Answer: 48 is the smaller integer
Step-by-step explanation: 48+49=97 48 and 49 are the two integers, 48 is smaller than 49.
2) a truck rental company rents a moving truck one day by charging $31 plus $0.13 per mile. write a linear equation that relates the cost c, in dollars, of renting the truck to the number x of miles driven. what is the cost of renting the truck if the truck is driven 180 miles? a) c(x)
The equation is c = 31 + 0.13x and total cost on driving 180 miles is $54.4.
Firstly we will form the equation using one time charge and the product of number of miles and charge per mile. Then we will keep the value in equation to find the total cost.
Forming the equation -
c = 31 + 0.13x
Keep the value of x in formula for calculation of total cost.
c = 31 + 0.13×180
Performing multiplication on Right Hand Side of the equation
c = 31 + 23.4
Performing addition on Right Hand Side of the equation
c = $54.4
Thus, the equation for calculation of total cost is c = 31 + 0.13x and total cost is $54.4.
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the owner of a small deli is trying to decide whether to discontinue selling magazines. he suspects that only 8.4% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. assuming his suspicion that 8.4% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 11 customers buy a magazine?
The probability that exactly 3 out of the first 11 customers buy a magazine is 2.23%
The proportion of customers that buy a magazine = 8.4%
If 3 out of the first 11 customers buy a magazine, then this proportion is given as; 3/11 or 27.27%
Therefore, the probability that 3 out of the first 11 customers will buy a magazine is calculated as follows;
probability = 8.4% × 27.27%
probability = (8.4/100) × (27.27/100)
probability = 0.084 × 0.2727
probability = 0.0223
Converting it into percentage as follows;
probability = 0.0223 × 100
probability = 2.23%
Therefore, the probability that 3 out of the first 11 customers buy a magazine is calculated to be 2.23%.
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Rewrite all 3 fractions with the least common denominator between them.
Answer:
To rewrite the given fraction with the least common denominator between them
The given fractions are,
[tex]\frac{1}{3},\frac{5}{10},\frac{7}{30}[/tex]we get, LCM of 3,10,30 is 30
The equivalent fractions for the above factions as common denominator 30 is as follows,
For 1/3,
Multiply and divide by 10, we get,
[tex]=\frac{1}{3}\times\frac{10}{10}=\frac{10}{30}[/tex]Using this we get,
[tex]\frac{1}{3}=\frac{10}{30}[/tex]For 5/10,
Multiply and divide by 3, we get,
[tex]\frac{5}{10}=\frac{5}{10}\times\frac{3}{3}=\frac{15}{30}[/tex]Using this we get,
[tex]\frac{5}{10}=\frac{15}{30}[/tex]For 7/30,
Since the denominator 30, we get same fraction,
[tex]\frac{7}{30}=\frac{7}{30}[/tex]Answer is:
[tex]\frac{1}{3}=\frac{10}{30}[/tex][tex]\frac{5}{10}=\frac{15}{30}[/tex][tex]\frac{7}{30}=\frac{7}{30}[/tex]I need help with this
Angle XBC is a corresponding angle to angle AXY.
The value of angle BXC is 30 degrees.
How to find measure of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.
Therefore, XY and BD are parallel lines and are cut by the transversal line AB and XC.
XBC forms an isosceles triangle.
∠AXY = 75 degrees.
∠XBC is a corresponding angle to ∠AXY.
Corresponding angles are congruent.
Therefore,
∠AXY = ∠XBC
Let's find the angle BXC.
The sum of angle in a triangle is 180 degrees.
The triangle BXC is an isosceles triangle. An isosceles triangle has base angles equal to each other.
Hence,
75 + 75 + ∠BXC = 180°
∠BXC = 180 - 150
∠BXC = 30°
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Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)
A button hyperlink to the SALT program that reads: Use SALT.
= 6; = 2
P(5 ≤ x ≤ 9) =
The probability P(5 ≤ x ≤ 9) is 0.6847
Assume that x has a normal distribution
We have been the mean and standard deviation μ = 6; σ = 2.
To calculate this probability we use the standardized normal distribution and the z-value for 5 and 9.
z = (5 - 6)/2
= -0.5
and z = (9 - 6)/2
= 1.5
Then the probability is calculated as:
P(x ≤ 5) = 0.3085
P(x ≤ 9) = 0.9932
P(5 ≤ x ≤ 9) = 0.9932 - 0.3085
P(5 ≤ x ≤ 9) = 0.6847
Therefore, the probability P(5 ≤ x ≤ 9) is 0.6847
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If the following fraction is reduced, what will be the exponent on the p ? -
2
5
4
3
The p has an exponent of 3 when the fraction is reduced
How to determine the exponent on p?The expression is given as
5p^5q^4/8p^2q^2
Remove all other variables, except the variable p
So, we have the following expression
p^5/p^2
Apply the law of indices in the above expression
So, we have the following equation
p^5/p^2 = p^5 - 2
Evaluate the difference
p^5/p^2 = p^3
The index on p is 3
Hence, the exponent on the p is 3
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Complete question
If the following fraction is reduced, what will be the exponent on the p? - 5p^5q^4/8p^2q^2 5 4 3 2
mad elf is a holiday beer that is 11.0% abv. a 12 oz bottle of mad elf has 300 calories. the rest of the calories, other than alcohol, come from carbohydrates. approximately how many grams of carbohydrates are in mad elf?
The bottle contains 9.36 g of carbohydrates.
We have,
12 oz bottle contains 300 calories
We know, 1 oz = 23.35 g
12 oz = 12 * 23.35 g =280.2 g of bottel
Alcohol content = 11 %
So, the total number of alcohol in the bottle is [tex]\frac{11}{100} *280.2 = 30.8 g[/tex]
So, the bottle contains 30.8 g of alcohol.
1 gram of alcohol 7 cal of energy,
So, 30.8 g of alcohol = 7 * 30.8 cal of energy
= 215.7 cal of energy
So, out of a total of 300 calories of mad elf, 215.7 calories come from alcohol.
So, (300-215.7 ) = 84.3 calories come from carbohydrates.
Each gram of carbohydrate produces 9 calories of energy.
9 calories of energy from 1 gram of carbohydrate,
1 calorie of energy from 1/9 of carbohydrate.
So, 84.3 calories from [tex]\frac{1}{9}*84.3 = 9.36 g[/tex]
Hence, the bottle contains 9.36 g of carbohydrates.
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The simple interest charged on a 65 day loan of $1250 is $7.75. Find the annual simple interest rate in precent for this loan round to the nearest tenth of a percent. Use 360 days in 1 year
We have a loan of 65 days.
The principal is $1250 and the interest is $7.75.
We have to find the annual simple interest rate.
We can express the interest of a loan of this type as:
[tex]I=r\cdot\frac{t}{360}\cdot P[/tex]where r = annual interest rate, t = period of the loan in days, I = interest and P = principal.
Then, we can rearrange the equation and replace with the values:
[tex]\begin{gathered} I=r\cdot\frac{t}{360}\cdot P \\ r=\frac{I\cdot360}{t\cdot P} \\ r=\frac{7.75\cdot360}{65\cdot1250} \\ r=\frac{2790}{81250} \\ r\approx0.03433846 \\ r\approx3.4\% \end{gathered}[/tex]Answer: the annual simple interest rate is 3.4%.
Which of the following are polynomials? Check all that apply.
The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.
What are polynomials?A polynomial is a type of algebraic expression in which the exponents of all variables should be a whole number. The exponents of the variables in any polynomial have to be a non-negative integer. A polynomial comprises constants and variables, but we cannot perform division operations by a variable in polynomials.
A) [tex]x^{-2}+15x-3[/tex]
Here, the exponent of x is -2. So, the expression is not a polynomial.
B) [tex]-x^3+5x^2+7\sqrt{x} -1[/tex]
Here, the power of one of the term is 1/2. So, the expression is not a polynomial.
C) [tex]\frac{3}{5}x^4-18x^2+5-\frac{10}{x^2}[/tex]
Here, the power of one of the term is -2. So, the expression is not a polynomial.
D) 5.3x²+3x-2
Here, the power of each term is positive integer. So, the expression is a polynomial.
E) [tex]4x^4-10[/tex]
Here, the power of each term is positive integer. So, the expression is a polynomial.
The power of each term in the expressions is D and E are positive integer. So, the expressions are a polynomial.
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45 POINTS PLEASE HELP!!!
Decide whether inductive or deductive reasoning is used to reach the conclusion
the wolf population in a park has increased each year for the last 10 years. So, the wolf population will increase again next year
39% of 80 74% of 240 91% of 82 66% of 160
9% of 71 126% of 80 234% of 145 97.9% of 39
52% of 57.9 33% of 15.3
Answer:
39% of 80 = 39.2
74% of 240 = 177.6
91% of 82 = 74.62
66% of 160 = 105.6
9% of 71 = 63.9
126% of 80 = 100.8
234% of 145 = 339.3
97.9% of 39 = 38.181
52% of 57.9 = 30.108
33% of 15.3 = 5.049
Step-by-step explanation:
In order to find the percentage of each equation, we will use the first one as an example. We take the 39%, and convert it to 0.39 and get rid of the %. Then, "of" means multiplication.
So, we have:
0.39 x 80 = 39.2
Darnell and emma are college students . darnell currently has 22 credits and he plans on taking 6 credits per semester . emma has 4 credits and plans to take 12 credits per semester . after how many semesters , s will darnell and emma have the same number of credits ?
After 3 semesters Darnell and Emma have same number of credits as 40.
Given,
Current credit score of Darnell = 22
Current credit score of Emma = 4
Darnell plans to score a credit per semester = 6
Emma plans to score a credit per semester = 12
Now, we have to find that after how many semesters will Darnell and Emma have the same number of credits .
Here,
Current credit score of Darnell = 22
Current credit score of Emma = 4
After 1 semester,Credit score of Darnell = 22 + 6 = 28
Credit score of Emma = 4 + 12 = 16
After 2 semester,Credit score of Darnell = 28 + 6 = 34
Credit score of Emma = 16 + 12 = 28
After 3 semester,Credit score of Darnell = 34 + 6 = 40
Credit score of Emma = 28 + 12 = 40
That is,
After 3 semesters Darnell and Emma have same number of credits as 40
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A pet store makes a profit of $4.75 per bag on its line of organic dog food. The store wants to make a profit of no less than $5,700. Could selling 1,300 bags of dog food meet this goal?
all you need is in the photo please answer fastplease
Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
Match each number to its opposite. 1. -8 8 2. -1 -11 3. -17 17 4. 31 -31 5. 11 1
The opposite for each number is: ( -8, 8), (-1,1), (-17,17), (31,-31) and (11,-11).
Number Classification Whole Numbers - They are the numbers represented by positive real numbers where the fractions and decimal numbers are not included. Integer Numbers - They are the whole numbers. They are represented by zero, positive and negative numbers. Opposite numbers - They are numbers that the distance to 0 is equal. The numbers are classified as the opposite when the sum between them is equal to zero (0).Thus, you can conclude that the opposite number of a positive number is a negative number. And the opposite number of a negative number is a positive number.
The question gives the follow numbers
1. -8 8
2. -1 -11
3. -17 17
4. 31 -31
5. 11 1
The opposite for:
-8 is the number 8-1 is the number 1-17 is the number 1731 is the number -3111 is the number -11Read more about number classifications here:
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can you take 73 devided by 17 and it be a whole number
Two cylinders have the same volume. The first has a radius of 5cm and a height of 10 cm. The second has a radius of 10cm. The surface area of the first cylinder is and the surface area of the second i s
ANSWER
[tex]\begin{gathered} 1)150\pi \\ 2)250\pi \end{gathered}[/tex]EXPLANATION
For the first cylinder;
[tex]\begin{gathered} r=5 \\ h=10 \end{gathered}[/tex]Recall, the formula for calculating the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Now, substitute the values for the first cylinder;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times5\times10+2\times\pi\times5^2 \\ =100\pi+50\pi \\ =150\pi \end{gathered}[/tex]The volume of the first cylinder is calculated using the formula;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ \end{gathered}[/tex]Substitute the values of r and h for the first cylinder;
[tex]\begin{gathered} V=\pi \cdot \:r^2\cdot \:h \\ =\pi\times5^2\times10 \\ =\pi\times25\times10 \\ =250\pi \end{gathered}[/tex]To get the surface area of the second cylinder, we need to calculate the height (h).
To get the height, we use the volume of the first cylinder to get the height of the second (since they have the same volume).
Hence;
[tex]\begin{gathered} V=250\pi \\ r=10 \\ V=\pi r^{2}h \\ 250\pi=\pi\times10^2\times h \\ h=\frac{V}{\pi \cdot \:r^2} \\ h=\frac{250\pi }{\pi 10^2} \\ =2.5 \end{gathered}[/tex]Substitute the height to calculate the surface area is calculated thus;
[tex]\begin{gathered} A=2\pi rh+2\pi r^{2} \\ =2\times\pi\times10\times2.5+2\times\pi\times10^2 \\ =50\pi+200\pi \\ =250\pi \end{gathered}[/tex]Sara buys $30 of produce at the farmer's market. She spends $5more on green vegetables than she does on fruit. How much didSara spend on green vegetables? How much did she spend onfruit? Write and solve a system of equations.
Okay, here we have this:
Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:
According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:
[tex]\begin{gathered} x+y=30 \\ x+(x+5)=30 \end{gathered}[/tex]Now let's solve for x in the second equation:
x+x+5=30
2x+5=30
2x=30-5
2x=25
x=25/2
x=12.5
Now from the value of x that we got, then we will plug it into the first equation to get the value of y:
[tex]\begin{gathered} x+y=30 \\ 12.5+y=30 \\ y=30-12.5 \\ y=17.5 \end{gathered}[/tex]Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.
ILL Give one hundred points and Branly only if you do it right though
Answer:
1) -2
2) -2
3) -2
4) -3
5) -4
6) -15
7) -13
8) 3
1b) -9
2b) -2
3b) 7
4b) 17
5b) -4
6b) -9
7b) -16
8b) 0
1c) -5
2c) -3
3c) 0
4c) -2
5c) -8
6c) -11
7c) -3
8c) 15
Jeez, I hope this helps xD
According to the distributive property, a(5 + b) =
Answer:
From the bit that you have given , we can say = 5a + ab = to the rest of the equation
help please i need it
I will give 100 points to anyone who can answer my question.
Answer:
A system of nonlinear equations is a system where at least one of the equations is not linear. Just as with systems of linear equations, a solution of a nonlinear system is an ordered pair that makes both equations true. In a nonlinear system, there may be more than one solution.
Answer:
The answers are (-10, -4) and (0, 1)
Step-by-step explanation:
The solution to a system of equations is the point where both lines intersect. In this case, all you have to do is mark the points of intersection and look at their coordinates.
Hope this helps!
Change 6.3 kg to grams pls it's urgent
Answer:
6,300 grams
Step-by-step explanation:
kg to g is multiply by 1,000
Answer:
Step-by-step explanation:
630%
pls explain with working out
Answer: 26m
Step-by-step explanation:
The area is 36m^2, the possible measurement that could've worked is 4m for width and 9m for length (4x9=36). Now just do 4+4+9+9 = 26m.
Hope this helped
If a train runs on a circular track of radius 400 meters through all four sections of the park, about how long is the part of the train track that runs through Water World?
The arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]In this case the radius is 400 m and the angle is 36°, plugging these values we have:
[tex]\begin{gathered} s=2\pi(400)(\frac{36}{360}) \\ s=251.33 \end{gathered}[/tex]Therefore, the part of the train track that runs through water world is approximately 250 meters.
Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)?
The equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line that is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2),
The midpoint of line joining (-4,4) and (2,-2) will be -
x[m] = (- 4 + 2)/2 = -1
y[m] = (4 - 2)/2 = 1
Coordinates of the midpoint will be M(-1, 1)
Slope of the line joining (-4,4) and (2,-2) will be -
m = (- 2 - 4)/(2 + 4)
m = -6/6
m = - 1
Then, the slope of the line perpendicular to this line will be -
m[p] = -1/-1
m[p] = 1
Assume that the equation of the perpendicular line as -
y[p] = x + c
Since it passes though (-1, 1) so -
1 = -1 + c
c = 2
Therefore, the equation of the line perpendicular to the line line joining (-4,4) and (2,-2) will be → y = x + 2.
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PLS HELP DUE NOWWWWWWWWWW
The correct statement will be:
A. The rate of change is the number of inches grown per month, and the initial value is the starting height.
We can form the following equation from the given data:
H(m) = 13 + 41m,
Where H ( Height ) is a function of the number of months ( m ).
We can see that the height changes with respect to months i.e. as the number of months increases, the height of the sunflower also increases.
The initial value or the initial height of the sunflower remains constant throughout and has less impact on its height.
So, option A will be the ultimate explanation for the data given.
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Answer:
Step-by-step explanation:
This is a linear function of time, as mentioned.
A linear function is always in the form of:
[tex]y=mx+b[/tex]
The 'sunflower's height is a linear function of time', so the [tex]x[/tex] variable represents the time (which is in terms of months here), and the [tex]y[/tex] would represent the sunflower's height after time has passed.
The initial value is when [tex]x=0[/tex].
[tex]x=0[/tex] means at the very beginning.
At the very beginning, the height would be the starting height, so the initial value would be the starting height.
The rate of change means the change in [tex]y[/tex] in respect to [tex]x[/tex].
Since [tex]y[/tex] represents the height after [tex]x[/tex] months, the rate of change would be the change in height per month.
You could also write it as the number of inches grown per month.
The initial value is the starting height, and the rate of change is the number of inches grown per month, so the correct answer is (A).
Kaj invests money in an account paying a simple interest of 1.2% per year. If she invests $90 and no money will be added or removed from the investment, how much will she have in one year, in dollars and cents?
Answer:
$91.08
Step-by-step explanation:
Interest = $90 × .012 = $1.08
Total amount = $90 + $1.08 = $91.08
Hi, can y oh please me I’m stuck on this question.
The measure of angle 2 is 81° because angles 1 and 2 are corresponding angles.
Corresponding angles:
Corresponding angle means the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.
Given,
Two electricity poles are built standing parallel to each other, as shown below. The measure of angle 1 is 81°.
Here we need to find the measure of the angle 2.
We know that,
If the lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet.
And as per the definition of corresponding angles, we know that, if any two lines are said to be parallel if the Corresponding angles so formed are equal.
Then the measure of the angle 2 is 81° because angle 1 and 2 are parallel.
Therefore, those angles are the corresponding angles also.
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Can anyone please answer this question, Ill give points.
Answer:
(0,1) and (-10.-4)
Step-by-step explanation:
To find the solutions, find the points where both the curve and line intersect and read off the coordinates