-7/3 this expression can be represented on the Number Line.
Number Line:
A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.The numbers on a horizontal number line grow as we walk to the right and decrease as we get to the left. A straight line of numbers is shown visually as a number line. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals. The numbers on a horizontal number line grow as we walk to the right and decrease as we get to the left.
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kylie works for a large nursery and is investigating whether to use a new brand of seeds. the new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using. she will change over to this new brand unless the actual germination rate is less than what is advertised. kylie conducts an experiment by randomly selecting 76 seeds of the new brand and plants them. she finds that 70 of those seeds germinated. what are the null and alternative hypotheses for this hypothesis test?
The null and alternative hypotheses for this hypothesis test is H₀ : p = 0.93, Hₐ : p > 0.93.
What is Hypothesis ?A hypothesis in a scientific context, is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
What is Null and Alternative Hypotheses?Null and alternative hypotheses are used in statistical hypothesis testing. The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Let 'p' be the population proportion.
Given statement : The new brand of seeds advertises that 93% of the seeds germinate, which is higher than the germination rate of the seeds she is currently using.
Since null hypothesis shows that there is no significant difference between the quantities where as alternative hypothesis believes that there is some difference,
Hence, the null and alternative hypotheses for this hypothesis test will be :- H₀ : p = 0.93
Hₐ : p > 0.93
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Big Ideas: Graph f(x) = 0.5x^3 - 2x + 2.5. Identify the x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary.
The x-intercept is x = (blank).
The local maximum is (blank, blank).
The local minimum is (blank, blank).
The function is increasing when x < (blank) and x > (blank).
The function is increasing when (blank) < x < (blank).
Answer:
The x-intercept is x = 0.
The local maximum is (-0.38, -0.46).
The local minimum is (0.38, -0.46).
The function is increasing when x < -0.38 and x > 0.38.
The function is increasing when -0.38 < x < 0.38.
Step-by-step explanation:
To find the x-intercepts, we can set the function equal to 0 and solve for x. This gives us the equations:
0.5x^3 - 2x + 2.5 = 0
To find the points where the function has local maximums and minimums, we can take the derivative of the function and set it equal to 0. This gives us the equation:
1.5x^2 - 2 = 0
To find the intervals where the function is increasing or decreasing, we can take the derivative of the function and determine the sign of the derivative. A positive derivative indicates that the function is increasing, while a negative derivative indicates that the function is decreasing.
Based on the information above, we can fill in the blank answers as follows:
The x-intercept is x = 0.
The local maximum is (-0.38, -0.46).
The local minimum is (0.38, -0.46).
The function is increasing when x < -0.38 and x > 0.38.
The function is increasing when -0.38 < x < 0.38.
In gym class, the yellow team and the blue team played soccer. Ali doesn't remember the final score of the game, but she does remember the following. what's the score There were six goals scored in total. Neither team scored more than two goals in a row at any point in the game. Determine all the possible final scores and the different ways each score could have been obtained. The blue team won the game.
Answer:
Step-by-step explanation:
i need help
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407f(x) = x²+x-6
g(x) = 4x +9
Find: g(f(x))
The value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The fundamental concept of functions was the connection between fluctuating quantities and other variables. One illustration of this is the impact of time on a planet's position. Beginning at the end of the 17th century and continuing until the 19th century, the concept was developed using the infinitesimal calculus.
Given,
f(x) = x²+x-6
g(x) = 4x +9
f(g(x))=f(4x+9)
g(f(x))=4(x²+x-6)+9
g(f(x))=4x²+4x-24+9
g(f(x))=4x²+4x-15
Therefore, the value of the function g(f(x))=4x²+4x-15 if f(x) = x²+x-6
g(x) = 4x +9.
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the value of a car constantly depreciates after it is purchased. the original value of a car (zero years after purchased) was , and the value decreased by each year. the formula that describes the value of the car () in terms of the number of years after it was purchased () is . find an equation that provides the number of years since the car was purchased in terms of its value.
The equation that provides the number of years since the car was purchased in terms of its value is (v/2000) - 8.5
What is a algebra question?In algebra questions, values that are ambiguous or subject to change are represented by letters or symbols.
Why is algebra useful?When it comes to solving for an unknown variable, algebra becomes very useful.
For example, how much money will I save if item retailing for $20 is offered at a 10% discount?
Savings = Full Price * Discount = $20 * 10% = $2
or I spent $30 on items, with each item costing $5, how many items should I have?
Total = No. Items * Item Price
$30 = No. Items * $5
No. Items = Total / Item Price
No. Items = 6
Let the number of years = t
v = 17000 - 2000t
Value = 17000 by row/year
(v - 17000)/2000 = t
Therefore,
t = (v/2000) - 8.5
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Tell whether the point (13, 17) is a solution to the system of linear equations?
y = -x + 30
y = x + 6
yes
no
Answer:
No
Step-by-step explanation:
When the 2 equations are graphed the point (13, 17) is not
a solution to the system of linear equations.
So the answer is no.
If you want to look for the solution**- the solution to the equation is (12, 18)
r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750. How much should each student raise, on average, in order to meet the goal?
On average the 50 students need to raise $25 each.
What is average?
In plain English, an average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
Given: Fifty students in the seventh grade are trying to raise at least $2,000 for sports supplies. They have already raised $750.
To find the number of students should each student raise, on average, in order to meet the goal.
Let, $2000 - $750 = $1250
So,
$1250/50 = 25
Hence, on average the 50 students need to raise $25 each.
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There were two candidate A and B conteting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, find the number of vote received by B
There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.
What is municipal corporation election?A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.
A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this
Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.
Given that,
Total number voters = 80,000
Total number of votes polled = 90%
Thus,
= (90/100) × 80,000
= 72,000
So, total percent of votes received by B if A gets 60% of polled votes.
= 100% - 60%
= 40%
Hence, total number of votes received by B
= (40/100) × 72,000
= 28,800
Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.
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1. you have three baskets of fruit. one has apples, one has oranges, and one is a mix of the two. all the baskets are mislabeled. how many fruits do you need to pull out of how many baskets to correctly label them all.
To label the three basket correctly , We have to pull out total two fruits from all of them
Let Say , We are drawing a fruit from a basket labelled "Mixture"
If this fruit is an apple, then indicate such on the label (Because this basket does not contain Mixture, so if one is apple, all are apples only). We've now discovered that the basket marked "Mixture" solely includes apples.
Therefore , the Correct Label is "apples"
Now, Drawing another fruit from basket labelled "Oranges," we can see that it either contains solely apples or mixture. The basket marked "Oranges" contains "Mixture," as we already know which basket only contains apples. Put "Mixture" on the label.
Oranges will be the name of the third basket.
The same reasoning holds true if you suppose that you initially chose an orange from the basket marked "Mixture."
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Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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In a box of chocolates, of the chocolates are white chocolate, are milk
chocolate, and the rest are dark chocolate.
What fraction of the chocolates are dark chocolate?
......................................................................
Part F: Order the integers from least to greatest. 12, -6, 20, -47, -11
The integers are -47, -11, -6, 12, 20 in order of least to greatest.
Explain about the integers?A whole number that can be positive, negative, or zero is called an integer. It is not a fraction. -5, 1, 5, 8, 97, and 3, 043 are some examples of integers. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
Positive numbers, negative numbers, and zero make up integers. Thus, integers include 0 through 3, as well as -1, -2, and -3. No further parts, such as fractions or decimals, are allowed in integers. Therefore, fractional and decimal numbers like 3 1/2 and -7.5 are NOT integers.
Integer is derived from the Latin integer, which means whole or untouched, from the prefix in (for "not") with tangere ("to touch"). The words "entire" and "integer" are both derived from the same root, which is the French word entire.
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14x+17.5<−66.5 can you guys help me
Answer: < -6
Step-by-step explanation:
Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078Write a linear function f with the values.
The equation of the line is f(X)=(-1/6)x—(19/6)
What is equation?
In arithmetic, an equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
first linear functions have their general form as y= mx + c, where y belongs to the range and X belongs to the domain, m is the slope, and c is the y-intercept.
So using f(x) =y
Given that f(—5)=-4 , X=—5 and y=-4, hence by substituting into the general eqn y= mx+c, You get
-4= -5m+c ------(1)
Also given that f(1)=—3, X=1 and y=—3, hence by substituting into the general eqn y= mx+c, You get
-3= m+c --—-(2)
Solve equation (1) and (2), simultaneously to find the value of m and c. After which you will substitute into y=mx+c or f(X)=mx+c to get your f(X).
Note: you will get m=—1/6 and c=-19/6, from the simultaneous equations.
Hence f(X)=(-1/6)x—(19/6) and correct option is D.
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By identifying the vertical asymptote, one can determine the denominator of this
function is
The denominator of function is -x/2 - 1 and vertical asymptote x = -2.
What is vertical asymptote?A vertical line that is not a part of the function's graph but serves as a guide is known as a vertical asymptote. Because it occurs at an x-value outside of the function's domain, the graph cannot cross it. There may be more than one vertical asymptote for a function.
Given graph
the function of graph is F(x) = [tex]2\frac{\left(-\frac{x}{2}\ +\ 1\right)}{\left(\frac{x^{2\ }}{4}-1\right)}[/tex] = 2(1- x/2)/(x²/4 - 1)
reducing the equation
F(x) = 2/(-x/2 - 1)
denominator is -x/2 - 1
for vertical asymptote -x/2 - 1 = 0
x = -2
Therefore for function is -x/2 - 1 and vertical asymptote at x = -2.
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A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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It's a mean and median frequency table
Pls answer
a) The mode is 2.
b) 32 Students were there altogether.
c) 15 dinners were served during the week.
d)The mean number of dinners is 2.5.
What is mode?This refers to the value that appears most often in a set of data values.
What is mean?
This refers to the average of the given set of numbers. It is calculated by dividing the sum of given numbers by the total number of numbers.
Given in the question:
a)The number of school dinners 2 has a frequency of 12.
Hence, the mode is 2.
b) To calculate the number of students altogether, we add then frequencies
Total number of students = 0 + 8+ 12 + 6+ 4 + 2
Total number of students = 32
c) To get the number of dinners served during the week, we add the number of dinners together.
Number of dinners served during the week= 0 + 1 + 2 + 3 + 4 + 5
Number of dinners served during the week = 15
D) The mean number of dinners =
1+1+1+1+1+1+1+1+2+2+2+2+2+2+2+2+2+2+2+2+3+3+3+3+3+3+4+4+4+4+5+5
32
The mean number of dinners = 80
32
The mean number of dinners = 2.5
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(-20, 12)
(17, 2)
(-11, 8)
(17, 8)
(11, 2)
Is this relation a function?
Answer:
No because x-coordinate 17 appears twice.
Step-by-step explanation:
In a function, no two ordered pairs can have the same x-coordinate.
Here, points (17, 2) and (17, 8) have 17 as the x-coordinate. Since the same x-coordinate, 17, is used more than once, this relation is not a function.
Which undefined mathematical term can be described as a one-dimensional set of points with no beginning or end?a. line segmentb. linec. planed. ray
Answer:
Which undefined mathematical term can be described as a one-dimensional set of points with no beginning or end?a.line segment b.line c.plane d.
Missing: segmentb. linec.
What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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For which situation does one quantity change at a constant rate per unit interval relative to another quantity?
Responses
For every day that passes, a person drives 54 miles.
.
For every month that passes, a savings account earns interest at a rate of 1.5%
For every week that passes, a vine doubles in length 2 times a week.
.
For every year that passes, a population of insects increases by 6%
Answer:
(a) For every day that passes, a person drives 54 miles
Step-by-step explanation:
You want to know the situation in which one quantity changes relative to another at a constant rate.
DrivingThe rate of change is described as 54 miles for each day. This is a constant rate of change. Miles relative to days are described by a linear function.
SavingsWe assume the description means that the balance in the savings account increases by 1.5% with each passing month. While this interest rate is a constant, the amount by which the balance changes each month is not constant. The balance relative to time is described by an exponential function.
VineIf the vine doubles in length twice a week, its length increases by 300% each week. As with savings, this growth rate is constant, but the amount of growth each week is not. The length of the vine is described by an exponential function.
PopulationAs with savings, this growth rate is constant, but the amount of increase each year is not. The population is described by an exponential function.
The situation with a constant rate of change is ...
For every day that passes, a person drives 54 miles.
__
Additional comment
When the quantity is graphed, the "rate of change" refers to the slope of the curve on the graph. The graph of an exponential growth function does not have a constant slope, but has a slope that increases exponentially.
<95141404393>
Please hurry and help!
Graph the following linear equation using the intercepts.
\displaystyle -10 x-12 y=-60−10x−12y=−60
The x−intercept is 6 and the y-intercept is 5.
What is an equation of a line?
In high school algebra, "the equation of a line" is a crucial concept. This refers to an equation in the (x,y) plane with a line as its solution set. The "slope-intercept" form is the most widely used form in algebra. y = mx + b. In essence, x is used as a parameter in this formula, and y is written as a function of x: y = f(x) = mx+b.
Here, we have
The given equation of a line is:
−10x − 12y = −60
10x + 12y = 60
x/6 = y/5 = 1
Hence, the x−intercept is 6 and the y-intercept is 5.
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Rufus has collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. In how many weeks will Rufus have a total of 400 pounds of cans?
Answer: 12
Step-by-step explanation:
Rewrite the expression in
radical form:
3 2/5
Answer: Nothing further can be done with this topic. Please check the expression entered.
Step-by-step explanation:
You are designing one last sandbag-dolly system for the performance. this time, two actors will be on the dolly. the mass of the dolly and actors combined is 94 kg, and the mass of the sandbag is 35 kg. the coefficient of kinetic friction between the dolly and the stage floor is 0.20. what is the acceleration?
The acceleration of the dolly-sandbag system is 1.23 m/s²
How to calculate the acceleration?Given parameters:
The mass of the dolly and actor combined is: M = 94 kg
the mass of the sandbag is: m = 35 kg.
The coefficient of kinetic friction between the dolly and the stage floor is 0.20.
Let the acceleration is a.
Hence, From Newton's 2nd law of motion, we can write that:
ΣF = (m+M) a
mg - μMg = (m+M) a
a = g (m- μM)/ (m+M)
= 9.8 (35 - 0.20 × 94)/(35 + 94)
= 9.8 (16.2)/(129)
= 1.23 m/s².
Hence, the acceleration of the dolly-sandbag system is 1.23 m/s².
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