Answer: We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.
We know that:
x + y = 45 (the total number of gallons consumed by both cars)
15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)
We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.
From the first equation, we can solve for x:
x = 45 - y
We can substitute this expression of x into the second equation:
15(45 - y) + 30y = 975
Simplifying the left side of the equation:
675 - 15y + 30y = 975
Subtracting 675 from both sides:
15y = 300
And finally divide both sides by 15:
y = 20
So the second car consumed 20 gallons of gas that week.
We can substitute this value of y back into the equation x = 45 - y to find the value of x
x = 45 - 20 = 25
So the first car consumed 25 gallons of gas that week.
Step-by-step explanation:
please show solution thank you<3
For what positive integers $c$, with $c < 100$, does the following quadratic have rational roots?
\[ 3x^2 + 20x + c \]
If you find more than one, then list the values separated by commas.
Answer: A quadratic of the form $ax^2 + bx + c$ has rational roots if and only if its discriminant, $b^2 - 4ac$, is a perfect square. In this case, the discriminant is $(20)^2 - 4(3)(c) = 400 - 12c$. So, we need to find the positive integers $c < 100$ that make $12c$ a perfect square.
The perfect squares that are less than $100$ are $1,4,9,16,25,36,49,64,81$, so the possible values for $c$ are $33,44,55,66,77,88$.
So, the positive integers $c$, with $c < 100$, that make the quadratic have rational roots are $33,44,55,66,77,88$
Step-by-step explanation:
HELPPP PLEASEEE take your time , explanation please
Answer:
3 1/10 as a fraction
Step-by-step explanation:
3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.
33 is repeating
When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.
EXAMPLE:3.3% - the place value is ones. It is a whole number and called as three.
3.3% - the place value is tenths. It is called as three-tenths.
ANSWER= 3 3/10 as this can't be simplified.PERCENT TO DECIMAL
When you convert a percent to decimal, you must divide it by 100.
SOLUTION (in the photo)3.3 ÷ 100
ANSWER= 0.33i need help me alot plss
Evaluate. Write your answer as a fraction in simplest form.
Answer: 16/81
Step-by-step explanation:
To do this you have to do 2^4 which is 16.
Next, you have to do 3^4 which is 81
This gives you 16/81.
Now check if you can simplify it.
You can't so this is your answer :D
I hope this was able to help you :D
Quincy and Celine have to move 16 small boxes and 10 large boxes. the chart indicates the time that each person takes to move each type of box. they start moving the boxes at 9.00 a.m. the earliest time at which they can be finished moving all of the boxes is:
a. 9:41 a.m
b. 9:42 a.m
c. 9:43 a.m
d. 9:44 a.m
e. 9:45 a.m
The earliest time at which they can be finished moving all of the boxes is: d. 9:44 a.m
Quincy and Celine the earliest timeTo determine the earliest time at which Quincy and Celine can finish moving all of the boxes, we need to determine the maximum amount of time it will take for them to move all of the boxes. We can do this by calculating the time it will take for each person to move each type of box individually, and then adding those times together.
Quincy takes 1 minute to move a small box and 2 minutes to move a large box. Celine takes 2 minutes to move a small box and 3 minutes to move a large box.
So, for Quincy:Time to move 16 small boxes: 16 boxes * 1 minute/box = 16 minutes
Time to move 10 large boxes: 10 boxes * 2 minutes/box = 20 minutes
Total time for Quincy: 16 minutes + 20 minutes = 36 minutes
For Celine:Time to move 16 small boxes: 16 boxes * 2 minutes/box = 32 minutes
Time to move 10 large boxes: 10 boxes * 3 minutes/box = 30 minutes
Total time for Celine: 32 minutes + 30 minutes = 62 minutes
To get the earliest time they can finish moving all the boxes, we take the maximum of the two times:
Max(36 minutes, 62 minutes) = 62 minutes
Start time: 9:00 a.m.
End time: 9:00 a.m. + 62 minutes = 9:62 a.m.
So the earliest time they can finish moving all the boxes is 9:62 a.m.
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Mr. Jones invested a sum of money in 6% bonds. He invested $400 more than this sum in 4% bonds. If his total annual income was $116, how much did he invest in each kind of bond?
a = amount invested at 6%
how much is 6% of "a"? (6/100) * "a", namely 0.06a.
b = amount invested at 4%
how much is 4% of "b"? (4/100) * "b", namely 0.04b.
we also know that the yielded amount in interest or the annual income he's got from both is $116, so if we simply add their interest, that'd be 0.06a + 0.04b = 116.
We also know that he invested 400 more in "b" than in "a", so whatever "a" might be, we know that b = a + 400.
[tex]0.06a~~ + ~~0.04(\stackrel{b}{a+400})~~ = ~~116\implies 0.06a+0.04a+16=116 \\\\\\ 0.10a+16=116\implies 0.10a=100\implies a=\cfrac{100}{0.10} \\\\\\ \boxed{a=1000}\hspace{5em}\stackrel{1000+400}{\boxed{b=1400}}[/tex]
Hame:
Date:
Per.
3. The distance between Venice and Florence is 171 miles. It takes 2% hours
to travel from Venice to Florence by train. Write an equation that
represents the distance travelled, d, and the time, t.
The equation that relates velocity, distance and time is given as follows:
v = 171/2.
How to obtain the equation?The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:
v = d/t.
In which:
v is the velocity.d is the distance.t is the time.The parameters for this problem are given as follows:
d = 171, t = 2.
Hence the equation that gives the velocity in miles per hour is of:
v = 171/2.
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Find the area of a window that measures 3 yards by 34 yard.
Answer:
102
Step-by-step explanation:
34x3=102
Consider the following sample data.
14 9 19 18 5
8
Calculate the z-score for the following values.
a. 12
b. 6
c. 15
d. 13
The z-score for a-d are?
(Round to two decimal places as needed.)
Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.
What are z-scores?In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.
A z-score is calculated using the following formula:
data point = mean standard deviation
Data point means with standard deviation equal to z
The same equation is given below in symbol form:
z= x−μ / σ
Some significant z-score details are as follows:
An elevated z-score indicates that the data point is.
When a data point has a negative z-score, it is below average.
The data point is considered to be roughly average if the z-score is near to 0.00.
If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.
At Almond, the average score on a history midterm is
= 85 = 85mu, which is equivalent to 85 with a standard deviation of
= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2
On the test, Michael received a score of 86.866.668.
Calculate Michael's exam grade in Z-score form.
His Grade = Mean Grade Standard Deviation
= 86 − 85 / 2
= 1 /2 = 0.5 z z z
= standard deviation of his grade and mean grade.
= 2 / 86−85
= 2 / 1 =0.5.
The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.
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Zachary measures the area of a glacier at
the start of every year.
2
At the start of this year, the glacier had an
area of exactly 56.20 km². This is 0.2%
less than it was at the start of last year.
Work out what the area of the glacier was
at the start of last year.
2
Give your answer in km² to 2 d.p.
The area of the glacier at the start of last year was 56.31 km², based on a percentage reduction of 0.2%.
What is a percentage decrease?A percentage decrease represents the difference between the starting and ending values, expressed as a percentage of the starting value.
In working out the percentage reduction, we determine the difference between the ending and starting values. This difference is divided by the starting value and multiplied by 100.
The current area of the glacier = 56.20 km²
The percentage reduction = 0.2%
Proportionately, the current area, in percentage terms = 99.8% (1 - 0.2%)
99.8% = 56.20 km²
100% = 56.31 km²
Thus, to 2 decimal points, the area of the glacier at the start of last year was 56.31 km².
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1. If m angle ABD = 60°, find m angle
BDC.
Answer:
If angle ABD = 60°, then angle BDC can be found using the fact that the measures of the angles in a triangle add up to 180°.
So, m(angle BDC) = 180 - (m(angle ABD) + m(angle BDA))
Therefore, m(angle BDC) = 180 - (60 + m(angle BDA))
So the measure of angle BDC is not fixed, it depends on the measure of angle BDA.
The following loan is discounted. Find (a) the discount, (b) the amount of money received, and (c) the true interest rate. P=$13,300.0, r=3 1/2%, t=4 years
a) The discount on the loan is $1,862.
b) The amount of money the borrower received on the discount loan is $11,438.
c) The true interest rate paid on the discounted loan is 4.1%.
What is a discount loan?A discount loan is a type of loan in which the interest (cost of borrowing) is deducted upfront or at the time the loan is granted.
The implication of getting a discount loan is that the amount received is less than the principal amount because the grantor has reduced it by interest and other fees (finance charges).
The principal = $13,300
Discount rate = 3¹/₂%
Time = 4 years
Discount = $1,862 ($13,300 x 3.5% x 4)
Amount received = $11,438 ($13,300 - $1,862)
Real interest rate = 4.1% ($1,862/$11,438 x 100)/4
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Insurance cost is to be distributed among manufacturing, selling and administration in the ratio of 1/10 to 1/3 to 1/9. If the total cost was $12,005 how should it be distributed to these departments
Manufacturing should pay $2206.80, Selling should pay $7356.0and Administration should pay $2452.00
What is the distribution?Generally, To find out how much each department should pay, you can use the proportion of the cost that corresponds to their respective ratio.
First, calculate the total ratio by adding the three ratios together:
1/10 + 1/3 + 1/9 = 0.544
Then, divide the total cost by the total ratio to find the unit cost:
$12,005 / 0.544 = $22068.01
Next, multiply the unit cost by the ratio for each department to find out how much they should pay:
Manufacturing: $22068.01 x 1/10 = $2206.80
Selling: $22068.01 x 1/3 = $7356.0
Administration: $22068.01 x 1/9 = $2452.00
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quantify the statement A(x) the square root of x raise to power 2 plus 4x plus 3 is a real number
A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic.
Which quadratic equation is the most fundamental?Quadratic equations or quadratic functions. A polynomial equation of the second degree, or a quadratic, must contain at least one squared term to be considered a quadratic. Equations using quadratics is another name for it. The quadratic equation is expressed in its general form as ax2 + bx + c = 0.
For instance, 6x2 + 11x - 35 = 0, 2x2 - 4x - 2 = 0, 2x2 - 64 = 0, x2 - 16 = 0, x2 - 7x = 0, 2x2 + 8x = 0, etc. are examples of quadratic equations.
Three kinds of quadratics are frequently employed:
Standard Form: y = an x 2 + b x + c y = an x 2 + b x + c
y = a (x r 1, x r 2) is the factored form. y=a(x-r 1)(x-r 2) y=a(x−r1)(x−r2)
Vertex Formula: y=a (x h) 2 + k y=a (x-h)2 + k y=a (x-h) 2+k.
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14. Higher Order Thinking Lake Trail is 4 3/5ths miles long. Outlook Trail is 5 5/6ths miles long. Pinewoods Trail is 1 3/10ths miles longer than Lake Trail. Which trail is longer, Pinewoods Trail or Outlook Trail? Explain.
please help me :)
The Pinewoods Trail is longer than the Outlook Trail.
What are fractions?The definition of a fraction is a portion of a whole. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin.
Given the length of Lake Trail = 4 and 3/5 mile
length of Lake Trail = 23/5 miles
length of Outlook Trail = 5 and 5/6 mile
length of Outlook Trail = 35/6 miles
length of Pinewoods Trail = 1 and 3/10 miles longer than Lake Trail
length of Pinewoods Trail = 33/10 + 23/5
length of Pinewoods Trail = (33 + 46)/10
length of Pinewoods Trail = 79/10 miles
comparing the length of Outlook Trail and Pinewoods Trail,
which is 35/6 and 79/10 miles respectively,
the common denominator for both is 30,
35/6 = (35*5)/(6*5)
35/6 = 175/30
and 79/10 = (79*3)/(10*3)
79/10 = 273/30
here 273/30 > 175/30
Hence Pinewoods Trail is longer.
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Adding and subtracting fractions
1 These diagrams show the distances four cyclists have cycled.
Write a calculation of the total distance each cyclist cycled.
a -
7/8 km
9/10 km
3/2km
Total distance travelled by the cyclist is 131/40 km in fraction.
What is fraction ?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.
The three main sorts of fractions are as follows. Proper fractions, improper fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its kinds based on these two parameters.
Total distance travelled by the cyclist is 7/8 + 9/10 + 3/2 = 131/40 km
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paula used these steps to solve an equation
We can conclude that the division property of equality was done between step 4 and step 5.
What is linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then
a/c = b/c
At step 4: The equation was -6x = 57
To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below
-6x = 57
---- Divide both sides by -6 (Step 4)
-6x / -6 = 57 / -6
---- (Intermediary between step 4 and 5)
x = -9.5
----- Step 5
Hence, we can conclude that the division property of equality was done between step 4 and step 5
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(A+7) (A+7) (A+7) (A+7)
Write the expression using exponential form
Answer:
(A+7)^4
Step-by-step explanation:
If you do a report on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, are you using a sample
or population?
Answer: If you are reporting on the age, occupation, and zip codes of all breast cancer patients the hospital saw last year, you are using a population.
A population is a complete set of all the individuals or elements that share a common characteristic, such as all breast cancer patients seen at a hospital in a given year. A sample, on the other hand, is a subset of a population that is selected for analysis or study.
In this case, since you are reporting on all breast cancer patients seen at the hospital last year, you are using the entire population of breast cancer patients, rather than just a sample of them.
Step-by-step explanation:
Write an expression to represent:
3 minus the product of 2 and x
.
Answer: 3 - 2x
Step-by-step explanation:
Product = Multiplication
Product of 2 and x = 2*x
3 minus 2x
3-2x
Answer:
3−2×x or 3-(2xx)
find examples that contradict the conclusions of proposition 2.4.10 if a and b are not coprime (i.e. share a factor greater than ).
The conclusion of the proportion is if a and bare not coprime, when it share a factor greater than 1
Here we have given that if and are not coprime that is share a factor greater than.
And we need to find the examples that contradict the conclusions of proposition.
While we looking into the given question, we have identified that if and are not coprime.
In order to find the conclusion to this one, we must know the definition of co prime.
The term co prime is referred as those umbers that do not have any common factor other than 1.
As per the definition, we have clearly know that if the two number has the factor greater than one then it will not a co prime to each other.
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When the function f(x) is divided by 2x + 1, the quotient is x² - 8x + 8 and the
remainder is 5. Find the function f(x) and write the result in standard form.
Please help
The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.
What will be the function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5?The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:
f(x) = (2x + 1)(x² - 8x + 8) + 5
Simplifying the above gives the following:
f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5
f(x) = 3x³ - 15x² + 8x + 13
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Randomly selected adults at a coffee shop were asked how many hours they work in a typical workday. The results are tabulated in the following frequency table.
The histogram that accurately summarizes the data in this problem is given by the second image presented at the end of the answer.
How to draw the histogram?The histogram of a data-set shows the number of times that each item was observed in the data-set.
From the first image given at the end of the answer, the absolute frequencies are given for each observation, which is the height of each bin of the histogram.
Missing InformationThe problem is given by the first image presented at the end of the answer.
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If using the method of completing the square to solve the quadratic equation x^2-16x-34=0, which number would have to be added to "complete the square"?
To complete the square, you would add (16/2)^2 = 64/4 = 16 to both sides of the equation.
What does a math quadratic equation mean?x ax2 + bx + c = 0 is a quadratic equation, which is a 2nd quadratic formula in a single variable. a 0. It has at most one solution since it is a 2nd polynomials equation, which is guaranteed by the algebraic fundamental theorem.
How can you tell whether or not an equation is quadratic?In other terms, you have a quadratic equation if a times the squares of the equation after b plus b twice that the same phrase not square plus c equals 0. The initial equation will change to a quadratic equation if the value in the () is replaced with such a variable like t.
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Find the area of the figure.
Answer: 38
Step-by-step explanation:
You can split this shape into 2 rectangles. The area of the two rectangles = 5 * 4 + 6 * 3
= 20 + 18
= 38
if f(x)=x^2 and g(x)=x, determine the value(s) of x that satisfy the equation f(x) = g(x)
Answer:
1 or 0
Step-by-step explanation:
in order for a number's square equals to itself, it has to be 1 or 0.
Which verbal expression best represents the equation 2(n - 7) = -14
a) twice a number less than seven is equal to negative fourteen
b) the product of two and seven less than a number is equal to negative fourteen
c) seven less than twice a number is equal to negative fourteen
d) negative seven minus twice a number is negative fourteen
The verbal expression that best represents the equation 2(n - 7) = -14 is: c) seven less than twice a number is equal to negative fourteen.
What is verbal expression?Verbal expression can be defined as the way of writing mathematical expression into words or translating equation into words.
Now let interpret this equation 2(n - 7) = -14 into verbal expression.
n = a number
2n = twice a number
2n - 7 = seven less than twice a number
-14 = negative fourteen
Therefore we can conclude that the correct option is C.
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y=3+4+369/2 plas helppppp
Answer:
191.5
Step-by-step explanation:
determine if (x-3) is a factor of (x^4-13x^2+36) using synthetic division
Answer:
Yes, (x-3) is a factor of (x^4-13x^2+36) using synthetic division.
Synthetic division:
| x -3 |
x^4 -13x^2+36
x^3 -10x^2+27x-108
The remainder is zero, so (x-3) is a factor of the polynomial (x^4-13x^2+36).
Step-by-step explanation: