A truck has a full 50-gallon gas tank. It uses 7 1/4 gallons on the first part of its journey, 13 1/2 gallons on the second part of its journey, and 15 1/4 gallons on the third part of its journey. How many gallons of gas remain in the gas tank?
The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and a standard deviation of 16 days. between what two values do the middle 95% of the lengths of all pregnancies fall?
Which pair of expressions is equivalent using the Associative Property of Multiplication? (3 points) 5(3a ⋅ 4) = 15a ⋅ 20 5(3a ⋅ 4) = (3a ⋅ 4) ⋅ 5 5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4 5(3a ⋅ 4) = 5 ⋅ 3a ⋅ 4 6
Answer:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Step-by-step explanation:
The Associative Property is applied to two types of operations: addition and multiplication. This property indicates that, when there are three or more terms in these operations, the result does not depend on the way in which the terms are grouped.
In this sense, the associative property for the sum is mathematically given by:
[tex](x+y)+z=x+(y+z)[/tex]
and for the multiplication by:
[tex](xy)z=x(yz)[/tex]
Now, let:
[tex]x=5\\y=3a\\z=4[/tex]
Using the Associative Property of Multiplication:
[tex](xy)z=x(yz)\\\\Replacing\hspace{3}the\hspace{3}values\\\\(5\cdot 3a)\cdot4=5(3a\cdot 4)[/tex]
Therefore the equivalent expressions are:
5(3a ⋅ 4) = (5 ⋅ 3a) ⋅ 4
Answer: C
Step-by-step explanation: Sorry If I am wrong, ty!!
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Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <1, -2>, v = <-4, 8>
A) Orthogonal
B) Neither
C) Parallel
Find the area of a parallelogram with base b and height h. B= 74cm H=14.8 cm
General Idea:
The formula to find the area of parallelogram is given below:
[tex] Area \; of\; the\; parallelogram=BASE \times HEIGHT\\ \\ [/tex]
Applying the concept:
Given, [tex] BASE\; (B)= \; 74\; cm\\ HEIGHT \;(H)=14.8 \;cm\\\\ Area \; of \; the \; Parallelogram = 74 \; cm \times 14.8 \; cm = 1095.2 \; cm^{2} [/tex]
what direction is 45 degrees in clockwise from due east?
A direction of 45 degrees clockwise from due east would put you in the South-East quadrant of a compass or geometric plane.
Explanation:When discussing directions in terms of degrees, it's commonly understood with the idea of a compass rose or a unit circle in mind. Here, 'Due East' is represented as 0 or 360 degrees. A clockwise rotation would mean we are moving in a positive direction.
Therefore, if you start from Due East which is 0 degrees and rotate 45 degrees in the clockwise direction, you would end up in the south-east direction. This is because in the coordinate system, the +x direction is East and moving in the clockwise direction, the next quadrant would be the South-East quadrant. So, 45 degrees clockwise from due east would be considered as South-East direction on a compass rose or geometrically on a plane if you are looking at it in terms of degrees on a circle.
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solve and write multiplication equations
72=0.6r
Prove that the angle bisector of the angle opposite to the base of an isosceles triangle is also the altitude to the base
how can a ratio's number can be changed without changing the ratio itself
The ratio is a fraction that tells us how many times longer a thing is compared to another thing. In mathematics, we express a ratio as the relationship between two numbers, namely [tex]a \ and \ b[/tex], so the ratio can be written as:
[tex]r=\frac{a}{b}[/tex]
If we can change this number without changing the ration we need to multiply both the numerator and the denominator by the same number. For instance, if we have the following ratio:
[tex]r=\frac{2}{3}[/tex]
We can multiply both the numerator and denominator, say, by 7. Then:
[tex]r=\frac{7\times 2}{7 \times 3}=\frac{14}{21}[/tex]
As you can see, the ratio's number has changed but without changing the ratio itself because:
[tex]\frac{2}{3}=\frac{14}{21}[/tex]
An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered?
What is the distance between (-6,8) and (-3,9)
Answer:10
Step-by-step explanation:I seen the answer
One angle is eight times it’s supplement increased by 45 degrees. What is the measures of the two supplementary angles?
What is the lower quartile of the following set?
28, 45, 12, 34, 36, 45, 19, 20
28.5
19.5
19
28
There are 80 sixth grade students at Howard elementary school.If 25% of the students have green eyes how many sixth grade students have green eyes
Could you please help me out ??
find the area of an equilateral triangle (regular 3-gon) with the given measurement
 Jen wants to buy a dress that originally had the price of $33, but now it is on sale 10% off. How much will Jen pay for the dress
Answer:
$29.70
Step-by-step explanation:
The word of in an equation or expression = multiply.
10 percent of $33 = 1/10 x 33/1 or 33/10 ($3.30)
$33 - $3.30 = $29.70
Keith had 694 green, yellow and blue marbles altogether. he had 3 times as many blue marbles as yellow marbles. there were 90 fewer green than blue marbles. how many blue marbles did Keith have?
Marianne has been collecting donations for her biscuit stall at the school summer fayre. There are some luxury gift tins of biscuits to be sold at £5 each, normal packets at £1 each, and mini- packs of 2 biscuits at 10p each. She tells Amy that she has received exactly 100 donations in total, with a collective value of £100, and that her stock of £1 packets is very low compared with the other items. Amy wants to work out how many of each item Marianne has. Show how she can do it.
Number of luxury gift tins of biscuits L sold is 18.
Number of mini- packs of 2 biscuits M sold is 80.
Number of normal packets N sold is 2.
Step-by-step explanation:Let L, M, N represent the number of Luxury, Mini, and Normal packets sold.
Total earned by selling luxury gift tins of biscuits = 5L
Total earned by selling normal packets = £1N
Total earned by selling 2 biscuits at 10p = 0.1M
Marianne tells Amy that she has received exactly 100 donations in total:
Equation becomes:
[tex]L+N+M=100[/tex] .... (1)
total earning is £100, so another equation becomes:
[tex]5L+N+0.1M=100[/tex] .......(2)
Given is that stock of £1 packets is very low compared with the other items:
so, N<L and N<M
Putting y = 0 in equation 1 and 2
[tex]L+M=100[/tex] or [tex]L=100-M[/tex] .....(3)
[tex]5L+0.1M=100[/tex] ......(4)
Replacing L by 100-M in the equation 4
[tex]5(100-M)+0.1M=100[/tex]
[tex]500-5M+0.1M=100[/tex]
4.9M=400
M=81.63
As, L=100-M
[tex]L=100-81.63=18.37[/tex]
L=18.37
We can round L and M to 18 and 81 respectively and solve for N from 1 and 2 equations.
[tex]L+M+N=100[/tex]
=>[tex]18+N+81=100[/tex]
=>[tex]N=1[/tex]
[tex]5(18)+N+0.1(81)=100[/tex]
[tex]90+N+8.1=100[/tex]
=> N=1.9
We will repeat the same process with N = 2 and get the following result.
Number of luxury gift tins of biscuits L sold is 18
Number of mini- packs of 2 biscuits M sold is 80
Number of normal packets N sold is 2
18.84 rouning to the nearest hundredth
When rounding 18.84 to the nearest hundredth, the result is 18.84 that means the number 18.84 remains unchanged when rounded to the nearest hundredth.
Given information:
The number is 18.84 and need to round it to the nearest hundredth.
Steps to round to the nearest hundredth:
Look at the digit in the thousandth place (the third decimal place). In this case, it is 4.Determine if the digit is 5 or greater. If it is, round up; if it is less than 5, round down.Since the digit in the thousandth place is 4, which is less than 5, there is no need to round.Therefore, the number 18.84 remains unchanged when rounded to the nearest hundredth.
Therefore, when rounding 18.84 to the nearest hundredth, the result is 18.84.
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are the fractions 1/2 and 1/8 equivalent fractions
The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.
The fraction numbers are given below.
1/2 and 1/8
In the fraction numbers, the numerator is the same. If the denominator is the same, then the numbers will be equal.
The denominator of the fraction number is different. Then the fraction numbers are not equivalent fractions.
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In a regression analysis of beef prices. What does the coefficient of beef price -12 tell me?
Which graph shows the new position of the rectangle after a translation? Rectangle with coordinates: (0, negative 1), (0, negative 6), (2, negative 1), and (2, negative 6). Rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6). Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4). Rectangle with coordinates: (1, 0), (1, 2), (6, 0), and (6, 2). Rectangle with coordinates: (0, negative 0.5), (1, negative 0.5), (0, negative 3), and (1, negative 3).
OPTION B.
The rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6) shows the new position of the original rectangle after a translation of 2 units upwards on the y-axis.
Explanation:In mathematics, a translation moves an object without changing its shape or orientation. You simply move it to another position in the plane. To find the new position of the rectangle after a translation, we need to find which set of coordinates matches those of our original rectangle but is located in a different spot.
Looking at the options given, the only rectangle that represents a translation of the original is the rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6). This rectangle is similar in shape and orientation to our original rectangle, but it is shifted 2 units upwards on the y-axis.
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A graph that shows the new position of the rectangle after a translation include the following: C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).
How to transform the preimage and image of a quadrilateral?In Mathematics, a translation is a type of transformation that is typically used for shifting every point of a geometric object in the same direction on the cartesian coordinate, as well as for the same distance.
In this scenario and exercise, we would apply a translation of 2 units to the right and 2 units up to the given rectangle, in order to determine the new position of the rectangle after a translation as follows;
(x, y) → (x + 2, y + 2)
Point (1, 0) → (1 + 2, 0 + 2) = (3, 2).
Point (1, 2) → (1 + 2, 2 + 2) = (3, 4).
Point (6, 0) → (6 + 2, 0 + 2) = (8, 2).
Point (6, 2) → (6 + 2, 2 + 2) = (8, 4).
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Complete Question:
Which graph shows the new position of the rectangle after a translation?
Rectangle with coordinates: (1, 0), (1, 2), (6, 0), and (6, 2).
A. Rectangle with coordinates: (0, negative 1), (0, negative 6), (2, negative 1), and (2, negative 6).
B. Rectangle with coordinates: (0, 1), (0, 6), (2, 1), and (2, 6).
C. Rectangle with coordinates: (3, 2), (3, 4), (8, 2), and (8, 4).
D. Rectangle with coordinates: (0, negative 0.5), (1, negative 0.5), (0, negative 3), and (1, negative 3).
a copper alloy that is 40% copper is to be combined with a copper alloy that is 80% copper to produce 120 kilograms of an alloy that is 70% copper. how many kilograms of each alloy must be used? please work it out
After setting up and correcting a system of equations, the student needs to use 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy to create 120 kg of a 70% copper alloy.
To solve this problem, we need to set up a system of equations. Let x be the amount of 40% copper alloy needed, and y be the amount of 80% copper alloy needed.
First, we have the total weight equation:
x + y = 120 kg (the final alloy's total weight)
Next, we have the copper content equation:
0.40x + 0.80y = 0.70 × 120 kg (the final alloy's copper content)
Now, let's solve this system of equations:
Address the second equation: 40x + 80y = 8400
Express x in terms of y: 40x = 8400 - 80y
Divide by 40: x = 210 - 2y
Substitute x in the first equation: (210 - 2y) + y = 120
Solve: 210 - y = 120, y = 90 kg
Finally, substitute the value of y back into x = 210 - 2y: x = 210 - 2 imes 90 = 210 - 180 = 30 kg
So, we need 30 kg of the 40% copper alloy and 90 kg of the 80% copper alloy.
Describe how dividing by 2 is the same as finding 1/2 of 1/4
is 127 prime or composite
The number 127 is a prime number as it has no divisors other than 1 and itself.
The number 127 is a prime number. A prime number is defined as a number that is greater than 1 and has no positive divisors other than 1 and itself. To determine if 127 is prime, we must check if it can be divided evenly by any number other than 1 and 127. When we perform this check, we find that 127 does not have any divisors other than 1 and itself, confirming that it is indeed a prime number.
during a hike, 3 friends equally shared 1/2 pound of trail mix. what amount of trail mix, in pounds, did each friends recieve
3 friends equally shared 1/2 pound of trail mix, during the hike.
Total quantity of trail mix = 1/2 pound
Quantity shared by each friend is 1/3 rd of the trial mix
= 1/3 * 1/2 pound
= 1/6 pound
Therefore, during the hike, each friend shared 1/6 pound of the trail mix.
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Can someone help with this question please?
For which of these does correlation most likely imply causation?
Answer:
As the use of a condition that increases the electricity bill increases as well
Step-by-step explanation:
Find the complete factorization of the expression. 32xy − 56xyz