Answer: he should have 348 cars and 173 trucks.
Step-by-step explanation:
Let x represent the number of cars that he should have.
Let y represent the number of trucks that he should have.
He has room on his lot for 521 vehicles. It means that
x + y = 521- - - - -- - - - -1
Ramon has 175 more more cars than trucks. It means that
x = y + 175
Substituting x = y + 175 into equation 1, it becomes
y + 175 + y = 521
2y = 521 - 175 = 346
y = 346/2
y = 173
x = y + 175 = 173 + 175
x = 348
To determine the number of cars and trucks on Ramon's lot, two equations were formed: T + C = 521 and C = T + 175. Solving these equations simultaneously, it was found that Ramon should have 173 trucks and 348 cars.
Explanation:Ramon's Car and Truck Problem
Let us define the number of trucks Ramon has as T and the number of cars as C. According to the problem, Ramon has room for 521 vehicles on his lot. The problem states that Ramon has 175 more cars than trucks, so we can express this as C = T + 175.
We know the total number of vehicles Ramon can have is 521, which leads us to the following equation: T + C = 521. Substituting the first equation into the second, we get T + (T + 175) = 521. Simplifying, 2T + 175 = 521. Subtracting 175 from both sides, 2T = 346. Dividing by 2, we find that T = 173. This means Ramon has 173 trucks on his lot.
Now, we substitute the value of T back into the equation for C: C = 173 + 175, which equals 348. So, Ramon should have 348 cars and 173 trucks on his lot.
A family has two cars during one particular week the first car consume 25 gallons of gas and the second consumed 15 gallons of gas the two cars Drove a combined total of 1075 miles and the sum of the fuel efficiencies was 55 miles per gallon what were the fuel efficiencies of each of the cars that week?
Answer: the efficiency of the first car is 25 miles per gallon.
the efficiency of the second car is 30 miles per gallon.
Step-by-step explanation:
Let x represent the efficiency of the first car.
Let y represent the efficiency of the second car.
Distance = car efficiency × number of gallons.
The first car consume 25 gallons of gas and the second consumed 15 gallons of gas. The two cars Drove a combined total of 1075 miles. It means that
25x + 15y = 1075- - - - - - - - - - -1
The sum of the fuel efficiencies was 55 miles per gallon. It means that
x + y = 55
Substituting x = 55 - y into equation 1, it becomes
25(55 - y) + 15y = 1075
1375 - 25y + 15y = 1075
- 25y + 15y = 1075 - 1375
- 10y = - 300
y = - 300/-10
y = 30
x = 55 - y = 55 - 30
x = 25
Is 3,4,5 a Pythagorean triple
Answer:
Yes because it fits the Pythagorean Theorem
Step-by-step explanation:
see: 5 ^2 = 25
and 3^2 + 4^2 = 9 + 16 = 25
25 = 25
so it is
Use the graphing tool to see what happens to the polynomial function when you change more than one parameter at a
time. In what ways is this new graph different from the parent graph of f(x) = x ? Write down your observations for
each of these transformed functions. Then try a few of your own
· g(x) = (x - 2) + 1
· g(x) = 3x4 - 6
· g(x) = 2(x + 3)* + 10
· g(x) = { (6x - 1)
Answer:
The parent graph of (x-2)^4+1 shifts 2 units to the right and one unit up.
The parent graph of 3x^4-6 is stretched vertically by a factor of 3 and then shifted 6 units down.
The parent graph of 2(x+3)^4+10 is shifted 3 units to the left, stretched vertically by a factor of 2 and shifted 10 units up.
The parent graph of 1/4(6x-1)^4 is shifted one unit to the right, compressed horizontally by a factor of 1/6 , and compressed vertically by a factor of 1/4.
Step-by-step explanation:
Identify the 4 basic transformations (reflections, rotation, translation, dialation,
Answer:
Reflection: your object or shape is either side by side (y axis) or above each other (x axis)
Rotation: Spinning your object or shape around a point
Translation: Shifting all the points of your object or figure
Dilation: The shape or object is either shrinking or expanding
Step-by-step explanation:
Gabriel makes a model of a pyramid with the dimensions shown. A square pyramid. The square base has side lengths of 12 inches. The triangular sides have a height of 11 inches. Gabriel wants to paint the model. How much paint will he need? The area of the square base is in.2. The area of each triangular face is in.2. Gabriel will need in.2 of paint.
Answer:
Area of the square base: 144 in²
Area of each triangular face: 66 in²
Amount of paint needed: 408 in²
Step-by-step explanation:
We basically want to find the surface area of this square pyramid.
First, find the areas of the 4 triangular sides. The area of a triangle is denoted by: [tex]A=\frac{1}{2} bh[/tex], where b is the base and h is the height.
Here, the base coincides with the side length of the square, so b = 12. The height is 11, so h = 11. Plug these in:
[tex]A=\frac{1}{2} bh[/tex]
[tex]A=\frac{1}{2}[/tex] * 12 * 11 = 66 inches squared
Each triangular face is thus 66 inches squared.
Since there are 4 triangles, multiply 66 by 4: 66 * 4 = 264 inches squared
Now, find the area of the square base. The area of a square is: A = s * s, where s is the side length. Here, the side length is 12, so s = 12. Plug this into the equation:
A = s * s
A = 12 * 12 = 144
So, the square base is 144 inches squared.
Finally, add 144 to 264 to get the total area Gabriel needs to paint:
144 + 264 = 408 inches squared
Answer:
The area of the square base is 144 in²
The area of each triangular face is 66 in²
Gabriel will need 408 in² of paint.
Step-by-step explanation:
The area of the square base is:
12² = 144 in²
The area of each triangular face:
½(12×11) = 66 in²
Gabriel will need:
4(66) + 144 = 408 in²
It takes one student 12 hours to wash all of the cars at a school car wash. If 8 students wash all the cars, how many hours will each person spend washing cars?
Answer:
Each person will wash all cars for 0.1875 hours
Step-by-step explanation:
One student takes time to wash all cars = 12
8 students take time to wash all cars = [tex]\frac{12}{8}= 1.5 hours[/tex]
So, 8 students together takes 1.5 hours to wash the car
Each person spent hours on washing all cars =[tex]\frac{1.5}{8}[/tex]
Each person spent hours on washing all cars =0.1875 hours
So, Each person will wash all cars for 0.1875 hours
The diameter of a circleis 170inches. The circle has two chords of length 26 inches. What is the distance from each chord to the center of the circle?
Answer:
Hence the Distance from each other chord to center is 84 inches.
Step-by-step explanation:
Given:
Diameter =170 inches
2 chords with each length =26 inches.
To Find:
Distance of each chord from the circle.
Solution:
Consider a circle with center as O ,
And OA as Radius
(Refer the attachment)
So as chord be BC and DE respectively with each of 26 length
They have both same length so they should located at same distance from center but as mirror images of each other opposite side of the diameter as shown in fig.
Hence we can calculate for one chord as follows:
Radius =diameter/2=170/2=85
r=85 inches.
Let distance from center t o chord be 'x'
Now draw perpendicular to chord BC with F as midpoint for chord and join endpoints of chord to the center which forms triangle OFC as right angled triangle,
By using pythagorus Theorem
[tex]OC^2=FC^2+OF^2[/tex]
Here OC=85 inches , FC=26/2=13 inches.
So
[tex]85^2=13^2+OF^2[/tex]
[tex]OF^2=85^2 -13^2[/tex]
[tex]OF^2=7225-169[/tex]
[tex]OF^2=[/tex]7056
[tex]OF=84[/tex] inches
Hence the Distance from each other chord to center is 84 inches.
Suppose that the ages of members in a large billiards league have a known standard deviation of σ = 12 σ=12sigma, equals, 12 years. Hernando plans on taking a random sample of n nn members from this population to make a 95 % 95%95, percent confidence interval for the mean age in the league. He wants the margin of error to be no more than 5 55 years. Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Answer:
[tex]n\geq 23[/tex]
Step-by-step explanation:
-For a known standard deviation, the sample size for a desired margin of error is calculated using the formula:
[tex]n\geq (\frac{z\sigma}{ME})^2[/tex]
Where:
[tex]\sigma[/tex] is the standard deviation[tex]ME[/tex] is the desired margin of error.We substitute our given values to calculate the sample size:
[tex]n\geq (\frac{z\sigma}{ME})^2\\\\\geq (\frac{1.96\times 12}{5})^2\\\\\geq 22.13\approx23[/tex]
Hence, the smallest desired sample size is 23
Hernando needs to take a sample size of at least 23 members.
To determine the smallest sample size required for Hernando to achieve a 95% confidence interval with a margin of error no more than 5 years, we can use the formula:
n = (Z * σ / E)²
where:
Z is the Z-value from the standard normal distribution for a 95% confidence level, which is 1.96σ (sigma) is the standard deviation, which is 12 yearsE is the desired margin of error, which is 5 yearsPlugging in the values, we get:
n = (1.96 * 12 / 5)²
n = (23.52 / 5)²
n = (4.704)²
n ≈ 22.14
Since the sample size must be a whole number, we round up to the nearest integer, making the smallest required sample size n = 23.
A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?
system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is [tex]x+8y=68[/tex] and [tex]3x+4y=64[/tex] .
Step-by-step explanation:
Here we have , A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. We need to find Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y . Let's find out:
Let the price in dollars of each large candle, x, and each small candle, y .So
A customer at a store paid $64 for 3 large candles and 4 small candles
Equation is :
⇒ [tex]3x+4y=64[/tex] .....(1)
At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.
Equation is :
⇒ [tex]x+8y=68[/tex] .......(2)
3(2)-(1) i.e.
⇒ [tex]3(x+8y)-(3x+4y)=68(3)-64[/tex]
⇒ [tex]20y=140[/tex]
⇒ [tex]y=7[/tex]
So , [tex]x+8y=68[/tex]
⇒ [tex]x+8(7)=68[/tex]
⇒ [tex]x=12[/tex]
Therefore , system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is [tex]x+8y=68[/tex] and [tex]3x+4y=64[/tex] .
The system of equations that can be used to find the price in dollars of each large candle, x, and each small candle, y are;
3x + 4y = 64
x + 8y = 68
$64 was paid for 3 large candles and 4 small candles. If large candle cost x and small candle cost y, then;
3x + 4y = 64
Now, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.
Thus;
x + 8y = 64 + 4
x + 8y = 68
Thus, the system of equations that can be used to find the price in dollars of each large candle, x, and each small candle, y is;
3x + 4y = 64
x + 8y = 68
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How to write 4 divisors of 240 that are multiples of tens
The divisors of 240 which are multiples of tens are 10, 20, 30, and 60.
Explanation:To identify divisors of 240 that are multiples of tens, we must first understand what a divisor is. A divisor is a number that divides another number evenly. For example, in the case of 240, some notable divisors are 1, 2, 3, 4, 5, and so on. However, we are specifically looking for divisors that are themselves multiples of 10. These are numbers that end in zero and could be multiplied by some integer to get 240. In this instance, four such divisors are 10, 20, 30, and 60. For each of these examples, one can multiply these by a whole number to produce 240. For instance, 10*24 is 240, so is 20*12, 30*8, and 60*4.
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PLEASE ANSWER FAST!! (and correctly)
Answer:
1/10 or 10%
Step-by-step explanation:
Step 1: Find the probability of selecting a card with an A
Picked amount / Total Times
3 / 30
1/10 or 0.1 or 10%
Answer: 1/10 or 10%
What is the answer for 4x + 2y = 12
Answer:
(1,4), (2,2) (3,0)
Step-by-step explanation:
adjust the equation so that the y is isolated so subtract 4 x
2y=4x +12
Every number is divisible by 2 so you can further isolate the y
y=-2x+6
Plug your x coordinates into the equation so get the y coordinates
Answer:
y=-2x+6
Step-by-step explanation:
You want to to turn the given equation 4x+2y=12 into y=mx+b
** m is the slope and b is the y-intercept
The first step is to isolate y. First subtract 4x from both sides:
4x+2y=12
2y=-4x+12
Now you have y mostly isolated, all you have to do is divide both sides by 2:
2y=-4x+12
y=-4/2x +12/2
y=-2x +6
Now you have your equation, plug in values for x to find y to fill in the table:
ex: y=-2(2)+6
y= -4+6
y= 2
** an order pair ex.: (2,2)
2. A football coach recorded his team’s game scores over a football season. The scores are 21, 45, 21, 14, 21, 28, 24, 14, 24, 28.
(a) Find the mean absolute deviation of the data. Round to the nearest tenth.
(b) Interpret the mean absolute deviation of the data within the context of the problem.
(c) Explain how removing the outlier, 45, affects the mean absolute deviation.
Answer:
(a) The mean is 24
The Absolute deviation is 8.367
(b) Mean is the number of score per game
(b) The standard deviation is the normal expected score difference from the mean
(c) Mean reduce
Standard deviation reduce
Step-by-step explanation:
The data is as follows;
21, 45, 21, 14, 21, 28, 24, 14, 24, 28
The data with n = 10 is presented as follows
x (x - μ) (x - μ)²
21 -3 9
45 21 441
21 -3 9
14 -10 100
21 -3 9
28 4 16
24 0 0
14 -10 100
24 0 0
28 4 16
∑x/n =240 ∑(x - μ)² = 700
24 ∑(x - μ)²/n = σ² = 70
The mean = 24
The Absolute deviation √70 = 8.367
(b) The mean indicates that within the football season, the average game score per game was 24 and the normal variation from the average was 8.367
(c) Removing the outlier, 45 which ls most equal to two means will reduce the mean or average score per game of the team to as follows
21 , 21 , 14, 21, 28, 24, 14, 24, 28
∑x = 195 and μ = (∑x)/n = 195/9 = 21.67
The standard deviation = 4.83
Therefore, removing the outlier 45 which is almost double the mean will reduce the mean by almost μ/n and the standard deviation is also reduced.
The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term with a standard deviation of $1,200, but a financial administrator believes that the average cost is MORE. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. Let alpha = 0.05. What is the critical z-value for this test?
Answer:
z=3.8196
Step-by-step explanation:
-We notice that this is a normal distribution problem.
-Given the mean is $8500, standard deviation is $1200 , and n=350, the critical z-value using alpha=0.05 is calculated as:
[tex]z=\frac{x-\mu_o}{\sigma/\sqrt{n}}\\\\=\frac{8745-8500}{1200\sqrt{350}}\\\\\\=3.8196[/tex]
Hence, the test statitic is z=3.8196
How much material is required to make a pipe that is 300 cm long whose outer diameter is 8 cm with an inner diameter of 5 cm? Show or explain your work.
Answer:
Step-by-step explanation:
If you had a solid cylinder, in order to find the amount of material that makes up that solid cylinder, you would find the volume using the radius of 4 (half of the diameter 8). BUT we want to know the volume of the solid with the radius of 4 minus the solid that has a radius of 2.5 (half of the diameter 5).
[tex]V_o-V_i[/tex] That's volume outer - volume inner. To find the outer volume:
[tex]V=\pi r^2h[/tex] so
[tex]V_o=\pi (4^2)(300)[/tex] and
[tex]V_o=4800\pi[/tex] and do the same for the inner volume:
[tex]V_i=\pi (2.5^2)(300)[/tex] and
[tex]V_i=1875\pi[/tex]
Subtract the inner from the outer:
[tex]4800\pi-1875\pi=2925\pi cm^3[/tex]
If you need your answer in decimal form, then the volume is
9189.16 cm³
In a survey of 2,000 people who owned a certain type of car, 400 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car.
What is the circumference of a circle with a diameter of 9 inches? (use 22/7 for pi)
Answer:
c=28.2857142857 inches
Step-by-step explanation:
The circumference of a circle can be found using:
[tex]c=\pi d[/tex]
We know the diameter is 9, and we are using 22/7 for [tex]\pi[/tex], so we can substitute them in
c=22/7*9
Multiply
c=28.2857142857
The circumference is 28.2857142857 inches
The parallelogram has vertices at (–2, 2), (4, 2), (1, –2), and (–5, –2).
Answer:
A) base = 6 units
B) height = 4 units
C) Area = 24 square units
Step-by-step explanation:
Base on the gragh given,
The base = |-5| + |1| = 6 unit
The height = |2| + |-2| = 4 unit
The area = base × height
The area = 6 × 4 = 24 square units.
Answer:
The parallelogram has vertices at (–2, 2), (4, 2), (1, –2), and (–5, –2).
Complete each sentence.
The base of the parallelogram is
✔ 6
units.
The height of the parallelogram is
✔ 4
units.
The area of the parallelogram is
✔ 24
square units.
Step-by-step explanation:
what is the missing value for x-5y=-15
Answer:
y= 1/5 (fraction)
x=−3
Step-by-step explanation:
Let's solve for x.
x−5y=15
Step 1: Add 5y to both sides.
x−5y+5y=15+5y
x=5y+15
Let's solve for y.
x−5y=15
Step 1: Add -x to both sides.
x−5y+−x=15+−x
−5y=−x+15
Step 2: Divide both sides by -5.
−5y
−5
=
−x+15
−5
In the diagram, which pair of angles are vertical angles
Answer:
C: <6 and <8
Step-by-step explanation:
students at springfield school can join either the orchestra or the marching band. students cannot join both groups. how many 7th graders are in the band?
Answer:56 students
Step-by-step explanation:
So look 6th grade total 42 and 8th is 72 and the total is 170 but he want 7th grade total so what I did is 42+72=114
Then I did 170-114=56 so the total of 7th grade is 56.
The value of the variables x, y, and z will be 45, 24, and 56.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
The students at spring field school can join either the orchestra or the marching band.
Let the missing value x, y, and z are given in the table.
The table is given below.
Orchestra Band Total
6th Grade 24 18 42
7th Grade 32 x y
8th Grade z 27 72
Total 101 69 170
Then the value of x, y, and z are calculated below.
For value of z, the equation will be
72 = z + 27
z = 72 – 27
z = 45
For value of x, the equation will be
18 + x + 27 = 69
x + 45 = 69
x = 69 – 45
x = 24
For value of y, the equation will be
y = 32 + 24
y = 56
Then the value of the variables x, y, and z will be 45, 24, and 56.
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It rained 0.61 inches every day for 12 days straight. How many inches did it rain altogether during the 12 days?
Answer: 7.32 inches
Step-by-step explanation: We can set up an equation to solve: y = 0.61x where y is the total amount of rain in inches and x is how many days it rained.
Multiply 0.61 by 12 to get how many inches total it rained: y = 0.61(12)
y = 7.32 inches
Who most often wins in a credit transaction?
companies often win in a credit transaction, due to their clients continually pay them for their usage.
Final answer:
The 'winner' in a credit transaction varies; it could be the lender earning interest or the borrower who benefits from immediate funds. Credit transactions do not create new money but reallocate it, and for personal debt management, debts with higher interest should be paid first.
Explanation:
In credit transactions, the winner is not easily defined as it depends on the perspective and the outcome of the transaction. If we consider a credit card transaction where a customer makes a purchase, the credit card issuer initially appears to win by providing funds to the customer and earning interest on the borrowed amount. The customer benefits by receiving the goods or services they need immediately, with the expectation of repaying the funds.
In a typical credit transaction, one party relinquishes money today while the other party promises to return a specified sum, possibly with interest, at a future date. This does not create new money but shifts existing money from one party to another. The perceived 'winner' could be the lender, who will receive the original amount plus interest, or the borrower, who gets immediate use of the funds.
When managing personal finances, it's advisable to pay off debts with the highest interest rates first, as suggested by the adage, "A penny saved is a penny earned".
Which equation can be used to find the volume of this solid?
O V=2x4x5
O V=2+5+4
O V=2x5
OV=4x5
Answer:
V=2x4x5
Step-by-step explanation:
Volume of a solid can be obtained by multiplying lengths of all the three dimensions i.e. Length, width and height.
[tex]V = l \times b \times h \\ \therefore V = 2 \times 4 \times 5[/tex]
The Volume of Solid is, V=2x4x5.
What is Volume?'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
We know few formulas for Volume as
Volume of cuboid = l × w × h
Volume of cube = a³
Volume of Cylinder = πr²h
Volume of Prism= B × h
Volume of sphere = (4⁄3)πr³
Volume of Cone = (1⁄3)πr²h
From all the options given we have to find the relation with multiplication.
So, the volume of this solid is V=2x4x5 which is same as Volume of cuboid = l × w × h
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whats 15x times 14 y
Answer:
210xy
Step-by-step explanation:
15x * 14y can be written as 15 * x * 14 * y. Due to the commutative property of multiplication, we can change around the order of these numbers to make this expression easier to understand.
We're going to move the expression around so it is now 15 * 14 * x * y. Now, you can see clearly that you can multiply 15 and 14 together, which will get you 210.
And naturally what you have left is 210 * x * y, which simply appears as 210xy.
I hope this helped!
What does x equal???????
Answer:
-4x + 10x - 12 = -3x - 39
6x - 12 = -3x - 39
9x - 12 = -39
9x = -27
x = -3
Step-by-step explanation:
Rectangle A, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(2, 0), B(6, 0), C(6, 7), and D(2, 7)
The dimensions of the rectangle would be (6-2) x (7-0) = 4 x 7
That makes the area (4)(7) = 28.
That makes the perimeter (7+4)(2) = 22
That makes the diagonal sqrt((7^2)+(4^2)) = sqrt(49+16) = sqrt(65)
Naming arcs and finding arc measures Which statements are correct ?
Answer:
Both are corrects but bear different meaning
Step-by-step explanation:
While naming arcs is to name arcs based on their angle.
While finding arc measures is a measure of the angle of the arcs.
The dot plots represent the results of people being asked to rate their dining experience.
Blue Terrace mean rating = 6.1
Paradiso Grill mean rating = 6.3
Find the mean absolute deviations.
Blue Terrace:
Paradiso Grill:
Which restaurant has the most variation in customer ratings?
Answer:
Blue Terrace: 0.92 and Paradiso Grill 1.1 and Which restaurant has the most variation in customer ratings = Paradiso grill
Step-by-step explanation:
Answer:
.92 and 1.1
Step-by-step explanation:
Find the volume of the sphere with a radius of 13 inches Round your answer to the nearest tenth
Answer:
V= 9202.77 in³
Step-by-step explanation: