Dad's car's gas tank holds 14.8 gallons of the gas.
Define the term mixed fraction?A mixed fraction is one generated by integrating a whole number as well as a fraction.
When the car's gas tank is nearly half full, Dad fills it up. Later, when the tank is about 3/4 full, he fills it. Total gas purchased = 18 1/2 gallons of gas.Changed the mixed fraction in decimal.
Total gas purchased = 37/2 = 18.5 gallons of gas.
Let x be the gallons of gas tank contains.
Then,
(1/2)x + (3/4)x = 18.5
Multiply both sides by 4,
2x + 3x = 74
5x = 74
x = 14.8 gallons
Thus, Dad's car's gas tank holds 14.8 gallons of the gas.
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Which of the ordered pairs below is a solution to the system of inequalities?
The ordered pair which is a solution to the system of inequalities is: (-1, 0).
How to determine the solution?In order to determine which ordered pairs are true solutions based on the given system of inequalities, we would have to test each of the ordered pairs by substituting their values into the system of inequalities as follows;
For ordered pair (4, 3), we have:
-7x + 3y > -1
-7(4) + 3(3) > -1
-28 + 9 > -1
-19 > -1 (False).
For ordered pair (2, 8), we have:
-7x + 3y > -1
-7(2) + 3(8) > -1
-14 + 24 > -1
10 > -1 (True).
5x - 9y > -6
5(2) - 9(8) > -6
10 - 72 > -6
-62 > -6 (False).
For ordered pair (-1, 0), we have:
-7x + 3y > -1
-7(-1) + 3(0) > -1
7 + 0 > -1
7 > -1 (True).
5x - 9y > -6
5(-1) - 9(0) > -6
-5 - 0 > -6
-5 > -6 (True).
For ordered pair (-2, 2), we have:
-7x + 3y > -1
-7(-2) + 3(2) > -1
14 + 6 > -1
20 > -1 (True).
5x - 9y > -6
5(-2) - 9(2) > -6
-10 - 18 > -6
-28 > -6 (False).
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A circle has a circumference of 3.143.143, point, 14 units.
What is the diameter of the circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
The diameter of the circle is 4.45 units.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. Every line that passes through the circle forms the line of reflection symmetry. Also, it has rotational symmetry around the centre for every angle.
A line segment having both the endpoints on the circle and is the largest chord of the circle is called diameter.
Given,
the circumference of circle = 14 units
circumference = πd
14 = 3.14(d)
14/3.14 = d
d = 4.45
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the letters that spell mississippi are each written on separate tiles lying facedown on a table. a tile is selected at random, the letter is recorded, and then the tile is placed facedown on the table. then the process repeats. what is the theoretical probability of choosing a tile with the letter p? responses 14 1 fourth 411 4 over 11 111 1 over 11 211
The theoretical probability of choosing a tile with the letter p is 1/8
The letter of the word MISSISSIPPI are written on separate tiles lying down on the table and tile is chosen at random and the the letter is noted and then the tile is lied again on the table.
Probability of the event is,
P(E) = Total favorable outcomes/Total possible outcomes.
Total possible outcomes in this case are 11 because there are a total of 11 letters.
The total favorable outcomes that the chosen letter is P is,
Total favorable outcomes = ¹¹C₁/(2!)(2!)(2!)
Total favorable outcomes = 11/8
Probability P that chosen number is P is,
P = (11/8)/11
P = 1/8
So, the probability that the chosen tile is with letter P is 1/8.
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please help me with this math problem
Answer:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
Step-by-step explanation:
When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator. To do this, find the lowest common multiple (LCM) of the denominators.
The given subtraction is:
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}[/tex]
The LCM of the denominators 2 and 8 is 8. Therefore, we need to rewrite the first fraction as an equivalent fraction with 8 as its denominator. To do this, multiply its numerator and denominator by 4:
[tex]\implies \sf \dfrac{1}{2} \times\dfrac{4}{4}=\dfrac{4}{8}[/tex]
Therefore:
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}[/tex]
To subtract fractions with the same denominator, simply subtract the numerators. (The denominator stays the same).
[tex]\implies \sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{4}{8}-\dfrac{1}{8}=\dfrac{4-1}{8}=\dfrac{3}{8}[/tex]
Final solution
[tex]\sf \dfrac{1}{2}-\dfrac{1}{8}=\dfrac{\boxed{4}}{8}-\dfrac{1}{8}=\dfrac{\boxed{3}}{\boxed{8}}[/tex]
If ΔLMN is similar to ΔPQR, what is the length of PR?
If ΔLMN is similar to ΔPQR then length of PR = 15 by corresponding sides of similar triangles property.
What is the relation between corresponding sides of two similar triangles?
Two figures are said to be similar if they have same shape but size may vary.If two triangles are similar then their :-Corresponding angles are congruent. Corresponding sides are in the same ratio.ΔLMN is similar to ΔPQR
Corresponding angles are equal - ∠L = ∠P, ∠M = ∠Q, ∠N = ∠R.Corresponding sides are in same ratio - [tex]\frac{LM}{PQ} = \frac{LN}{PR} = \frac{MN}{QR}[/tex]According to the given data:
ΔLMN is similar to ΔPQR, therefore their corresponding sides are in same ratio,
LM/PQ = 8/6
LN/PR = 20/(2x - 1)
Substituting the values and solving for 2x -1 which is given length of PR
[tex]\frac{8}{6} = \frac{20}{2x -1} \\\\8(2x -1) = (20)(6)\\\\PR = 2x - 1 = \frac{120}{8} \\\\[/tex]Therefore, length of PR = 15.
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The perimeter of an equilateral triangle is 63 inches. If the length of each side is (3x-9), find the value of x.
Answer:
x=
Step-by-step explanation:
There are 2 ways to do this.
4(3x-9)=63; 12x-36=63; 12x=99; x=8. Or: (3x-9)+(3x-9)+(3x-9)+(3x-9)=63; 12x-36=63; 12x=99; x=
five whole numbers are written in order
4 6 x y 10
median and mean of the five numbers are the same.
Workout the values of x and y
The values of x and y if the mean and median are equal are:
x = 7
y = 8.
What is the Mean and Median of a Data Set?The mean is the total sum of the values in a data set divided by the number of values of the data set.
The median of a data set is the center value when the data distribution is ordered.
Given the ordered data set as, 4, 6, x, y, and 10.
The center value is x. Therefore, the median of the data set is x.
The mean of the data = (4 + 6 + x + y + 10)/5
The mean of the data = (20 + x + y)/5
The mean and the median are equal, therefore:
(20 + x + y)/5 = x
20 + x + y = 5x
20 + y = 5x - x
20 + y = 4x
The value of x cannot be less than 6, if x = 7, we woud have:
20 + y = 4(7)
20 + y = 28
y = 28 - 20
y = 8
The values of x = 7, y = 8.
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simplify (4i+1)^2
show all work
The simplified answer is 8i-15.
What do you mean by iota?
Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.
According to the given question,
We have: [tex](4i+1)^{2}[/tex]
Now, we will solving this by formula,
[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]
Putting the values in it,
[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]
Therefore, the required answer is 8i-15.
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The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
The temperature at the end of the day was 87 degrees. The temperature had decreased twice during the day, once by 9 degrees and another time by 7 degrees.
Which expression shows what the temperature was at the start of the day?
71+9+771+9+7
87−9−7
87+9+7
87+9−7
PLS HELP !! ITS DUE tommorow!!
In the given square, the values of f and g are equal that is 4√3cm.
What is a square?A square is a regular quadrilateral in Euclidean geometry, which means that it has four equal sides and four equal angles. It can alternatively be explained as a rectangle with two neighboring sides that are of equal length.The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.So, the values of f and g are:
From the given diagram we know that ABCD is a square.So, all sides are the same.The area of ABCD is 48cm².
Now, calculate for sides as follows:The formula for the area of the square: A = s²Then,
A = s²48 = s²s = √48s = √2×2×2×2×3s = 2×2√3s = 4√3Since f and g are 2 sides of the square, their values are 4√3cm.
Therefore, in the given square, the values of f and g are equal that is 4√3cm.
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Please Help!
Solve the inequality and graph it’s solution.
An ice skater is penalized 1.2 points for a fall. Write an expression for the ice skater’s final score.
The expression for the given case can be written as F = P - 1.2n.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
The addition and subtraction can only take place between like terms.
Given that,
The penalty for an ice skater for a fall is 1.2 points.
Suppose the total points of ice skater be P, the number of falls be n and the final score be F.
Then following expression can be written for final score,
F = P - 1.2n
Hence, the expression for ice skater's final score is F = P - 1.2n.
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Are these parallel or perpendicular or neither? 3x+2y=10 and 2x+3y=-3
Answer:
These lines are neither parallel nor perpendicular.
Step-by-step explanation:
Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.
Using desmos, you can find your solution.
I hope this helps
-No one
What is the slope of the secant line that intersects the graph of f(x) = √4x+1 at x = = 0 and x = 6?
=
Susan has two coupons for a bicycle. Coupon A: 20% off of a $81 bicycle Coupon B: $19 rebate on a $81 bicycle Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
The coupon that gives the lower price, based on the percentage discounts is Coupon B.
How to find the better coupon?To find the coupon that gives the lower price, apply the coupons to the price of the bicycle to see which value would be less after the coupon is applied.
Coupon A value after discount is:
= 81 x ( 1 - discount)
= 81 x ( 1 - 20%)
= $64.80
Coupon B value after discount is:
= 81 - 19
= $62
The coupon that gives the lower price is Coupon B.
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Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
Which expression equals 9/10 ?
O 5√10+4√10
O5 10+4 10
O 5√10+43/10
O 5 10+4 10
Answer:
The second answer:
5cubrt10 + 4cubrt10
Step-by-step explanation:
In order to get a cubrt10 answer you have to add cubrt10's.
The first answer has squareroots, so that's a no.
The last two have cubrt + sqrt, which cannot be simplified.
5cubrt10 + 4cubrt10 = 9cubrt10
If $3000 is invested at tan interest rate if 4.8%, compounded hourly for two years what is the ending balance?
The final balance is $97,920.
Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.
Given this, The principal is $3000.
Interest rate = 4.8%
Time = 2 years We must find the final balance.
The end balance formula is
C = P[ 〖(1+r)〗^n – 1]
C = 3000[ 〖(1+4.8)〗^2 – 1]
C = 3000 [ 〖(5.8)〗^2 – 1]
C = 3000 [ 33.64 – 1]
C = 3000 ( 32.64)
C = 97,920
Therefore the ending balance is $97,920
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a) 4 x -3 x 2 =
b) -2 x 5 x -4 =
c) -3 x -1 x -6 =
Answer:
a) 4 x -3 x 2 = -24
b) -2 x 5 x -4 = 40
c) -3 x -1 x -6 = -18
Answer:
a.4 x -3 x 2 =
use the rules for multiplication
-(4×3×2)
-(12×2)
=2
----------------------------------
b. -2 x 5 x -4 =
note:
-2×5(-4)
multiplying an even number of negative terms makes the product positive.
-2×5= 10
10×-4
=40
----------------------------------
C. -3 x -1 x -6 =
note:
multiplying an odd number of negative terms makes the product negative.
-(3×1×6)
=-18
Ms. Nettleton wants to create an outdoor space for her dogs. The distance between the furthest corners is 4 feet. The width of the area is 2 feet. How long is the length of the area?
(please help)
The length of the area is 8 feet.
What is the shape of outdoor space?
We know that Square has equal length, Rectangle has opposites sides of equal length.By the given length we found that it is Rectangular outdoor space.Step-by-step explanation:
Given :
Distance between the furthest corners(Length)= 4 feet
Width(breadth) = 2 feet
Area of rectangle = Length * Breadth
= 4 * 2
=8 feet
Hence, The length of the area is 8 feet.
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Williams and Co. is spliting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million. What is their Total pre-split Market Capitalization?
Total pre-split Market Capitalization is $1,08,125,000.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
Williams and Co. is splitting their stock at a ratio of 3:1. The pre-split price is $43.25 and the pre-split number of shares is 2.5 million.
Total Value of Shares = $43.25 Share Price × 2.5 × 10⁶ Shares
Total Value of Shares = $1,08,125,000
Let’s say the company’s board decides to approve a 3-for-1 split.
Total Shares = 2.5 × 10⁶ × 3 = 75,00,000
Share Price = $43.25 ÷ 3 = $14.416
Total Value of Shares = $14.416 Share Price × 75,00,000 Shares
Apply the multiplication operation,
Total Value of Shares = $1,08,120,000
Thus, the total pre-split Market Capitalization is $1,08,125,000.
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Graph this system of equations on the coordinate plane:
y=4/3x+4
3y=-2x-6
The graph the system of linear equations on a coordinate plane is added as an attachment
How to graph the system of linear equations on a coordinate plane?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
y=4/3x+4
3y=-2x-6
Rewrite the equations in the system of equations as follows:
So, we have the following representation
y = 4/3x + 4
3y = -2x - 6
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, 0)
This means that the solution to the system of equations is (-3, 0)
See attachment for the graph of the system of equations
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Sean drew a vertical line segment and labeled the top endpoint W and the other endpoint X.
He then found the midpoint of WX and labeled it Y. Starting at Y and moving to the right, he
drew a line segment of length WY perpendicular to WX, and he labeled the new endpoint Z.
Finally, he drew a line segment parallel to YZ, also of length WY, starting at W and moving to
the right.
What letter did Sean draw?
E
F
L
T
PLEASE HELP
Sean drew a letter (b)F.
What is Geometry construction?
Drawing precise shapes, angles, or lines is referred to in geometry as "construction." These structures only require a compass, a straightedge (a ruler), and a pencil.
according to the question, WX is a straight line having a midpoint at Y.
YZ is drawn perpendicular to WX. And parallel to YZ a line segment is drawn After this Geometrical construction, a letter is drawn which is F.
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How do you solve #4 - #9?
4. There is no enough information.
5. ΔPEF ≅ ΔREF are congruent by SAS.
6. ΔKMO ≅ ΔOLK are congruent by SSS.
7. No enough information.
8. ΔPAN ≅ ΔKLC are congruent by SSS.
9. ΔABC ≅ ΔDEF are congruent by SSS.
What is the SSS and SAS Theorems?The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.
4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.
5. Triangles PEF and REF are congruent by SAS.
6. Triangles KMO and OLK are congruent by SSS.
7. No enough information.
8. Triangles PAN and KLC are congruent by SSS.
9. Triangles ABC and DEF are congruent by SSS.
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Let the function f be defined as p (x) = -5 (-3x + 4) and function g be
defined as m (x)= 5x - 2 (5x - 6). What value of x satisfies the
equations m (x)= p (x)?
If the functions are equal. Then the value of the variable 'x' will be 1.6.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let the capability f be characterized as p(x) = - 5(- 3x + 4) and work g be characterized as m(x) = 5x - 2(5x - 6).
If the functions are equal. Then the value of the variable 'x' will be given as,
m(x) = p(x)
- 5(- 3x + 4) = 5x - 2(5x - 6)
15x - 20 = 5x - 10x + 12
15x - 20 = - 5x + 12
20x = 32
x = 1.6
If the functions are equal. Then the value of the variable 'x' will be 1.6.
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1. The measures of the angles in a triangle are in the extended ratio of 1:4:7. Find the measures of the angles.
i need help with my homework
Answer:
1 : 4 : 7
15 : 60 : 105
Step-by-step explanation:
1 + 4 + 7 = 12
180⁰ ÷ 12units = 15⁰
1 unit = 15⁰
4 units = 15⁰ × 4 = 60⁰
7 units = 15⁰ × 7 = 105⁰
i need help also i don't know what to do with x. 3(4x-12) = 84
Answer:
x=10
Step-by-step explanation:
3(4x-12)=84
12x-36=84
+36. +36
12x=120
/12. /12
x=10
Hopes this helps please mark brainliest
The points (4, -3) and (x, 3) lie on the same straight line.
If the slope of the line is 2, what is the value of x ?
answer:
(1,3)
step-by-step explanation:
desmos.
The value of x will be equal to 7 for the given slope of 2 for the line.
What is the slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Given that the points (4, -3) and (x, 3) lie on the same straight line. The slope of the line is 2.
The slope of the line is calculated by the formula,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
2 = ( 3 + 3 ) / ( x - 4)
2(x-4) = 6
2x - 8 = 6
2x = 8 + 6
2x = 14
x = 14 / 2
x = 7
Therefore, the value of x will be equal to 7 for the given slope of 2 for the line.
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Someone help pleaseeee !
The value of x and y which is on midsegment of the triangle is 1 and 11.
What is midsegment?
A triangle's midsegment is the section of the triangle's shape that connects the midpoints of its two sides. a section of a line connecting the midpoints of two triangle's sides. There are three possible midsegments in a triangle. The section of a line between the midpoints of two triangle sides is known as a midsegment. Due to the fact that triangles have three sides, they also have three midsegments. A line drawn by joining the midpoints of any two of a triangle's sides is known as the midsegment.
let us assume triangle as ABC and DE is the midsegment .
Where DE=2x+1 and BC = 8x-2 .
According to the midsegment theorem ,
=> DE = 1/2 BC
=> 2x+1 = 1/2(8x-2)
=> 2x+1=4x-1
=> 2x=2
=> x=1
Now AB divided intp AD=3z and DB=z+22
Then, AD=DB
=> 3z = z+22
=> 2z = 22
=> z = 11.
Hence the value of x=1 and z= 11.
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professor elderman has given the same multiple choice final exam in his principles of microeconomics class for many years. after examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. what is the probability professor elderman's class of 36 has a class average below 78
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
Given that;
In his principles of microeconomics subject, Professor Elderman has utilized the same multiple-choice final exam for many years. He looks over the last ten years' worth of statistics and discovers that the scores have a mean of 76 and a standard deviation of 12.
µ = 76 , σ = 12 , n = 36
Using Normal Distribution;
For x = 70
z = (x - µ) / (σ/√n) = (70-76)/(12/√36) = -3.00
P( average greater than 70 ) = P(X>70)
= 1 - P(X<70)
= 1 - P(Z<-3.00)
= 1 - 0.0013
= 0.9987
The probability Professor elderman's class of 36 has a class average below 78 is 0.9987.
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