|In8Word problem on unit rates associated with ratios of fractions1days, a construction crew built miles of road.4What is the unit rate in miles per day?Write your answer in simplest form.miles per dayI need help solving this problem
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ANSWER :
2 miles per day
EXPLANATION :
In 1/8 day, they finished 1/4 miles of the road.
We just need to divide the work done by the time to get the rate :
[tex]\frac{1}{4}\div\frac{1}{8}[/tex]Division can be expressed as multiplication by taking the reciprocal of the divisor.
That will be :
[tex]\frac{1}{4}\times\frac{8}{1}=2[/tex]Related Questions
this text goes with this question: Francesca wants to glue this 3-inch by 5-inch photo on top of a mat that will increase the length of each side by another x inches. Find an expression representing the area of the mat and use this expression to find the area and cost of the mat for different values of x. i need help with question #9.
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Check values for white and black mat
Area of photo is = 3 x 5 = 15 inches ^2
The area most apropiate for this photo is
69 inches^2, because is the most similar in size
If FRANCESCA wants to save costs ,she should pick WHITE MAT
But , if she is not afraid of cost, then she should pick Black price mat of any size.
Monty documented the amount of rain his farm received on a monthly basis, as shown in the table. Month, x Rainfall (in.), 4 2 2 3 4.5 8 5 5 3 Part 1 Is the relationship linear? Why or why not? Complete the explanation. The change between months is constant, but the change in the amount of rain is not constant. So, the relationship is not linear. Part 2 out of 2 Can an equation be entered to describe the amount of rain? Complete the explanation. An equation (select) be written to describe the amount of rain because there is (select) pattern in th (select) Che can can not Next
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so the answer is
the change between months is constant, but the change in the amount of rain is not constant. So, the relationship is not linear.
An equation can not be written to describe the amount of rain because there is not a fixed or variable pattern in the rainfall
Match up the system of equations with the appropriate graph
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Solution
Match up the system of equations with the appropriate graph
Equation 1 :
[tex]\begin{gathered} y=2x+2 \\ y=2x+4 \end{gathered}[/tex]Equation 2:
[tex]\begin{gathered} y=-x+4 \\ y=6x-3 \end{gathered}[/tex]Equation 3
[tex]\begin{gathered} 4x=-y+1 \\ -1=-y-4x \end{gathered}[/tex]Equation 4
[tex]\begin{gathered} 2y=-3x-4 \\ y=-\frac{1}{2}x+1 \end{gathered}[/tex]Which logarithmic equation is equivalent to the exponential equation below?9x = 27A.27 = log9 xB.9 = log27 xC.x = log27 9D.x = log9 27
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Given:
[tex]9^x=27[/tex]Required:
To calculate which option is correct
Explanation:
[tex]\begin{gathered} 9^x=27 \\ \\ log_927=x \end{gathered}[/tex]Required answer:
Option d
I believe the answer to be this: but I'm not too sure-99.2016I'm not understanding what it mean by win or lose I don't know which one to mark
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Hello there. To solve this question, we'll have to remember some properties about probabilities.
First, remember that there are 4 suits in a standard card deck, each containing 13 different cards.
Most specifically, there are only one of each number in each suit, so this means that there are only 4 cards with the number 5 in a 52 card deck.
The probability of taking three fives in succession from this deck, with replacement, is given by the ratio between the favorable events of taking a 5 (4) and the total number of cards (52), cubed:
[tex]P(\text{taking a 5 three times in succession)}=\frac{4}{52}\cdot\frac{4}{52}\cdot\frac{4}{52}=\frac{1}{13^3}=\frac{1}{2197}[/tex]Notice the probabilities are the same for each succession because we were replacing the cards. If we weren't replacing, then the probabilites would go down as 4/52 * 3/51 * 2/50, which is not the case.
Obviously, this is the probability of winning and if you get three fives in succesion, you get $70.
To find the probability of not getting 5's three times in succession, simply subtract the probability we found from 1:
[tex]P(\text{not get 5's three times in succession)}=1-\frac{1}{2197}=\frac{2196}{2197}[/tex]Now, we multiply the probabilities by the number in dollars we would get by winning and the number in dollars (negative) we would pay for losing, respectively:
[tex]\begin{gathered} 70\cdot\frac{1}{2197}-10\cdot\frac{2196}{2197} \\ \\ \frac{70}{2197}-\frac{21960}{2197} \\ \\ -\frac{21890}{2197} \end{gathered}[/tex]By calculating the fraction, we get:
[tex]-9.9635[/tex]Which equation shows a proportional relationship between x and y?DA. Y = 3xB. y = 3x - 1C. y = 2 + 3D. None of these
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the equation that shows proportional relationship is
y = k x
here k is proportionality constant
so by comparing all the given equation with the above expression
we can see that
Y = 3x is the showing proportional relation.
hre
One triangular face of the prism shown has an interior angle with a measure of 65° and an exterior angle with a measure of 120°. What is the measure of the marked interior angle?
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For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings of 77 breakfast cereals produced the regression model Potassium=39+27Fiber. *If your cereal provides 8 grams of fiber per serving, how much potassium does the model estimate you will get? ______________milligrams of potassium
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255 milligrams of potassium
Explanation:[tex]\begin{gathered} \text{The regression model:} \\ Potassium\text{ = 39 + 27 Fiber} \\ \\ \text{where Potassium is in milligrams} \\ \text{Fiber is in grams} \end{gathered}[/tex][tex]\begin{gathered} \text{Amount of fiber = 8 grams of per serving } \\ \text{replace Fiber with 8 in the model:} \\ \text{Potassium = 39 + 27(8)} \end{gathered}[/tex][tex]\begin{gathered} Amount\text{ of Potassium in the model:} \\ \text{Potassium = 39 + 216} \\ \text{Potassium = 255} \end{gathered}[/tex]It is estimated to get 255 milligrams of potassium from the 8 grams of fiber
If AB = 5 and AO = 8. What is the length of the radius (r)?AB is tangent to circle O at B. Diagram not drawn to scale.
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Answer:
6.24 units
Explanation:
Recall that the angle between a tangent AB and the radius, BO is always 90 degrees.
Therefore, triangle ABO is a right triangle.
Applying the Pythagorean Theorem:
[tex]\begin{gathered} AO^2=AB^2+BO^2 \\ \implies8^2=5^2+r^2 \end{gathered}[/tex]We solve the equation above for r:
[tex]\begin{gathered} r^2=8^2-5^2 \\ r^2=64-25 \\ r^2=39 \\ r=\sqrt[]{39} \\ r\approx6.24 \end{gathered}[/tex]The length of the radius is approximately 6.24 units.
Tell whether the ordered pair is a solution to the system of equations. You must show work to support your answer.
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x + y = -2
x + 5y = 2
Ordered pair (-3, 1) ==> x = -3, y = 1
For the fisrt equation:
x + y = -2
-3 + 1 = -2
-2 = -2 True
For the second equation:
x + 5y = 2
-3 + 5(1) = 2
-3 + 5 = 2
2 = 2 True
Answer:
Yes, the ordered pair is a solution because it satisfies both equations
A student sketched some art on an 8.5 inch × 11inch piece of paper. She wants to resize it to fit an 5 inch × 7 inch fram (as show below)what percent of the original sketch was still able to be included in the frame?
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A tv screen is 41 cm long and 31 cm high. the length of the diagonal is closest to
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the length of the tv screen is,
l = 41 cm
the width of the tv is
b = 31 cm
the length of the diagonal will be the hypotenuse of the triangle,
so, diagonal length is,
[tex]\text{diagonal}=\sqrt[]{41^2+31^2}[/tex][tex]\text{diagonal}=\sqrt[]{1681+961}[/tex][tex]\begin{gathered} \text{diagonal}=\sqrt[]{2642} \\ \text{diagonal}=51.04 \end{gathered}[/tex]so, the length of the diagonal is closest 51.04 cm
a. it represents a moderate negative linear association. B. It represents a moderate positive linear association. C. It represents a strong negative linear association. d. It represents a strong positive linear association.
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The graph of the linear model is shown above.
Notice that the slope of the line is positive.
Notice that most of the points lie near the line.
Therefore, the association is strong and positive.
D. It represents a strong positive linear association.
You decided to erect A statue of yourself in your homeroom class is 10.25 feet tall fire code forces you to leave 1.5 feet of space between your statue in the ceiling right any quality showing the possible height of the statue
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The inequalty equations are constructed by noting a value in terms of another one using the expressions ">", "<" etc.
So here, the height of the class is 10.25 feet.
And you have to leave 1.5 feet space between the statue and the ceiling, so the maximum height that the statue can have is,
[tex]10.25\text{ ft - 1.5 ft = 8.75 ft}[/tex]So the satue can have a height of this 8.75 ft or less than that, and we can write it as,
[tex]h\leq8.75\text{ ft}[/tex]Number 3.Solve the inequalities and represent the possible values of the variable on a number line.
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We are given the following inequality:
[tex]1<2+k[/tex]We will solve for the variable "k". To do that we will subtract 2 from both sides of the inequality:
[tex]1-2<2-2+k[/tex]Solving the operations:
[tex]-1The solutions are the values of "k" that are greater than -1. In a number line this can be represented as:Since the solution does not involve an equal sign this means that -1 is not included in the solution. We represent that using a hollowed circle on -1.
Select the correct choice below and fill in any answer boxes in your choice.
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To answer this equation we must first simplify it and apply the general rule of math when it comes to dealing with equations.
Remember the rule that, whatever you do on the left side of the equation you must do the same to the other side.
Let's start.
We are given the equation:
[tex]8x-(5x+2)=5x-12[/tex]Now for our first step let us simplify the left side of the equation first. Since we have a parenthesis in our equation let us remove it by distributing the negative (-) sign outside the parenthesis into the terms inside the parenthesis.
[tex]8x-5x-2=5x-12[/tex]Notice that we can combine 8x and -5x since they are like terms.
[tex]\begin{gathered} 8x-5x-2=5x-12 \\ 3x-2=5x-12 \end{gathered}[/tex]Now we have simplified the left side of the equation and looking at the right side, it can't be simplified further.
Now let us evaluate the equation to find the value of x. Looking at our new equation which is:
[tex]3x-2=5x-12[/tex]We can see that both terms with the same variable are separated, so let us manoeuvre so that they can be together on the same side of the equation.
To do that let us subtract 3x in the left side of our equation in order to cancel the original 3x in there, and do the same to the right side of the equation by the virtue of the general rule we talked about earlier. Now we have an equation that looks like this:
[tex]3x-2-3x=5x-12-3x[/tex]Notice that 3x and -3x on the left side of our equation can be cancelled since they will just add up to 0. And the 5x and -3x on the right side of the equation can be combined since they have like terms. Now our equation becomes:
[tex]-2=2x-12[/tex]Now let us do the same thing to the -12 in the right side of the equation, let us transfer it to the left side of the equation so that we can combine it with -2.
To do that we only have to add 12 on the right side of the equation to cancel out the -12, and do the same to the left side of the equation. Our equation now becomes:
[tex]-2+12=2x-12+12[/tex]Notice again that 12 and -12 on the right side can be cancelled out since they are just equal to 0. And -2 and 12 can be combined since they are like terms. Now our equation becomes:
[tex]10=2x[/tex]Now we have simplified our equation to its simplest form it is now time to evaluate the equation. To do that simply divide both sides by 2 so that only x remains on the right side of the equation, and we can now know the value of x.
[tex]\begin{gathered} \frac{10}{2}=\frac{2x}{2} \\ 5=x \\ x=5 \end{gathered}[/tex]Therefore the value of our x is 5.
Therefore the answer to our question is LETTER A. The solution set is {5}.
Multiply 543.542 and 4 together.
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You have to do the following multiplication
[tex]543.542\cdot4[/tex][tex]undefined[/tex]00:00If the volume of a cube-shaped box is 729 cubic inches, which equation would you use to determinehow many 1-inch cubes could fit along one side?S =729s =✓ 729S =7292S= 7293
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let s be the side of the cube
Volume of cube = s³
From the the question volume = 729 cubic inches
Substitute into the formula;
729 = s³
Take the cubic root of both-side of the equation
[tex]\sqrt[3]{729}=s[/tex][tex]S=\sqrt[3]{729}[/tex]4 ft 5 ft 3 ft 11 ft y ft
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Which shows two triangles that are congruent by the SSS congruence theorem?Im not sure how to solve this....
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The last one from top to botttom
1) Since we need to find the SSS congruence case, we need to consider that that all sides must be congruent.
2) So, examining the options, we can tell that AC is congruent to itself, due to the Reflexive Property.
Thus, this is the SSS congruence case.
2. Lee Hays has obtained a $240,000mortgage loan at 7.00% for 25 years.a. What is the monthly payment?b. What is the total amount paid?c. What is the total interest?
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Given:
[tex]\begin{gathered} Present-value=240000 \\ rate(r)=7\%=0.07 \\ n=term(in-months)=25\times12=300 \end{gathered}[/tex]To Determine: a. What is the monthly payment? b. What is the total amount paid?
c. What is the total interest?
Solution
Using the formula below
[tex]PMT=\frac{PVr(1+r)^n}{(1+r)^n-1}[/tex]Substitute the given
[tex]\begin{gathered} PMT=\frac{240000\times0.07(1+0.07)^{300}}{(1+0.07)^{300}-1} \\ PMT=\frac{16800(1.07)^{300}}{(1.07)^{300}-1} \\ =\frac{16800\times\:1.07^{300}}{653331059.14479} \\ PMT=16800.0002 \end{gathered}[/tex]The total amount paid is
[tex]\begin{gathered} Amount-paid=PMT\times n \\ =16800.00002\times300 \\ =5040000.01 \end{gathered}[/tex]The interest paid is
[tex]\begin{gathered} Interest=Amount-paid)-Present-value \\ =5040000-240000 \\ =4800000 \end{gathered}[/tex]A car traveling at a rate of 54 Kilometers per hour How many kilometers will the car travel in 10 minutes
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EXPLANATION
If the speed of the car is 54 kph and the traveled time is 10 minutes, we first need to turn the 10 minutes into hours by applying the unitary method as shown as follows:
[tex]\text{?hours=10 minutes}\cdot\frac{1\text{ hour}}{60\text{ minutes}}=0.16[/tex]Now, we can get the mount of kilometers by multiplying the time with the speed (unitary method) as following:
[tex]\text{?kilometers }=\text{ }0.16\text{ hours }\cdot\text{ }\frac{54\text{ kilometers}}{1\text{ hours}}\approx9\text{ kilometers}[/tex]The distance traveled in 10 minutes was 9 kilometers.
I will insert a photo
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Thus, the required value of p(x) is (5x+1) and k is 7.
How do you divide the fractions 3/8 divided by 1/24?
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How do you divide the fractions 3/8 divided by 1/24?
We will divide the problem as follows:
[tex]\frac{3}{8}\div\frac{1}{24}=\frac{3}{8}\times\frac{24}{1}=\frac{3\times24}{8}=3\times3=9[/tex]Note: the divide sign becomes multiplication sign, then write the reciprocal of the second fraction, then simplify.
A high school student needs 9 more classes to graduate. If she has met the prerequisites for all the classes, how many possible schedules for next semester could she make if she has 5 class periods to fill? (enter answer with no commas, i.e. as 1000 not 1,000.)
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GIVEN
The number of classes needed by the student is 9.
The number of class periods to fill is 5.
SOLUTION
The number of classes she can pick per period is gotten using the combination formula. This multiplied by the total classes will give us the required answer. The answer can thus be calculated as follows:
[tex]N=9C5\times5![/tex]The combination formula is given to be:
[tex]nCr=\frac{n !}{r ! (n-r) !}[/tex]Therefore, we can calculate the answer to be:
[tex]\begin{gathered} N=\frac{9!}{5!(9-5)!}\times5! \\ N=\frac{9!}{5!\times4!}\times5! \\ \text{Simplifying, we have:} \\ N=\frac{9\times8\times7\times6\times5\times4!\times5!}{5!\times4!} \\ N=9\times8\times7\times6\times5 \\ N=15120 \end{gathered}[/tex]ANSWER
There are 15120 possible schedules that can be made.
Which of the following is not a perfect square trinomial?144 + 12y + y2100 + 20y + y264 – 16y + y225 + 10y + y2
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1) Analyzing those trinomials, a perfect square trinomial must satisfy some conditions like (ax+b)²
2) Given
y² +12y +144 ≠ (y +6)²
y² +20y +100 = (y+10)²
y²-16y +64 =(y-8)²
y² +10y +25 = (y +5)²
3) So since b/2=12/2 = 6 ≠ 12² in the y² +12y +144 is different from 12², then
y² +12y +144 is not a perfect square trinomial.
Given the function: y = 4x - 1, find f-¹ (7)
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Step 1
Given;
[tex]y=4x-1[/tex]Required; To find
[tex]f^{-1}(7)[/tex]Step 2
Find the inverse of f(x)
Set x =y and y =x
[tex]x=4y-1[/tex]solve for y
[tex]\begin{gathered} 4y=x+1 \\ y=\frac{x+1}{4} \\ f^{-1}(x)=\frac{x+1}{4} \end{gathered}[/tex][tex]\begin{gathered} Find\text{ f}^{-1}(7) \\ \text{ f}^{-1}(7)=\frac{7+1}{4}=\frac{8}{4}=2 \\ \text{ f}^{-1}(7)=2 \end{gathered}[/tex]Answer;
[tex]\text{ f}^{-1}(7)=2[/tex]answer the following questions about this graph:evaluate f(1)f(5)what is the y intercept of this graph
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1) Looking at the graph, locate point x=1 for f(1)
f(1) =4 since x=1, then y=4 according to that function
f(5) = -2 since x=5, then y=-2 according to that function
solve the equation of 5/2x=25/4
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The given equation is expressed as
[tex]\frac{5}{2x}\text{ = }\frac{25}{4}[/tex]The first step is to cross multiply. This means that we would multiply 5 with 4 and 2x with 25. It becomes
[tex]\begin{gathered} 50x\text{ = 20} \\ We\text{ would divide both sides of the equation by 50. it becomes} \\ x\text{ = }\frac{20}{50} \\ x\text{ = }\frac{2}{3} \end{gathered}[/tex]Julie is at the store buying groceries. She needs to get a quart of orange juice and some preaches. The quart of orange juice costs $2.25, and the peaches are $0.75 each. The function f(x)=0.75x+2.25 represents julies expenses at the grocery store. What do the f(x) and the x represent?
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SOLUTION
From the funtion
[tex]f\mleft(x\mright)=0.75x+2.25[/tex][tex]\begin{gathered} f\mleft(x\mright)\text{ represents the total amount of money Julie spent on the grocery } \\ \text{store, } \end{gathered}[/tex]While
[tex]x\text{ represents the number of peaches Julie bought }[/tex]