We have that:
[tex]\text{velocity}=\frac{\text{distance}}{\text{time}}[/tex]then, in this case, we have:
[tex]\begin{gathered} d=15.6m \\ t=17.2s \\ v=\frac{d}{t} \\ \Rightarrow v=\frac{15.6m}{17.2s}=0.90\frac{m}{s} \\ v=0.9\frac{m}{s} \end{gathered}[/tex]therefore, the velocity of the cart is 0.9 meters per second.
Directions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.Solve for x.( + 0.5) + 5.24 = = + ( + 2.2)The value of x is
1/5 (x+0.5) +5.24 = 3/2x + 7/10 (x+2.2)
First, apply the distributive property to solve the parentheses
1/5(x)+ 1/5 (0.5) +5.24 = 3/2x + 7/10(x) + 7/10 (2.2)
1/5x +0.1 +5.24 = 3/2x + 7/10 x + 1.54
Combine like terms
1/5x +5.34 = 11/5x +1.54
Move the x terms to the left side of the equation:
1/5x-11/5x = 1.54-5.34
-2x = -3.8
Divide both sides by -2
-2x/-2 = -3.8/-2
x = 1.9
find the equation of a line perpendicular to y=5x-3 that passes through the point (-5,3)?
The equation of the line that passes through point (-5,3) and perpendicular to y=5x-3 is y = -(1/5)x + 2.
What is the equation of line that passes through the given points and is perpendicular to the given line?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line: y = 5x - 3Point: (-5,3)First, determine the slope of the initial line using the slope intercept-form. y = mx + b
y = 5x - 3 compared with the slope intercept form,
Slope m = 5
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/5
Next, find the equation of the perpendicular line, by using the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -1/5 ) and point (-5,3).
y - y₁ = m( x - x₁ )
y - 3 = -1/5( x - (-5) )
y - 3 = -1/5( x + 5 )
y - 3 = -1/5(x) -5/5
y - 3 = -1/5(x) - 1
y = -1/5(x) - 1 + 3
y = -(1/5)x + 2
Therefore, the equation of the perpendicular line is y = -(1/5)x + 2.
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if 63 Naira is shared in the ratio 4 ratio 5 what is the larger share
Answer:
35
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide 63 by 9 to find the value of 1 part of the ratio
63 ÷ 9 = 7 , then
4 parts = 4 × 7 = 28
5 parts = 5 × 7 = 35 ← larger share
21 A forklift has a maximum carrying capacity of 960 pounds. Each cargo box weighs 60 pounds.
a. Write and solve an inequality that represents the maximum number of cargo boxes the
forklift can carry.
b.
A 120-pound carrying case is used to hold the cargo boxes. What is the maximum number
of cargo boxes the forklift can carry when the carrying case is used? Show that your answer
is correct by showing that one more than your answer would exceed the forklift's capacity
Using the concept of inequality, it can be concluded that;
a) Maximum number of cargo boxes the forklift can carry is 16.
b) Maximum number of cargo boxes the forklift can carry when the carrying case is used is 14.
What is the inequality in mathematics?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to contrast two numbers on the number line based on their sizes.
Let the no. of cargo box be x.
So the equation is 60x≤960
x≤960/60
x≤16
Now the 120 pound additional weight is needed so the equation is:
120 + 60x≤960
60x≤840
x≤14
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The equation of a line is given below.2x+6y=-18Find the x-intercept and the y-intercept.Then use them to graph the line.X-intercept:0Х5?ca loxy-intercept:0?
Given equation of the line is
[tex]2x+6y=-18[/tex]Dividing both sides of the above equation by -18, we get
[tex]\frac{x}{-9}+\frac{y}{-3}=1[/tex]The line cuts the x axis at (-9,0) and the y axis at (0,-3).
Therefore, the x intercept is -9 and the y intercept is -3.
The graph of the line is shown below.
Find the value of x for which i II m?
Answer:
16. 36.67
17. 40
Step-by-step explanation:
See attached worksheet
owen is the owner of the french realty company. he knows that the average number of homes sold per day is one. let x be the number of homes that french realty sells tomorrow. (a) (2 pts) what is the distribution of x and its parameter(s)? (b) (2 pts) what is the standard deviation of x ? (c) (2 pts) what is the probability that x is (inclusively) within one standard deviation of the mean of x
A) distribution of x and its parameter(s) is (λ^x e^-λ ) / x!
B) standard deviation of x is 1
C) probability that x is (inclusively) within one standard deviation of the mean of x is 0.7358
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A) The poisson distribution with mean is followed by X = λ = 1
Therefore, ≈ (λ = 1)
Distribution of X is:
(λ^x e^-λ ) / x! , x = 0, 1, 2, 3 ......
B) Standard Deviation of X is :
σx = √x = 1
C) Probability of X = P (-1 ≤ x ≤ 1)
P(x = 0) + P(x = 1)
= (1⁰ e⁻¹) / 0! + 1¹ e-¹ / 1!
= 2e⁻¹
= 0.7358
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The dot plot shows predictions for the winning time in the 200-meter sprint. The winner finished the race in 22.3 seconds. What is the greatest percent error among the predictions?
2.69%, is the required maximum percent error among the predictions.
Given,
The predicted winning time in 200 meter sprint shows in the dot plot
The winner finished the race in 22.3 seconds
We have to find the greatest percent error among the predictions;
Here,
The actual time to complete is 22.3 seconds.
22.9 seconds is the prediction that is the most off.
The difference is, 22.9 - 22.3 = 0.6 seconds
To obtain a prediction, divide this by the actual time value.
= 0.6/22.3 = 0.0269 = 2.69
Therefore, 2.69%, is the required maximum percent error among the predictions.
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in linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the
It is called the slope of the regression line.
The slope of the regression line including the intercept displays the linear relationship between 2 variables and can also be used in estimating an average change rate.
The slope of a regression line depicts the rate of change in the dependent variable as the independent variable alters because the dependent variable y is dependent on the independent variable x.
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Is the function positive or negative over the interval (–8, –6)?
Answer:negative
Step-by-step explanation:
Because it should be on the bottom left corner if you are using a graph it is different in each corners of the graph. There is four sides for the graph.
Airfare from Atlanta, GA to Nashville, TN was decreased from $250 to $180. By what percentage did the cost of the airfare change
this is junior high math
Step-by-step explanation:
100% = $250
1% = 100%/100 = 250/100 = $2.50
the price decreased by
250 - 180 = $70
how many % are $70 ?
as many as how many times 1% ($2.50) fits into $70 :
70 / 2.50 = 28%
it changed (decreased) by 28%.
Expand and simplify.2(2x+1)-3(4x-5)is the answer -8x+17?
Hello
To expand this, we will multiply the value outside the bracket with the one inside the bracket.
[tex]\begin{gathered} 2(2x+1)-3(4x-5) \\ 4x+2-12x+15 \\ \text{collect like terms} \\ -8x+17 \end{gathered}[/tex]The answer to this question is -8x +17
value outside the bracket with the one inside the bracket.
A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
The number of feet from the tent pole to the rope along the ground will be 12 Feet.
Let:
PR be the tent pole 9 Feet tallPQ be the piece of rope 15 Feet longRq be the distance between the tent pole and the rope along the groundRQ = x
According to Pythagoras Theorem:
[tex]Hypotenuse^{2} = Perpendicular^{2} + Base^{2} \\PQ^{2} = PR^{2} + RQ^{2} \\15^{2} = 9^{2} + x^{2} \\225 = 81 + x^{2} \\x^{2} = 225 - 81\\x^{2} = 144\\x = 12[/tex]
Therefore, the number of feet from the tent pole to the rope along the ground will be 12 Feet.
Pythagoras Theorem is widely used to establish the relation between the three sides of a right-angled triangle. The applications of Phythagoras Theorem are the angle of depression, angle of elevation, etc. Even the Eiffel tower is one of its applications.
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Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb. How much does each weight now?
The weight of Brad is 70 lb and the weight of Sean is 150 lb now.
According to the question,
We have the following information:
Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb.
Now, let's take Brad's weight to be x lb.
So, we have:
Sean's weight = (10+2x) lb
Now, when Brad gains 10 lb, we have the following expression:
(x+10)+(10+2x) = 230
3x+20 = 230
3x = 230-20
3x = 210
x= 210/3
x = 70 lb
Now, Sean's weight = (10+2x) lb
Putting the value of x:
Sean's weight = 10+2*70
Sean's weight = 10+140
Sean's weight = 150 lb
Hence, the weight of Brad is 70 lb and the weight of Sean is 150 lb now.
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considering the function for what values of x is f constant Options: (negative infinity,10]never(10,15)[15, infinity)
So, as shown at the function
f(x) is constant at the middle interval (10 , 15)
at which f(x) = 2 and the digit 2 is constant
so, the answer is (10 , 15)
Find the slope of the line that passes through (4,2) and (2,1)
Given
Points (4,2) and (2,1)
Find
Slope of the line
Explanation
Slope of line is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]so ,
[tex]\begin{gathered} m=\frac{1-2}{2-4} \\ \\ m=-\frac{1}{-2} \\ \\ m=\frac{1}{2} \end{gathered}[/tex]Final Answer
Hence , the slope of line is m = 1/2
Which of the following rational functions is graphed below?
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form. 5 12 4 5/3
The dimensions of the left triangle are equal to the right triangle's dimensions times 1/3.
Given,
The right triangle on the right is a scaled copy of the right triangle on the left.
The measure of first triangle = 3,4
The measure of second triangle = 2, 3/2
We have to find the scale factor
The figure indicates that the right triangle on the left would be three times larger than the right triangle on the right. In this case, the right triangle's dimension is one third of the left triangle's dimension.
The left one is three times bigger than the right one. In other words, the dimensions of the left triangle are equal to the right triangle's dimensions times 1/3.
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What is the solution to this equation?
5(x-3) = 21
A x =
OB x=
36
5
D x=
65
6
5
24
OC X= 5
18
5
Answer:
x = 7.2
Step-by-step explanation:
[tex]5(x - 3) = 21[/tex]
[tex]x - 3 = 4.2[/tex]
[tex]x = 7.2[/tex]
1. Seafood plays an important part of our daily nutrition. Mr. Beeg ate 1/6 of the fish for breakfast and 2/5 of the fish over lunch. What fraction of the fish has he already consumed?
expression: ___________
solution: ___________
final answer: ___________
2. Tita Flan planted trees around the barangay mini garden. She covered 2/3 of the garden on the 1st day, 1/5 of the garden on the 2nd day. How much of the garden is left for her to completely cover the mini park with trees?
expression: ___________
solution: ___________
final answer: ___________
3. Oil and Gas is one of the major causes of Global warming. Last 2020, it was estimated to 2/5 of depletion of the ozone layer. Projections revealed that by the year 2050, its effect will have increased three times. How much has oil and gas affected the ozone layer in the projection?
expression: ___________
solution: ___________
final answer: ___________
4. Mr. Bredwyn splits his monthly salary to family expenses. Half of it goes to savings and the other half is allocated to bills payment. 1/10 to water bill, 1/6 to electricity, 2/15 to Internet, and 3/5 to House Rental. What fraction of his total salary is allotted to House Rental?
expression: ___________
solution: ___________
final answer: ___________
Improper/random answer = Report!
Correct and complete answer = heart/brainly!
1. The fraction of the fish has he already consumed is 17/30.
2. The fraction of the garden is left for her to completely cover is 2/15.
3. The oil and gas that affected the ozone layer in the projection is 1 1/5.
4. The fraction of his total salary is allotted to House Rental is 3/10.
How to calculate the fraction?1. Mr. Beeg ate 1/6 of the fish for breakfast and 2/5 of the fish over lunch. The fraction already consumed will be:
= 1/6 + 2/5
= 5/30 + 12/30
= 17/30
2. Tita Flan covered 2/3 of the garden on the 1st day, 1/5 of the garden on the 2nd day. the fraction of the garden is left for her to completely cover the mini park with trees will be:
= 1 - (1/5 + 2/3)
= 1 - 13/15
= 2/15
3. It estimated to 2/5 of depletion of the ozone layer and projections revealed that by the year 2050, its effect will have increased three times. This will be:
= 2/5 × 3
= 6/5
= 1 1/5
4. The fraction of his total salary is allotted to House Rental will be:
= House rental / 2
= 3/5 / 2
= 3/10
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a bicycle path and a road cross at right angles. a police woman stands on the road 70 meters south of the crossing and watches an eastbound cyclist traveling at 6 meters per second. at how many meters per second is the cyclist moving away from the police woman 4 seconds after passing the intersection?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, or, in standard algebraic notation, a² + b² = c².
What is meant by Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b² = c².
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
First use the Pythagorean theorem. a² + b² = c²
then take the first derivative of it to get
2a(a') + 2b(b') = 2c(c')
Now figure out how far the train is after 4 seconds
6(4)=24
70² + 24² = c²
c = 74
Now plug in the variables you know
2(70)0 + 2(24)6 = 2(74)c' and solve for c' or the rate of change of c.
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The length of a rectangle is twice its width. If the area of the rectangle is 162in^2, find its perimeter.
We know that the length of a rectangle is twice its width. Then:
The area of a rectangle is the product of its width and length. Then:
[tex]A=2x\cdot x=2x^2[/tex]Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:
[tex]\begin{gathered} 162=2x^2 \\ 81=x^2 \\ x=9\text{ in} \end{gathered}[/tex]Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:
[tex]2P=2\cdot(2x+x)=6x=6\cdot9=54\text{ in}[/tex]What is the quotient in simplest form?
12/7 divided by 3
A. 7/36
B. 4/7
C. 1 3/4
D. 5 1/7
Answer:
Step-by-step explanation:
the answer would be the second option
cenario 2: the directors of an annual community concert want to learn the musical preferences of the audience. the directors choose 2 and 6 from a random number generator and place a survey card on every sixth seat beginning with the second seat. all the cards are returned as the audience leaves. they are using
The sampling method used here is systematic sampling.
What is systematic sampling?
To generate a representative sample from a population, systematic sampling is a probability sampling technique.An advantage of systematic sampling is that it does not necessitate a comprehensive population list in advance. A sort of probability sampling technique called systematic sampling involves choosing individuals from a broader population using random beginning points and defined intervals.Random systematic samples, linear systematic samples, and circular systematic samples are the three primary categories of systematic samples.Here , this scenario is systematic sampling since it entails choosing n at random and selecting every nth person in the audience starting at a random point.To learn more about systematic sampling , refer:
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After the expression (x10)^3/5 Is simplified as much as possible, x is raised to what exponent?
The exponent of x in the expression (x¹⁰)³⁺⁵ is 6.
What is an exponent?Exponent rules, commonly referred to as the "laws of exponents" or "properties of exponents," facilitate the task of simplifying exponent-based statements. These rules can help simplify formulas with exponents that are decimals, fractions, irrational numbers, or negative integers.
The mathematical process known as an exponent often indicates the power of a variable.
As of right now, we are aware that under the scenario of
[tex](x^{a})^{b} = x^{ab}[/tex]
Therefore, solve the power by multiplying 10 by 3/5, and we get
10 × (3/5)
=6
Thus, the expression simplified as
(x¹⁰)³⁺⁵ = x⁶
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find the ratio of the shaded pattern to the total area of the figure.
We are given a rectangle with the following dimensions;
[tex]\begin{gathered} l=(x+3) \\ w=(x+1) \end{gathered}[/tex]Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;
[tex]\begin{gathered} l=(x+1) \\ w=x \end{gathered}[/tex]The ratio of both figures can be expressed as follows;
[tex]\text{Ratio}=a\colon b=\frac{a}{b}[/tex]Substituting for the values of both figures, we now have;
[tex]undefined[/tex]What is the degree of the polynomial above?
(A.) 1
(B.) 2
(C.) 3
(D.) 4
Answer:
The answer is B.
Step-by-step explanation:
I remember this question.
Answer:
c
Step-by-step explanation:
Write a simplified explession for the perimeter of the triangle.
[tex]p =( 1.5x - 3) + (1.5x - 3) + (0.75x - 1) \\ = 1.5x + 1.5x + 0.75x - 3 - 3 - 1 \\ p= 3.75x - 7[/tex]
ABOVE IS THE SIMPLIFIED PERIMETER OF THE TRIANGLE.
pls help with whats in image!!!
The slope of the line will be positive 9. Then the correct option is C.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope is given as,
Slope = m = (y₂ - y₁) / (x₂ - x₁)
Determine whether a line's slope, which represents the linear connection, is positive, negative, zero, or undefined without using a graph. Next, locate the slope. A babysitter may make $9 per hour and $36 per 4 hours.
Slope = (36 - 9) / (4 - 1)
Slope = 27 / 3
Slope = 9
The slope of the line will be positive 9. Then the correct option is C.
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Write the expression 16x + 28 as a product using the GCF as one of the factors.
Please help.
Answer:
4(4x + 7)
Step-by-step explanation:
To answer this question you need to understand what GCF is
GCF is Greatest Common Factor
GCF is the highest number that divides exactly into two or more numbers.
The expression is 16x + 28
The highest number that can divide 16 and 28 is 4
Dividing 16x + 28 gives => 16x/4 + 28/4 => 4x + 7
So the factored expression is
4(4x + 7)