To simplify the fraction we will need to facto
Molly was on a long 136 mile road trip. The first part of the trip there was lots of traffic, she only averaged 16 mph. The second part of the trip there was no traffic so she could drive 44 mph. If the trip took her 5 hours, how long did she travel at each speed? In traffic she drove for _____ hours After the traffic cleared she drove for ____ hours.
Answer:
In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
Explanation:
Given that the road trip was 136 miles;
[tex]d=136[/tex]The first part of the trip there was lots of traffic, she only averaged 16 mph;
[tex]v_1=16[/tex]The second part of the trip there was no traffic so she could drive 44 mph;
[tex]v_2=44[/tex]She traveled for a total of 5 hours;
[tex]t=5[/tex]let x represent the time in traffic when she traveled at 16 mph
[tex]t_1=x[/tex]the time the traffic is clear would be;
[tex]t_2=t-t_1=5-x[/tex]Recall that distance equals speed multiply by time;
[tex]d=v_1t_1_{}_{}^{}+v_2t_2[/tex]substituting the values;
[tex]136=16x+44(5-x)[/tex]solving for x;
[tex]\begin{gathered} 136=16x+220-44x \\ 44x-16x=220-136 \\ 28x=84 \\ x=\frac{84}{28} \\ x=3 \end{gathered}[/tex]So;
[tex]\begin{gathered} t_1=3\text{ hours} \\ t_2=5-x=5-3=2 \\ t_2=2\text{ hours} \end{gathered}[/tex]Therefore, In traffic, she drove for 3 hours
and After the traffic cleared she drove for 2 hours.
The following table represents C, an appliance repairman’s charges based on t, the hours it takes to make a repair.Which of the following equations could be used to determine the repairman’s charges for a repair?A: C=27t +3B: C=27tC: C=35tD: C=35t + 2
Given the table below
To find the equation of the values of the table, we will first calculate the rate of change, then use a point and the rate of change calculated fo find the equation for the repairman's charges for the repair
To find the rate of change we have
[tex]\text{ Point 1}\Rightarrow(1,62)\Rightarrow t_1=1,c_1=62[/tex][tex]\text{ Point 2}\Rightarrow(3,116)\Rightarrow t_2=3,c_2=116[/tex]The rate of change formula is
[tex]m=\frac{c_2-c_1}{t_2-t_1}=\frac{116-62}{3-1}=\frac{54}{2}=27[/tex]Having calculated the rate, we can use slope and one point form equation of a line to get the desired equation. This is given below:
[tex]c-c_1=m(t-t_1)[/tex]Substitute the given values of t and c and the rate in the formula above
[tex]\begin{gathered} c-62=27(t-1) \\ c-62=27t-27 \\ c=27t-27+62 \\ c=27t+35 \end{gathered}[/tex]Hence, the repairman's charges for a repair is given as C = 27t + 35
The measure of angle c below is(Hint: Slide 2)95/640
we know that
The sum of the interior angles in any triangle must be equal to 180 degrees
In the right triangle of the figure
we have
c+d+64=180
we have that
d=90 degrees (right angle)
substitute
c+90+64=180
c+154=180
c=180-154
c=26 degrees
Describe how the graph of the function g(x)=1/4|x|-2 can be obtained from the basic graph. Then graph the function.Start with the graph of h(x)=|x|. Then [__] it vertically by a factor of [__]. Finally, shift it [___] units.
Start the graph of h(x) = |x|, then stretch it vertically by a factor of 1/4 . Finally, shift it down by 2 units
The original graph can be seen above
what it becomes can be seen below
Hence the final answer is option B
Used two equations in two variables to solve the application.A 60 m pass around the rectangular garden. The width of the garden is 2/3 its length. Find the area in meters squared.
From the data provided, we can conclude:
The perimeter of the rectangle is 60m, so:
[tex]60=2w+2l_{\text{ }}(1)[/tex]Where:
w = width
l = length
The width of the garden is 2/3 its length, therefore:
[tex]w=\frac{2}{3}l_{\text{ }}(2)[/tex]Replace (2) into (1)
[tex]60=2(\frac{2}{3}l)+2l[/tex]Solve for l:
[tex]\begin{gathered} 60=\frac{4}{3}l+2l \\ 60=\frac{10}{3}l \\ l=\frac{180}{10} \\ l=18 \end{gathered}[/tex]Replace l into (2):
[tex]\begin{gathered} w=\frac{2}{3}(18) \\ w=12 \end{gathered}[/tex]Assume that a particular professional baseball team has 12 pitchers, 5 infielders, and 8 other players. If 3 players' names are selected at random, determine the probability that 2 are pitchers and 1
is an infielder.
What is the probability of selecting 2 pitchers and 1 infielder?
(Type an integer or a simplified fraction.)
Step-by-step explanation:
Pitchers(p) = 12
Infielders(i) = 5
Others(o) = 8
Total players = 25
Probability(2p and 1i) =
[tex]( \frac{2}{25} ) \times ( \frac{1}{25} ) = ( \frac{2}{625} )[/tex]
Find the length of the third side. If necessary, round to the nearest tenth. 12 5 x=what is the missing number x?
Step 1
Longest side is the hypotanuse = x
opposite = 5
Adjacent = 12
Apply pythagorus theorem
[tex]\begin{gathered} \text{Opposite}^2+Adjacent^2=Hypotanuse^2 \\ 5^2+12^2=x^2 \\ \\ 25+144=x^2 \\ x^2\text{ = 169} \\ x\text{ = }\sqrt[\square]{169} \\ x\text{ = 13} \end{gathered}[/tex][tex]undefined[/tex]pls help the hw is due today
Answer: the slope for the line is
y= -2x-4
21 - 7∆ = 4 - 8∆ 5∆ - 3 + 3∆ = ∆ + 7 + 6∆solve these.
We are given the following equation:
[tex]21-7\Delta=4-8\Delta[/tex]We need to solve for delta, to do that we will first add 8delta on both sides:
[tex]21-7\Delta+8\Delta=4-8\Delta+8\Delta[/tex]Now we add like terms:
[tex]21+\Delta=4[/tex]Now we subtract 21 on both sides:
[tex]21-21+\Delta=4-21[/tex]Adding like terms:
[tex]\Delta=17[/tex]Therefore delta is 17
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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In an experiment, the probability that event B occurs is , and the probability that event A occurs given that event B occurs is 3 7) What is the probability that events A and B both occur? Simplify any fractions.
We have to use the conditional probability formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]Where P(A|B) is the probability that A occurs given that B occurs, P(B) is the probability that B occurs, and P(A∩B) is the probability that both events A and B occur.
In this case, since we are asked for the probability that events A and B both occur, we need to solve the equation for P(A∩B):
[tex]P(A\cap B)=P(A|B)\cdot P(B)[/tex]And the information we have about the problem is:
[tex]\begin{gathered} P(A|B)=\frac{3}{7} \\ P(B)=\frac{2}{9} \end{gathered}[/tex]We substitute this into the formula for P(A∩B):
[tex]P\mleft(A\cap B\mright)=\frac{3}{7}\cdot\frac{2}{9}[/tex]Solving the multiplication of fractions:
[tex]\begin{gathered} P\mleft(A\cap B\mright)=\frac{3\cdot2}{7\cdot9} \\ P\mleft(A\cap B\mright)=\frac{6}{63} \end{gathered}[/tex]And finally, we simplify the fraction by dividing both numbers in the fraction by 3:
[tex]P\mleft(A\cap B\mright)=\frac{2}{21}[/tex]Answer: 2/21
Why was math created
SOLUTION:
Step 1:
In this quesdtion, we are meant to explain the topic:
Why was Math created?"
Step 2:
The details of the solution are as follows:
1. Mathematics is a body of knowledge and knowledge and practice, that is derived from the contributions of thinkers throughout the ages and across the globe.
2. It gives us a way to understand patterns, to quantify relationships, and to predict the future.
3. Math helps us understand the world — and we use the world to understand math.
4. Excellent for your brain: Creative and analytical skills are highly desired by employers.
5. It has a lot of real-world applications.
6. It helps in better problem-solving skills.
7. Mathematics is needed in almost every career and profession.
8. Mathematics helps understand the world better.
9. Mathematics is a universal language.
10. Numbers help us understand the world, and Mathematics helps us understand numbers.
The real-life applications of Mathematics are endless.
We are surrounded by numbers, equations and algorithms – especially in this age of data science, with huge data sets that can only be understood through statistical models and analysis.
Answer:
Maths was invented to understand the world and to make measurements, do calculations etc. make and measure shapes, measure angles, and to use these things in real life. The Egyptians used the Pythagoras theorem to accurately make their pyramids.
Which expression is equivalent to 4 * 4 * 4 * 5 * 5?34 x 2543 x 5244 x 501224 x 102
Any of those expressions are equivalent to 4*4*4*5*5
A bank offers a CD that pays a simple interest rate of 8.0%. How much must you put in this CD now in order to have $2500 for a home-entertainment center in 3 years.
Okay, here we have this:
Considering that the formula for the simple interest rate is:
A = P (1 + rt)
In this case A is equal to $2500, P is the value we need to find, r is the interest rate (in decimal) 0.08, and t is the time, so it's 3 years, replacing we obtain:
2500=P(1+0.08*3)
Now, let's clear P:
2500=P(1+0.24)
2500=P(1.24)
2500/1.24=P
P=2016.13
Finally we obtain that the bank must put $ 2016.13 on a CD to get $ 2,500 in three years.
A tree on a hillside casts a shadow c = 215 ft down the hill. If the angle of inclination of the hillside is b = 23° to the horizontal and the angle of elevation of the sun is a = 53, find the height of the tree. (Round your answer to the nearest foot.)
This is the figure, roughly. We want h.
Using smaller triangle, we can write:
[tex]\begin{gathered} \text{Cos}23=\frac{x}{215} \\ x=215\cdot\cos 23 \\ x=197.9 \end{gathered}[/tex]Also,
[tex]\begin{gathered} y=215\cdot\sin 23 \\ y=84 \end{gathered}[/tex]Now, taking the larger triangle:
The angle is 53 (30 + 23).
Let the larger side (right side) be m, which is basically:
m = h + y
Let's find m:
[tex]\begin{gathered} \tan 53=\frac{m}{x} \\ \tan 53=\frac{m}{197.9} \\ m=197.9\cdot\tan 53 \\ m=262.62 \end{gathered}[/tex]Now, we want height, h, which is:
m = h + y
262.62 = h + 84
h = 262.62 - 84
h = 178.62
Rounded to nearest feet
h = 179 feet
What is the slope of this horizontal line from 10-13 minutes?
We are asked to determien the slope of the line between 10 and 13 minutes. Since this is a horizontal line, it's slope is 0.
The circle graph shows the results of a survey by a bakery on which of their new products 105 customerspreferred most. How many customers preferred cake? Round your answer to the nearest whole number.
If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:
[tex]35\%=\frac{35}{100}[/tex]And the multiplication
[tex]105\cdot\frac{35}{100}=36.75[/tex]Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.
37 customers prefer cake.
i Which equation, when solved, results in a different value of x than the other three?' 7 3 4 37 X=-20 3 119-8-2014
You have the first equation:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]Let's analize the others equation.
You can see that the second equation is just like the first one, but it was multiplied by -1:
[tex]\begin{gathered} (-1)(-\frac{7}{8}x-\frac{3}{4})=(20)(-1) \\ \frac{7}{8}x+\frac{3}{4}=-20 \\ \frac{3}{4}+\frac{7}{8}x=-20 \end{gathered}[/tex]So the value of "x" of the first one and the second one will be the same.
The third equation is:
[tex]-7(\frac{1}{8})x-\frac{3}{4}=20[/tex]If you simplify it, you get:
[tex]-\frac{7}{8}x-\frac{3}{4}=20[/tex]So you can notice that the three equations are the same, therefore the result of the third one will be the same too.
You can identify that even simplifying the last equation, it is not the same equation, then you will obtain a different value of "x" than the other three.
Therefore,the answer is the Last option.
One pump can empty a pool in 7 days, whereas a second pump can empty the pool in 14 days. How long will it take the two pumps, working together, to empty the pool? (Fractional answers are OK.)The first pump's rate is_____per day.The second pump's rate is____per day.The combined pumps rate is____per day.It will take the two pumps_____per day.
The first step is to define the daily rates of each pump
From the information given,
First pump can empty the pool in 7 days. This means that
Daily rate of first pump = 1/7
The first pump's rate is 1/7 per day
Second pump can empty the pool in 14 days. This means that
Daily rate of second pump = 1/14
The second pump's rate is 1/14 per day
Let t be the number of days it will take both pumps, working together to empty the pool. Thus,
combined daily rate of both pumps = 1/t
The rates are additive. It means that
1/7 + 1/14 = 1/t
Simplifying the left side, we have
3/14 = 1/t
The combined pumps rate is 3/14 per day
By taking reciprocal of both sides,
t = 14/3 = 4.67
It will take the two pumps 4.67 days to empty the pool together
inding Total CostsStore AStore BWhat is the cost of the repair and sales tax combinedat Store B?ComputerRepair$1,200$1,350Sales Tax6%7%Gratuity15%15%ShippingFree2% of totalprice
Store B :
Computer repair : $1,350
Sale tax = 7%
To obtain the sale tax amount, multiply the price by the percentage in decimal form (divided by 100);
$1,350 x (7/100) = 1,350 x 0.07 = $94.5
Add both:
1,350+94.5=$1,444.5
A math book is 2.5 cm thick.
How many of these books can
be stored on a shelf that is
one meter long?
The number of books that can be stored on one meter-long shelf is (forty) = 40.
Given
a book is 2.5 cm thick
number of books required are
Convert meters into centimeters first 1m = 100 cm now, divide them:
= 100 cm ÷ 2.5 cm to remove the decimal point divide 2.5 by 10 = 2.5/10
= [tex]100 * \frac{10}{25}[/tex]
= 40
thus the total number of books that can be stored on a one-meter bookshelf is 40 books.
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A middle schooler is H inches tall at the beginning of the school year is the height of the middle school at the end of the year can be represented by the expression H + 0.02h, which statement is true?
Answer:
A
Step-by-step explanation:
h + 0.02h = (1+0.02)h = 1.02h
1.02h * 100% = 102%
102 - 100 = 2%
what does frilling mean
Answer:
A ruffled, gathered, or pleated border or projection, such as a fabric edge used to trim clothing.
Step-by-step explanation:
Brainlest, Please!
Which of the following are equal to sec x? Choose all that apply. 3 answers
Verify each option
A ---> 1/sinx=cscx -----> is not the answer
B ---> 1/cosx=secx ----> is the answerC ---> cosx/tanx=cosx/(sinx/cosx)=cos^2x/sinx -----> is not the answer
D ---> tanx/sinx=(sinx/cosx)/sinx=1/cosx=secx -----> is the answerE ---> cotxsinx=(cos/sinx)sinx=cosx ----> is not the answer
F ----> tanxcscx=(sinx/cosx)(1/sinx)=1/cosx=secx ----> is the answertherefore
The answer is
options B, D and FAnswer:
B, D, E.
Step-by-step explanation:
B: [tex]\frac{1}{cos(x)}[/tex]
D: [tex]\frac{tan(x)}{sin(x)}[/tex]
E: [tex]tan(x) csc (x)[/tex]
x-y=3x+y=5unit 7 systems of linear equations
then
[tex]\begin{gathered} x+y=5 \\ 3+y+y=5 \\ 3+2y=5 \\ 3+2y-3=5-3 \\ 2y=2 \\ \frac{2y}{2}=\frac{2}{2} \\ y=1 \end{gathered}[/tex]solve for x
[tex]\begin{gathered} x=3+y \\ x=3+1 \\ x=4 \end{gathered}[/tex]answer: C. (4,1)
please help me asap, Evaluate 9 exponent 2
81
Explanation
Remember
[tex]a^b=\text{ a multiplied by itself b times}[/tex]Step 1
apply
[tex]\begin{gathered} 9^2=9\cdot9 \\ 9\cdot9=81 \end{gathered}[/tex]use the distributive property to simplify the left side of the equation 2(x/8+3)=7+1/4x
Given data:
The given expression is 2(x/8+3)=7+1/4x.
The given expression can be written as,
2(x/8)+2(3)=7+1/4x
x/4+6=7+1/4x
x/4-1/4x=7-6
x/4-1/4x=1
x^(2)-1=4x
x^(2)-4x-1=0
Thus, the final expression is x^(2)-4x-1=0 after applying distributve property on left side.
Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record theheight, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t.t 0 1 2 3 4h 5 6 7 8 9
As we can see inthe table foe every year that pass the thre grows 1 ft
As we can see inthe table foe every year that pass the thre grows 1 ft
2(4-2x)-5=-2(x+5)+8x
The equation 2(4-2x)-5=-2(x+5)+8x has a value of 1.3 for x
How to determine the solution to the equation?From the question, the equation to solve is given as
2(4-2x)-5=-2(x+5)+8x
Rewrite the equation properly
This is represented by the following representation
2(4 - 2x) - 5=-2(x + 5) + 8x
Start by opening the brackets in the equation
So, we have the following equation
8 - 4x - 5 =-2x - 10 + 8x
Collect the like terms in the equation
So, we have the following equation
8x - 2x + 4x = 10 +8 - 5
Evaluate the like terms in the equation
So, we have the following equation
10x = 13
Divide both sides of the equation by 10
So, we have the following equation
x = 1.3
Hence, the solution to the equation for x is 1.3
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Parking spaces in a parking lot are parallel to each other. Find the measure of the two
unknown angles and explain your reasoning.
measure of angle m:
measure of angle n:
Answer:
m = 70° , n = 110°
Step-by-step explanation:
m and 110° are same- side interior angles and sum to 180°
m + 110° = 180° ( subtract 110° from both sides )
m = 70°
n and 110° are corresponding angles and are congruent , then
n = 110°