 2 apricots, and 3 oranges. We are required to determine the following probability;
P(Apple then Apricot) given that the fruits are drawn with replacement.
The probability of drawing an apple from the bag is;
(number of apples)/(total number of fruits)
= 4/10 = 2/5
The probability of drawing an apricot from the bag given that the apple drawn is replaced is;
(number of apricots)/(total number of fruits)
= 2/10 = 1/5
Now, P(Apple then Apricot) = 2/5 * 1/5 = 2/25
What is the equation !!! Math 3. 10 points HELP NEEDED!!!
ANSWER
B.
[tex]{f}^{ - 1} (x) = {x}^{2} - 3[/tex]
EXPLANATION
Given
[tex]f(x) = \sqrt{x + 3} [/tex]
Let
[tex]y= \sqrt{x + 3} [/tex]
Interchange x and y.
[tex]x= \sqrt{y + 3} [/tex]
Square both sides
[tex] {x}^{2} = y + 3[/tex]
Solve for y
[tex]y = {x}^{2} - 3[/tex]
Therefore the inverse of f(x) is
[tex] {f}^{ - 1} (x) = {x}^{2} - 3[/tex]
Which number line represents the solution to |-2x|=4
Step-by-step explanation:
l - 2 x l = 4
2 x = 4
x = 2
Answer:
Answer:
-2 & 2
( option C )
jane lives 1 3/8 miles from the airport. She drove from her house to the airport and back 2 times. How far did Jane drive? Move a number or numbers into the blank to show the answer
Answer:
[tex]5\frac{1}{2}\ mi[/tex]
Step-by-step explanation:
we know that
[tex]1\frac{3}{8}\ mi=\frac{1*8+3}{8}=\frac{11}{8}\ mi[/tex]
She drove from her house to the airport and back 2 times
so
Multiply the distance from her house to the airport by 4
[tex](4)*\frac{11}{8}=\frac{11}{2}=5\frac{1}{2}\ mi[/tex]
doroteo determined that the correlation coefficient for a set data was -0.9. what percent of the total variation in the y-values is not explained by the regression line?
Answer:
19% of the total variation in the y-values is not explained by the regression line
Step-by-step explanation:
The correlation coefficient, r, is a measure of the degree of association between two variables. It gives information on the direction and strength of the relationship.
On the other hand, [tex]R^{2}[/tex] is the coefficient of determination and is a measure of the percent of the total variation in the y-values explained by the regression line.
[tex]R^{2}[/tex] is simply the square of r;
[tex]R^{2}=r^{2}=(-0.9)^{2}=0.81[/tex]
This implies that 81% of the total variation in the y-values is explained by the regression line. Therefore, only 19% is not explained.