Using proportions, it is found that the car uses gas at a rate of 31.25 miles per gallon.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The gas consumption of the car is given by the proportion of number of miles divided by the number of gallons, hence:
(5/8)/(1/50).
To divide two fractions, we multiply the numerator by the inverse of the denominator, hence:
5/8 x 50 = 31.25.
The car uses gas at a rate of 31.25 miles per gallon.
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graph the function 2x +3y = -21
Answer:
check below
Step-by-step explanation:
2x + 3y = -21
3y = -21 - 2x
3y = - 2x -21
divide both sides by 3
y = -[tex]\frac{2}{3}[/tex]x - 7
{ x − 10 ≤ x ≤ 15 }
it also needs to be graphed please help its due in 20 minutes
The graph is attached below:
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Given:
x − 10 ≤ x ≤ 15
as, the given inequality we have to break the inequality is
x − 10 ≤ x and x ≤ 15
The graph to the inequality is attached below.
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Select the correct numeral form of this number written in scientific notation. 4.1 × 10 2
0.41
41,000
4,100
410
3× 1,250 in expanded form and use distributive property
How many solutions will each system of linear equations have? Match the systems with the correct number of
solutions.
y=x+6 and 3x-3y=-18
y=-2x+5 and 2x+y = -7
y=-4x+11 and -6x + y = 11
infinitely many solutions
no solution
one solution
The appropriate choices will be as follows in light of the provided information:
There are countless solutions to the equations: y = x + 6 and 3x - 3y = -18.2x + y = -7 and y = -2x + 5: Respectively, no answer.-6x + y = 11 and y = -4x + 11: One answer.What are equations?A mathematical statement known as an equation consists of two expressions joined by an equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.So,
y = -4x + 11 ... (1)-6x + y = 11 ... (2)Add equation I to equation II.
-6x + y = 11-6x + (-4x + 11) = 11-6x - 4x + 11 = 11-6x - 4x = 11 - 11-10x = 0x = 0Consequently, x=0 and y=11 Each variable's solution is provided by this.
y = -2x + 5 ... (1)2x + y = -7 ... (2)Put equation I into equation II.
2x + y = -72x + (-2x + 5) = -72x - 2x = -7 - 50 = -12This means there is no answer.
y = x + 6 ... (1)3x - 3y = -18 ... (2)Put equation I into equation II.
3x - 3y = -183x - 3(x + 6) = -183x - 3x - 18 = -183x - 3x = - 18 + 180 = 0This implies that there are an infinite number of possible answers.
Therefore, the appropriate choices will be as follows in light of the provided information:
There are countless solutions to the equations: y = x + 6 and 3x - 3y = -18.2x + y = -7 and y = -2x + 5: Respectively, no answer.-6x + y = 11 and y = -4x + 11: One answer.Know more about equations here:
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Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,4) and (-7,6).
The standard form of the equation is(x + 2)² +(y - 5)² = 26
The equation of a circle in standard form is
(x - a)² + (y - b)² = r²
where (a , b) are the coordinates of the centre and r the radius
The centre is at the midpoint of the endpoints of the diameter and r is the distance from the centre to either of the 2 endpoints
Find centre using the ' midpoint formula'
(a , b) = [ (3 - 7), (4 + 6) ] = (-2 , 5)
to find r use the ' distance formula '
with (-2 ,5) and (3 , 4)
r = √(3 + 2)² + (4 - 5)² = √(25 + 1 ) = √26 ⇒ r² = (√26)² = 26
(x + 2)^² + (y - 5)² = 26 it is the equation in standard form'
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. we can find the center point of the circle. Because the two points from the problem are the endpoints of a diameter, the midpoint of the line segment is the center point of the circle.
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A producer of printed circuit boards (PCBs) wishes to estimate the scoring depth of their circuits. To this end, they have collected 45 samples of measured depths. The mean and standard deviations of these samples is 0.165 mm and 0.022 mm respectively.
1. Create a plot showing the dependence of the size of the confidence interval (ρ) on the confidence level (γ) ranging from 0 to 1. Keep the sample size fixed at 45
2. Create a plot showing the dependence of the size of the confidence interval on the
sample size ranging from 1 to 100. Keep the confidence level fixed at 0.95. (Here you
can assume normality even where N <30)
3. Create a plot showing the pdf of the sample mean and with the area computed above shaded in. Hint: plt.fill between.
The mean and the standard deviations of the samples is 0.165 mm and 0.022 mm.
n = 45
[tex]\overline{X} = 0.165{~}mm[/tex]
s = 0.022 mm
Now, 95% of the confidence interval.
[tex]CI=\overline x {~}\pm t_{\frac{\alpha}{2}, n-1 }\frac{s}{\sqrt{n} }[/tex]
The critical values are:
α = 1 - 0.95 = 0.05
n - 1 = 45 - 1 = 44
[tex]t_{\frac{\alpha}{2} , n-1=t_{0.025,44}=2.0154[/tex]
So, 95% of CI = 0.165 ± 2.0154 × ( 0.022 ÷ √45 )
95% CI = ( 0.158, 0.172 )
1. The plot for the dependence of the size of the confidence interval on the confidence value ranging from 0 to 1.
2. A plot showing the dependence of the size of the confidence interval on the sample size ranging from 1 to 100.
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A car accelerates from rest to 27 m/s in 4.5 s. What is the car's acceleration?
Answer:
6 m/s²
Step-by-step explanation:
[tex]\frac{27 \text{ m/s}}{4.5 \text{ s}}=6 \text{ m/s}^2[/tex]
In the quation below all the asteriks stand for the same number.
What Is the number?
A dotplot of the distribution of height for Mrs. Navard’s class is shown, along with some numerical summaries of the data. Suppose that Mrs. Navard has the entire class stand on a 6-inch high platform and then asks the students to measure the distance from the top of their heads to the ground.
What are the mean and median of the new distribution of distance?
The new mean after adding a 6-inch high platform is 73 inches, while the median changes from 66 inches to 72 inches.
What are the mean and the median?The mean refers to the average of a data set and is the result of the sum of the values of the data set divided by the number of items.
The median is the middle value in the data set when arranged in an ascending or descending order.
For instance, the number of the data set is 25. The median value is the number 13, whose value is 66 inches in the old distribution or 72 inches in the new distribution.
Old Distribution of Heights:Height (in.) Number of Students Cumulative Total
60 1 60 (60 x 1)
61 0 60 (60 + 61 x 0)
62 2 184
63 4 436
64 2 564
65 1 629
66 3 Median 827
67 1 894
68 3 1,098
69 2 1,236
70 0 1,236
71 1 1,307
72 2 1,451
73 0 1,451
74 1 1,525
75 2 1,675
Mean = 67 (1,675/25)
New Distribution of Heights:Height (in.) Number of Students Cumulative Total
66 1 66 (66 x 1)
67 0 66 (66 + 67 x 0)
68 2 202
69 4 478
70 2 618
71 1 689
72 3 Median 905
73 1 978
74 3 1,200
75 2 1,350
76 0 1,350
77 1 1,427
78 2 1,583
79 0 1,583
80 1 1,663
81 2 1,825
Mean = 73 (1,825/25)
Thus, the new mean is 73 inches and the new median is 72 inches.
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1/3+1/5=
Gggg Gn jusgehrheh
Answer:
8/15
Step-by-step explanation:
1/3+1/5
Sharlene purchased a new truck, whose value over time depreciates. Sharlene's truck depreciates according to the function y = 45,529(0.78)x, where x represents the number of months since the truck was purchased. What is the range of the exponential function y based on its equation and the context of the problem?
ℝ
y ≥ 0
y < 45529
0 < y ≤ 45529
The range of the exponential function y based on its equation and the context of the problem is; 0 < y ≤ 45529
What is the range of a function?The range of a function is the set that contains all possible output values for the function.
In this question, the function is given as: y = 45,529(0.78)^x.
It is an exponential function with initial value 45,529 and rate of change of 0.78.
Now, it should be noted that exponential functions that are not shifted down, such as this one, are never negative nor zero. Thus, the range also has the restriction y > 0, and is given by:
D. 0 < y ≤ 45529
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Mia Cycled 23km, correct to the nearest km.
what is the least distance Mia could have
cycled?
Answer:
20km
Step-by-step explanation:
rounding down because it's not over five
help me with this
pls help
i love you <3
Answer:
Step by step evaluation
Formula
T = 4B + 10C
CAN SOMEONE HELP ME PLEASE? I JUST NEED THE CORRECT VALUE OF M THAT’S IT. THE PICTURE IS ALREADY ATTACHED
Step-by-step explanation:
the area of any triangle is
baseline × height / 2
so, in our case
12 × height / 2 = 48
6 × height = 48
height = 48/6 = 8 units
m with the height and half of the baseline creates a right-angled triangle. and we can use Pythagoras to get m.
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90° angle), which is m for this right-angled triangle.
a and b are the legs, which are in our case the height of the main triangle and half of the baseline of the main triangle.
so we get
m² = 8² + (12/2)² = 8² + 6² = 64 + 36 = 100
m = 10 units
Two concentric circles are of radii 5 cm and 3 cm. Determine the length of the chord of the larger circle which touches the smaller circle.
The length of the chord of the larger circle which touches the smaller circle.
The chord of the larger circle which is touches the smaller circle having the length of 8cm.
Given that
Two concentric circles are of radii 5 cm and 3 cm.To find
The length of the chord of the larger circle which touches the smaller circle.So, according to the question
we have,
The radius of larger circle = 5cm.The radius of smaller circle = 3cm.From attached figure of that problem,
BC = 5cm
CD = 3cm
AB = ........? (have to find) or from geometry
AB = 2 BD ---------(1)
Now, we have to find BD,
So, from right angle triangle BDC.
BD² = BC²-CD² ( by Pythagoras theorem )
BD = [tex]\sqrt{(BC)^2-(CD)^2}[/tex]
Putting the given values,
BD = [tex]\sqrt{(5)^2-(3)^2}[/tex]
BD = [tex]\sqrt{25-9}[/tex]
BD = [tex]\sqrt{16}[/tex]
BD = 4 (∵[tex]\sqrt{16} = 4[/tex])
Now, putting the value of BD in equation (1)
AB = 2 BD ---------(1)
= 2×4
AB = 8
Answer:
The length of the chord of the larger circle which touches the smaller circle is 8cm.To learn more about Pythagoras theorem, please click on the link:
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Question 2 of 10
f(x) = 3x³-2x^2+4x-5
g(x) = 6x - 7
Find (f+g)(x).
-
OA. (f+g)(x) = 3x³ - 2x² - 2x - 2
OB. (f+g)(x) = 3x³ - 2x² + 10x - 12
O c. (f+g)(x) = 3x³ - 2x² - 2x + 12
OD. (f+g)(x) = 3x³ - 2x² + 10x + 12
The correct option is (B) That'is
[tex] \bf \implies{{3x}^{3} - {2x}^{2} + 10x - 12}[/tex]
Step-by-step explanation:Step 1) : Operations of functions
[tex] \bf \longrightarrow{f(x) + g(x)} \\ \bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]
Step 2) : Simplify or expand
[tex]\bf \longrightarrow( {3x}^{3} - {2x}^{2} + 4x - 5) + (6x - 7)[/tex]
Determine the sign[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} + 4x - 5 + 6x - 7[/tex]
Reorder and gather or combine like terms[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4x + 6x) + (- 5 - 7)[/tex]
Collect coefficients of like terms[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +( 4 + 6) \times x+ (- 5 - 7)[/tex]
Calculate the sum or difference[tex]\bf \longrightarrow {3x}^{3} - {2x}^{2} +10x - 12[/tex]
DUE SOON! QUESTION BELOW! PLEASE WRITE IT OUT HOW IT WOULD BE ON A TEST! I NEED THE ANSWER SO I CAN USE IT AS A REFERANCE LATER ON!
The numbers given illustrates that the nth term will be:
1. n² + 1
2. n²
How to calculate the values?1. It should be noted that from the information given, the numbers are 2, 5, 10 and 17. It should be noted that the nth term will be:
n² + 1.
Therefore, the 5th term will be:
n² + 1 = 5² + 1 = 26
2. The numbers given are 0, 1, 4, 9. The nth term is n². In this case, the 4th number will be:
n² = 4² = 16
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Need help with this one.
Answer:
x ≠ 8, 5
Step-by-step explanation:
We only care about the denominator:
x² - 13x + 40
--------------------
-8 × -5 = 40
-8 + -5 = -13
--------------------
(x - 8) (x - 5) = 0
x - 8 = 0. x - 5 = 0
x = 8. x = 5
I hope this helps!
help me, i need to learn the Pythagorean theorem. ill pick brainliest!
Answer: The definition/meaning of it is a theorem attributed to Pythagoras that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Step-by-step explanation: If you need the equation solved, I can try just type under this.
4 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids. The
winner offers a bid of $4,000, how much will that bidder need to put into a kitty for the other bidders to
be compensated?
The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
An object may be claimed jointly by 4 persons with the intent to split it using the sealed bid method. The winning price is $4,000.00.
The amount of bidder is given as,
⇒ $4,000 - $4,000/4
⇒ $4,000 - $1,000
⇒ $3,000
The amount of bidder needs to put into a kitty for the other bidders to be compensated will be $3,000.
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Johnny earns $80 for 4 hours of work. At this rate, how
long would he have to work to earn $1,000 ?
Answer:
50 hrs
Step-by-step explanation:
80=4h (h=hours)
h=20 (1hr=20 bucks)
1000=xh (x=number of hrs.)
1000=20x (h=20 so sub that in)
x=1000 divided by 20
which is 50hrs til johnny gets 1000 bucks
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3. If there were 5334 total votes, how many yes votes were there?
The total of yes voter present in the election are 3048.
What is define as the ratio?When represented in numbers or amounts, a ratio is a comparison between two things. For example, if a room contains ten boys as well as thirty girls, the boy-to-girl ratio is 1:3, or one to three.Now, for the given question;
Let the number of yes voters be 'x'.
Let the number of no voters be 'y'.
The ratio of yes to no voters is 4:3.
Thus,
x/y = 4/3
or x = 4y/3
Now there are total 5334 voters;
Thus,
x + y = 5334
Put the value of x.
4y/3 + y = 5334
On simplification;
7y = 16002
y = 2286 (no voters)
Now, calculate 'x'.
x = 5334 - 2286
x = 3048 (yes voters)
Thus, the number of yes voters are 3048.
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Last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party. How many dollars should Laura expect to spend this time?
The number of dollars Laura should pay at the dinner party is $84.
Given that, the last time Laura hosted a fancy dinner party for her friends, she spent $108 to feed 9 people. This time, there will be only 7 people at the dinner party.
What is proportion?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the number of dollars paid by Laura for 7 people be x.
Now, 9:108::7:x
⇒9x=108×7
⇒x=12×7
⇒x=84
Therefore, the number of dollars Laura should pay at the dinner party is $84.
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The graph of f(x) is shown.
For what values of x does f(x)=0?
Answer: X = -4, 0, 2
Step-by-step explanation:
Wherever the line touches the x-axis the f(x) or y = 0
During Hurricane Matthew, Fayetteville received 14 ½ inches of rain in 21 %4 hours. What is the rainfall rate in inches per hour?
OA. inches per hour
OB. 1 inch per hour
O C. 1 ½ inches per hour
OD: 2 inches per hour
The rainfall rate in inches per hour is 2/3 inches per hour.
What is rate?A rate is a special ratio in which the two terms are in different units. a fixed ratio between two things2: a number, amount, or degree measured in relation to another quantity; examples include the heartbeat, metabolic rate, pulse, and sedimentation rate.
Given that,
The inches of the rain is 14×1/2is 29/2
The direction of the rain is 21×3/4 is 87/4
Rate is 29/2 /87/4
is29/2×4/87 is 2/3
Therefore, rate of rain is 2/3.
The rainfall rate in inches per hour is 2/3 inches per hour.
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Use proportions to solve the following problem.
A 30-pound bag of topsoil will cover a surface area of 9 ft^2.
a) How many pounds of topsoil are needed to cover a surface area of 270 ft^2?
b) How many bags of topsoil must be purchased to cover a surface area of 270 ft^2?
It would take 16 days for the number of magical coins to exceed 50,000.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
30 pound = 1 bag
30 pound = 9 ft²
a) For a surface area of 270 ft²:
Number of pounds = 270 ft² * 30 pound per 9 ft² = 900 pounds
b) For a surface area of 270 ft²:
Number of bags = 900 pounds * 1 bag per 30 pound = 30 bags
900 pounds is needed to cover a surface area of 270 ft² and 30 bags would be needed to be purchased
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Ivan and Tanya share £150 in the ratio 4:1 work out how much more ivan gets compared to tanya
Ivan and Tanya share £150 in the ratio 4:1 workout. lvan gets more compared to Tanya. = $ 90
Ratio :
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as 7:10.
Total Ivan and Tanya share = £150
Ivan and Tanya share in the ratio of 4:1 respectively.
Let 4x be the money got by Ivan and x be the money got by Tanya.
Then, according to the question, we have
4x+x= 150
5x = 150
x= 150/5
x= 30
∴ Ivan has Money = 4x
= 4*30
= $ 120
Tanya has Money = x
= $ 30
Difference = 120-30 = $ 90
Hence, Ivan gets more compared to Tanya. = $ 90
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Tanya and Ivan split £150 in the 4:1 workout. Tanya receives less compared to Ivan. = $ 90
Ratio:
A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other. For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.
Ivan and Tanya's combined portion is £150.
Tanya and Ivan each share in a ratio of 4:1.
Let x and 4x represent Tanya's and Ivan's respective earnings.
Then, according to the question, we have
4x+x= 150
5x = 150
x= 150/5
x= 30
∴ Ivan has Money = 4x
= 4*30
= $ 120
Tanya has Money = x
= $ 30
Difference = 120-30 = $ 90
Hence, Ivan gets more compared to Tanya. = $ 90
Which of the following is required to disprove a conditional (if-then) statement?
More than one counterexample that shows the statement is not always true.
An argument that the conclusion follows for all cases that fulfill the hypothesis.
OA single counterexample that shows the statement is not always true.
None of the above.
Submit Answer
The correct option regarding what is required to disprove a conditional statement is given by:
A single counterexample that shows the statement is not always true.
What is a conditional statement?A conditional statement has the following format:
If Clause 1 then Clause 2...
In which:
Clause 1 is the hypothesis.Clause 2 is the conclusion.The statement is disproved when there is even one single case in which Clause 1 is true and Clause 2 is false, that is, a counter example showing that the statement is not always true, hence the third option in this problem is correct.
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Given that mAngleKLH = 120° and mAngleKLM = 180°, which statement about the figure must be true?
AngleHLM is bisected by Ray L J .
AngleGLJ is bisected by Ray L H .
mAngleKLG = mAngleHLJ
mAngleHLI = mAngleILM
The measure of the angle of the straight line is equal to 180 degrees. the measure of the ∠HLI and ∠ILM is equal to the which is 30 degrees. Thus option 4 is the correct option.
What are lines and angles?An endlessly long row of evenly spaced dots that spans in both directions makes up a line. Its length is the only dimension it has. A geometry called an angle is created when two line segments, lines, or rays intersect.
Given information-
The measure of the angle KLH is 120 degrees.
The image is attached below for the given problem.
The angle of the straight line
The measure of the angle of the straight line is equal to 180 degrees.
The line KLM is a straight line thus the angle of the line KLM is equal to 180 degrees.
The value of the angle ILH is 30 degrees given in the figure.
The value of the angle KLH is given in the question which is equal to 120 degrees. Thus,
∠KLM = ∠ILM + ∠KLH + ∠ILH
Take the angle KLH and the angle ILH on the other side,
∠ILM = ∠KLM - ∠KLH - ∠ILH
∠ILM = 180 - 120 - 30
∠ILM = 30
Thus the measure of the is 30 degrees.
As the measure of the is equal to the which is 30 degrees. Thus option 4 is the correct option.
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Answer:
d. mAngleHLI = mAngleILM
Step-by-step explanation:
trust