Answer:
slope of line q = [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
calculate the slope of line p using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (8, 7 ) and (x₂, y₂ ) = (4, 4 )
m = [tex]\frac{4-7}{4-8}[/tex] = [tex]\frac{-3}{-4}[/tex] = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes
then slope of line q = [tex]\frac{3}{4}[/tex]
Need help pelase 7th grade math help
The constant of proportionality of the image of actual height and height on set of the items is 20 / 11
Table
= 15.4 inchesStool
= 9.9 incheswindow
= 4 inchesBucket
= 2 inchesHow to get the constant of proportionalityConstant of proportionality are used to increase or decrease image. The situation of increment is usually called magnifying.
solving for the constant of proportionality, assuming the factor is k
height on set * k = actual height
44 * k = 80
k = 80 / 44
k = 20/11
Height on set for other items
Table
= 28 ÷ 20/11
= 15.4 inches
Stool
= 18 ÷ 20/11
= 9.9 inches
window
= 80/11 ÷ 20/11
= 4 inches
Bucket
= 40/11 ÷ 20/11
= 2 inches
The Constant of proportionality is calculated to be 20/11
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Write the equivalent fraction with a denominator of 100100 .
\frac{9}{10}=
10
9
=
The equivalent fraction with a denominator of 100 will be;
⇒ 90 / 100
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ 9 / 10
Now,
Since, The fraction is,
⇒ 9 / 10
Hence, The fraction with denominator 100 is;
⇒ 9 / 10 = 9×10 / 10×10
= 90/100
Thus, The equivalent fraction with a denominator of 100 will be;
⇒ 90 / 100
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Need an answer help please
Answer:
see explanation
Step-by-step explanation:
the mistake is that a zero should be inserted to indicate the x - term
the standard form of a polynomial of degree 3 is
ax³ + bx² + cx + d
given
[tex]\frac{3m^3-2m^2-150}{m-4}[/tex]
there is no m- term in the numerator so a zero has to be inserted in its place, that is
4 | 3 - 2 0 - 150
↓ 12 40 160
---------------------------
3 10 40 10
To the nearest hundredth, 11.6÷0.95
is about
on dividing the given term we get
12.2105.
The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1-ekx)
When $675 is spent on advertising 2900 units are sold.
(a) Complete the model by solving for k. (Round your answer to 4 decimal places.)
k =
(b) Estimate the number of units that will be sold if advertising expenditures are raised to $925.
units
Answer:
as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).
Triangle DEF is similar to a triangle ABC. What is the slope of the line that passes through the hypotenuse of the Two similar triangles?
Answer:
D. Slope is 1
Step-by-step explanation:
Start at any point on the line. Go up 1 (rise of 1). Go right 1 (run of 1). You're on the line again.
slope = rise/run = 1/1 = 1
A clothing designer is selecting models to walk the runway for her fashion show. The clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. Which graph could be used to determine the possible variance levels that would result in an acceptable height, x?
The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.
How can one depict the graph?Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;
y = m·x + c
Where x is the height in inches
Given that the maximum height allowable is 70 inches, when x = 0 we have;
y = m·0 + c = 70
Therefore, c = 70
Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1
The equation becomes;
y ≤ x + 70
Also when x > 70, we have y ≤ -x + 70 with a slope of -1
In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.
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Kira wants to attend a college that will cost her $14,800 for the first year. To pay for it, her aunt gave her a special gift of $10,000 . Kira is also going to start saving $100 per month. How many years will it take Kira to save enough for the first-year cost?
Select all of the verbal phrases which can be represented by the expression 25.75x + 10.
25.75 plus 10
25.75 times a number x, plus 10
25.75 times a number x, plus 10 times a number x
the product of 25.75 and x, plus 10
the product of 25.75 and 10
The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
What is mathematical verbal expression?An algebraic expression that may contain various operations, quantities, and variables is translated into words as a mathematical verbal expression.This can be demonstrated by verbally expressing the mathematical statement "90 - 4(a + 8)" as "90 reduced by 4 times the sum of a number "a" plus 8."Students may also need to convert verbal expressions into algebraic expressions or equations when studying math. In word problems, where students must search for precise terms that identify the procedure required to answer the problem, this is frequently utilized. Decreased by, increased by, less than, more than, sum of a number and "x," and the total of two numbers are a few examples of these expressions.Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 12-x^2. What are the dimensions of such a rectangle with the greatest possible area?
Answer:
if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2
the area of a rectangle = length * width
thus, area = x*(7-x^2)= 7x-x^3
in order to maximize the area, you would need to take the derivative of the area and set it equal to 0
Area = 7x-x^3Area' = 7 - 3x^2
7-3x^2 = 0thus, x = 1.5275
this x represents the x needed to create the largest possible area with the given parameters.
Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667
The strongest recorded earthquake was in Chile in 1960 and had an intensity of 316227.77 cm. What was its magnitude? (Round your answer to one decimal place.)
Answer:
5.5
Step-by-step explanation:
earthquake is measured with the Ritcher Scale:
R (Magnitude) = ㏒base 10 (I)
where I = Intensity
thus,
R = ㏒ base 10 (316227.77)
R ≅ 5.5
In a class of 30 students, 16 have a cat and 15 have a dog. There are 11 students who have a cat and a dog. what is the probability that a student has a dog given that they do not have a cat?
Y varies directly as x and inversely as the square of z.y=8 when x=25 and z=5. Find y when x=2 and z=6
The value of y when x = 2 is 16/25 and when z = 6 is 200/36
What is proportionality constant?The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
Given that, Y varies directly as x and inversely as the square of z and y=8 when x=25
That means, y ∝ x and y ∝ 1/z²
Let constant of proportionality be k, then,
y = kx and y = k/z²
Now, finding k, when x = 25
8 = k25
k = 8/25
For x = 2,
y = 8/25X2
y = 16/25
Finding k when y = 5
8 = y/25
y = 200
Now, when z = 6
y = 200/36
Hence, The value of y when x = 2 is 16/25 and when z = 6 is 200/36
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Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
Answer:
HL
Step-by-step explanation:
to solve this we first must see what is congruent
we see that both triangles are right triangles
that means that we can use HL (hypotenuse length) to solve
we must first see if HL works though
we see that the hypotenuses are both equal
that means that we can use HL
that is your answer
If Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48 , what is the principal loan amount?
When Bobby takes out a mortgage for $30 years at 4% interest with $835.48 in monthly payments, the total principal loan amount is $255644.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
Here,
The interest paid per month=$835.48
Interest paid in 30 years=835.48*12*30
Rate of interest=4%=0.04
Time=30 years
Principal=I/RT
=(835.48*30*12)/(0.04*30)
=$250644
The principal loan amount is $250644 when Bobby takes out a mortgage for 30 years at an interest rate of 4% and his monthly repayments are $835.48.
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Calculate the distance between the points P=(0, 1) and J=(4, -2) in the coordinate plane. Give an exact answer (not a decimal approximation).
Using the distance formula, [tex]JP=\sqrt{(0-4)^2+(1-(-2))^2}=\boxed{5}[/tex]
The formula below models the number of calories consumed daily by a person owning x acres of land in a developing country. Estimate the number of a 2200 calories per day.
C(x)=270 ln (x+1)+1900
For an average intake of 2200 calories per day, the number of acres of land owned is approximately (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)
For an average intake of 2200 calories per day, the number of acres of land owned will be 2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, The function that models the number of calories consumed daily by a person owning x acres of land in a developing country is,
C(x)=270 ln (x+1)+1900
If an average intake of 2200 calories per day,
C(x)= 2200
2200=270 ln (x+1)+1900
2200-1900=270 ln (x+1)
270 ln (x+1)=2200-1900
270 ln (x+1)=300
ln (x+1)=300/270
ln (x+1)=1.11
(x+1)=ln⁻¹(1.11)
x+1=e¹¹¹
x=e¹¹¹-1
x=3.034-1
x=2.034≈2
Thus, for an average intake of 2200 calories per day, the number of acres of land owned will be 2.
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let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ[tex]\sqrt{n}[/tex]}/σ])
= P (z > [{12.7 - 10[tex]\sqrt{120}[/tex]}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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What is the answer to this?
Find the point of intersection for the pair of linear equations.
x+y= -8.5
y = 2x + 4.4
A. (-4.3, -4.2)
B. (-4.1, 4.4)
C. (1.9, -3.7)
D. (-3.1, 2.4)
A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer: 1058000 tickets
Step-by-step explanation:
23000 x 46 = 1058000
1058000 tickets
12
A culture of bacteria triples every hour. If there are 5 bacteria after the first hour,
how many bacteria will there be after one day?(One day= 24 hours)
5 x 3²⁴ bacteria will there be after one day.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Consider what is actually happening in the question.
You begin with 5 bacteria, and after 1 hour it has tripled so you now have
5x 3=15.
Next hour, it triples again so you now have 5 x 3 x 3=45
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴ means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
n x 324 where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is 5 x 3²⁴.
Hence 5 x 3²⁴ bacteria will there be after one day.
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An independent variable that studied using related samples in all conditions is called a
An independent variable studied by using related samples in all conditions is called a within subjects factor.
An independent variable is defines as the variable that is modified or controlled in a scientific experiment. It reflects the rationale or cause for an outcome.
The variables that the experimenter adjusts to test their dependent variable are known as independent variables. A change in the independent variable has a direct effect on the dependent variable. The impact on the dependent variable is assessed and documented.
Examples of Independent Variables
A scientist is experimenting with the effect of light and dark on the behaviour of moths by turning on and off a light. The amount of light is the independent variable, while the moth's reaction is the dependent variable.
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Write equations for the horizontal and vertical lines passing through the point (4,-3)
The equation of vertical line passing through the point (4,-3) will be x = 4
And, The equation of horizontal line passing through the point (4,-3) will be y = - 3.
What is mathematical expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The horizontal and vertical lines passing through the point (4,-3).
Now,
Since, The horizontal and vertical lines passing through the point (4,-3).
Hence, The equation of vertical line passing through the point (4,-3) is the value of x.
So, We get;
The equation of vertical line is,
⇒ x = 4
And, The equation of horizontal line passing through the point (4,-3) is the value of y coordinate.
So, We get;
The equation of horizontal line is,
⇒ y = - 3
Thus, The equation of horizontal line is , y = - 3
And, The equation of vertical line is, x = 4
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Determine whether each ordered pair is a solution of the given linear equation.
2x + 7y = 16;
a. (9,1)
b. (8,0)
c. (0,0)
Answer:
A. No
B. Yes
C. No
Step-by-step explanation: To determine if each pair is a solution to the equation, substitute the x and y variables in the pairs for the corresponding variables in the equation. If the left and right sides are equal once you solve, you will know that the pair is a solution,
(9,1) 2(9)+7(1)=16 18+7=16 25=16 No
(8,0) 2(8)+7(0)=16 16+0=16 16=16 Yes
(0,0) 2(0)+7(0)=16 0+0=16 0=16 No
which expressions are equivalent to 5x + 6y - 3x
Step-by-step explanation:
The expression 5x + 6y - 3x is equivalent to:
2x + 6y
This is because 5x and -3x can be combined by adding them together, which gives 2x.
The expression 5x + 6y - 3x is also equivalent to:
x + 6y - 3x
This is because 5x and -3x can be combined by adding them together, which gives x.
However, the expression 5x + 6y - 3x is not equivalent to:
2x - 3y
This is because the coefficient of the y term is 6, not -3.
The expression 5x + 6y - 3x is also not equivalent to:
x + y
This is because the coefficient of the y term is 6, not 1.
[5-TI] 4. The layout of Joe's yard is shown below. Joe must spread out topsoil to a depth
of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and
contains 10 cubic yards of topsoil. How much will the topsoil cost to complete
this job?
75 feet
64 feet
36 feet
53 feet
19 feet
22 feet
The total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB).
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that Joe must spread out topsoil to a depth of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and contains 10 cubic yards of topsoil.
In 10 yards³ = 466,560.1 in³
Assume the length and breadth to be [L] inches and [B] inches. The height is 15 inches.
Volume of the layout will be -
V = (15 x L x B) in³
466,560.1 in³ of the topsoil costs $67.89.
1 in³ of the topsoil will cost $(67.89/466560.1)
(15 x L x B) in³ of the topsoil will cost -
$(67.89/466560.1) x (15LB)
(1.46 x 10⁻⁴)(15LB)
Therefore, the total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB)
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James and Elizabeth buy some clothes.
James buys 5 shirts and 4 jumpers. He pays £163.
Elizabeth buys 3 shirts and 2 jumpers. She pays £89.
Assume that each shirt has the same cost and that each jumper has the same
cost.
Work out the cost of one shirt and the cost of one jumper.
Cost of one shirt £
Cost of one jumper £
Answer:
£15 and £22
Step-by-step explanation:
let,the cost of one shirt be X and one jumper be y.Then according to question,
5x+4y=163-----(1)
also,
3x+2y=89------(2)
Now, multiplying eqn (2) by 2 and then subtracting from (1),we get
5x+4y=163
6x+4y=178
- - -
_________
-x=-15
:.x=15
Putting value of X in eqn (1),
5×15+4y=163
or,4y=163-75
or,y=88/4
:.y=22
Hence cost of one shirt is £15 and one jumper is £22.
If n = 19,
¯
x
= 36, and s = 2, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.
<
μ
The three decimal places are :28.288< μ < 43.712
What is meant by normally distributed population?A normal distribution is one in which the values are evenly distributed above and below the mean. A population has a perfectly normal distribution if the mean, mode, and median are all equal. The mean, mode, and median for a population of 3,4,5,5,5,6,7 are all 5. The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, indicating that data near the mean occur more frequently than data far from the mean.degree of freedom = 17-1 = 16
critical t value = 2.1199
lower limit = 36-2.1199*15/sqrt(17) = 28.288
Upper limit = 36+2.1199*15/sqrt(17) = 43.712
Answer:28.288< μ < 43.712
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2. For each of the following functions, determine the average rate of change over the specified interval.
From x=4 to x=10
Average rate of change for given function from x=4 to x=10 is -0.66
What is average rate of change?Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.
At x = 4 we have y = 8
At x = 10 we have y = 4
As y is nothing but value of function f(x) at x.
So, we can write them as f(4) = 8 and f(10) = 4
Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using above formula of average rate of change and substituting for x=4 to x=10, we get
Average rate of change = [tex]\frac{4-8}{10-4} = \frac{-2}{3}[/tex]
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